WO2025132153A1 - Sonar clutter filtering - Google Patents

Abstract

System and method of clutter filtering a receive signal using a sonar system (110). The system and method generate a transmit signal using the sonar system (110), measure the receive signal using the sonar system (110), determine transmit windows of the transmit signal based on a desired velocity representing estimated velocity of objects of interest for clutter filtering, determine receive windows of the receive signal based on a desired range representing estimated range of objects of interest for clutter filtering, perform temporal cross correlation of each transmit window of the transmit signal with a corresponding receive window of the receive signal to identify correlation peaks, temporally shift and scale the transmit windows based on the correlation peaks to provide modelled clutter, and subtract the modelled clutter from the receive signal.

Description

SONAR CLUTTER FILTERING

TECHNICAL FIELD

[1] This disclosure relates to methods, systems, and computer readable media for clutter filtering a measured sonar signal in a signal processing pipeline. The present disclosure further relates to clutter filtering in a signal processing pipeline for identifying moving targets. Unlocking insights from Geo-Data, the present invention further relates to improvements in sustainability and environmental developments: together we create a safe and liveable world.

BACKGROUND

[2] Active sonar refers to a technique of measuring the distance to an underwater object, by means of transmitting a pulse of sound, commonly referred to as a ‘ping’, and subsequently listening to the echo. By analyzing the delay of the received echo, the distance to the object can be determined, using the speed of sound in water (c « 1500 m/s). Sonar systems may be mounted on the hull of a ship, e.g., to determine the depth of the seabed, or to detect certain objects under the ship. A sonar system may also be provided for monitoring a harbour and may include underwater sensors that emit sound waves and detect their echoes. These systems may be used for security, navigation, and detecting underwater objects or activities. They can identify vessels, monitor marine life, and detect environmental changes. In-air sonar systems, while less common than underwater systems, use sound waves to detect and locate objects in the air. They operate similarly to traditional sonar, emitting sound waves and analysing the echoes returned from objects. These systems can be used for various applications, including industrial sensing, security, and wildlife monitoring. In-air sonar typically operates at higher frequencies than underwater sonar due to the differences in sound propagation in air compared to water. The systems and methods described herein are applicable to such sonar systems.

[3] The use of sonar is particularly preferred for underwater surveillance systems. This is primarily because of the low attenuation of sound in water, which surpasses other surveillance methods such as radar or visual approaches. It can be used to detect moving targets such as human divers, for example, in an intruder alarm system to protect a harbor from underwater terrorist threats. It can similarly be used to detect wildlife such as whales entering certain regions. This can be used to protect whales from entering harbours or to detect certain species for conservation purposes. State-of-the-art active sonar systems capable of detecting moving targets most often rely on beamforming to make an ‘echograph’, which shows the positions of objects that have a strong echo. The detection of a moving target is addressed by looking for tracks that form in the echograph, which is updated after each transmitted pulse. Hence, the response of the moving target signal in the echograph is constrained to the strength of a single echo. The maximum detection range of such systems may vary but is several hundred of meters at most. This limitation can, in some systems, restrict the coverage of the system to the immediate waters of the harbour. Increasing the detection range enables earlier detection of a moving object, such as a mammal, approaching the harbour. This allows the operator to respond sooner, consequently reducing the risk of harm posed by or to the moving object. However, detecting long-range or weakly reflecting targets is challenging, due to a low signal-to-noise ratio (SNR) of a single echo, making it difficult to detect. Another disadvantage of existing systems for long-range detection is increased attenuation, due to the high frequencies used for beamforming, with typical carrier frequencies of around 70 - 500 kHz.

[4] Some sonar systems may struggle with accurate identification of moving targets due to the presence of clutter - unwanted echoes from various sources such as the sea floor, surface waves, or other stationary objects. These clutter signals can mask the echoes returned from actual targets, particularly in clutter-dominated environments like shallow waters or areas with substantial underwater structures. Known clutter filtering algorithms have shown limited effectiveness, especially with non-repetitive transmit signals like PseudoRandom Noise (PRN).

[5] An object of the present disclosure is to provide clutter filtering systems and methods in challenging environments where clutter is a major impediment to effective moving target detection. A further object is to provide such a clutter filter that is adaptable to a range of transmit waveforms. It is additionally desirable to facilitate identification and filtering of clutter.

SUMMARY

[6] The present disclosure provides methods, systems, and/or computer-readable media for improved detection of moving targets in low SNR conditions.

[7] In a first aspect, a method of clutter filtering a receive signal using a sonar system is provided. The method comprises generating a transmit signal using the sonar system, measuring the receive signal using the sonar system, determining transmit windows of the transmit signal based on a desired velocity representing estimated velocity of objects of interest for clutter filtering, determining receive windows of the receive signal based on a desired range representing estimated range of objects of interest for clutter filtering, performing temporal cross correlation of each transmit window of the transmit signal with a corresponding receive window of the receive signal to identify correlation peaks, temporally shifting and scaling the transmit windows based on the correlation peaks to provide modelled clutter, and subtracting the modelled clutter from the receive signal.

[8] In embodiments, the method includes receiving a doppler cut-off velocity and a clutter filtering range, determining a time length of the transmit windows based on the doppler cut-off velocity, wherein the transmit signal is divided into N transmit windows, determining a time length of the receive windows based on the clutter filtering range.

[9] In embodiments, the doppler cut-off velocity and the clutter filtering range are provided by user inputs through a user interface.

[10] In embodiments, the steps of performing temporal cross correlation, temporal shifting and scaling and subtracting are performed iteratively for a predetermined number of iterations or until a convergence criterion is reached.

[11] In embodiments, there are N temporal windows making up the transmit signal and the method includes, for n=0 to N-1 : determining a start of a current transmit window based on n multiplied by the time length of the transmit windows and an end of the current transmit window based on the start of the current transmit window and the time length of the transmit windows, determining a start of a current receive window based on the start of the current transmit window and the time length of the receive windows, cross correlating the current transmit window and the current receive window to provide a correlation result, finding the correlation peak time based on the correlation result, scaling the current transmit window based on an amplitude of the correlation result, temporally shifting the scaled current transmit window based on the correlation peak time to provide the modelled clutter, and subtracting the modelled clutter from the receive signal.

[12] In embodiments, the transmit signal is a continuous wave signal.

[13] In embodiments, the transmit signal is a continuous wave pseudo random noise signal.

[14] In embodiments, the method includes, prior to performing temporal cross correlation, temporally shifting and scaling, and subtracting the modelled clutter from the transmit signal, performing baseband demodulation on the measured receive signal to provide baseband data, segmenting the baseband data into a fast-time versus slow-time matrix of fast and slow time windows, and applying a matched filter to each fast time window to provide slow-time versus range data.

[15] In embodiments, the method includes applying coherent integration to the output of the clutter filter using a Radon Fourier Transform to obtain range and velocity data for moving targets.

[16] In embodiments, the applying coherent integration comprises: assuming a velocity from a predetermined set of potential velocities, an initial range and an initial slow-time, wherein the initial range corresponds to an initial range bin and the slow-time corresponds to an initial slow-time bin, selecting N slow-time bins of the matrix of slow-time bins and fasttime bins including the initial range bin based on the velocity, coherent integrating over the N slow-time bins, repeating the assuming, selecting and integrating steps over all combinations of range bins, slow-time bins and potential velocities to determine an integration response; and determining the range data and the velocity data for the moving target based on the integration response.

[17] In embodiments, the method comprises generating the range data and velocity data in the form of a matrix including velocity and range bins.

[18] In embodiments, the method comprises generating a range time image on a user interface based on the receive signal and receiving a desired velocity and a desired range from a user that has been estimated based on the time range image.

[19] In embodiments, the method comprises generating a time range image on the user interface based on a decluttered receive signal that is determined by subtracting the modelled clutter from the receive signal, receiving a second, different, desired velocity and a second, different, desired range from a user that has been estimated based on the time range image and repeating the steps of determining transmit windows, determining receive windows, performing temporal correlation, temporally shifting and scaling, and subtracting the modelled clutter.

[20] In another aspect, a sonar system is provided comprising: one or more processors, one or more memories having stored thereon computer readable instructions configured to cause the one or more processors to perform operations comprising the methods described herein.

[21] In a further aspect, one or more computer readable media are provided comprising instructions, that, when executed by a processor, cause the processor to perform operations comprising the methods described herein.

[22] The disclosure extends to a system comprising one or more processors and one or more memories having stored thereon computer readable instructions. The instructions are configured to cause the one or more processors to perform operations comprising any one or more of the methods described herein.

[23] The disclosure further extends to one or more computer readable media comprising instructions, that, when executed by a processor, cause the processor to perform operations comprising any one or more of the methods described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[24] Disclosed implementations will now be described by way of example and with reference to the accompanying drawings, in which: FIG. 1 shows a schematic diagram of a sonar system including a signal processing pipeline, in accordance with embodiments of the present disclosure;

FIG. 2 shows a schematic diagram of a signal processing pipeline for detection of moving targets, in accordance with embodiments of the present disclosure;

FIGS. 3(a) to 3(e) shows output images from the signal processing pipeline of FIG. 1 , in accordance with the present disclosure;

FIGS. 4(a) to 4(d) shows output images at sequential stages of clutter filtering, in accordance with the present disclosure;

FIG. 5 shows a computer system for carrying out the various methods of the present disclosure;

FIG. 6 provides a flow chart illustrating steps of a method of clutter filtering, in accordance with the present disclosure; and

FIG. 7 provides a flow chart of a method of operating a short-time matched filter, in accordance with the present disclosure.

DETAILED DESCRIPTION

[25] FIG. 1 shows a schematic diagram of a sonar (Sound Navigation and Ranging) system 110, which includes a transmitter 100, a receiver 102, and a signal processing pipeline 10 in accordance with embodiments of the present disclosure. The arrangement of these components can vary depending on the type of sonar system 110 and its application and the methods and systems of the present disclosure are applicable to various such sonar systems. For example, the sonar system 110 may be a single-transducer system where the same transducer acts as both transmitter 100 and the receiver 102. After emitting a sound pulse (original wave 106), it switches to receive mode to detect echoes in the form of reflected wave 104 from a target 108. The sonar system 110 may include separate transducers for transmission and reception, placed at different locations. This setup can provide more detailed information about direction and speed of the target 108. The sonar system 110 may be a multiple transducer system including multiple transmitters 100 and receivers 102 placed at various locations. The sonar system 110 may comprise a single transmitter 100 and multiple receivers 102, or vice versa. These arrangements enhance detection capabilities and coverage area. Arrays of transducers either in linear, planar, or volumetric configurations may be utilized by the sonar system 110. These arrays can steer and focus sound beams electronically, improving resolution and detection range. The sonar system 110 may be an in-air system or an in-water (e.g., at a harbour) system. The sonar system 110 may include transducers towed behind one or more vessels, allowing for wider area coverage. [26] The sonar system 110 operates based on the principles of sound wave transmission, reflection, and reception, combined with signal processing. The sonar system 110 generates a transmit signal, which is an acoustic wave (original wave 106) created by a transducer or transmitter 100. The original wave 106, or the transmitted acoustic signal, travels through the water or air until it encounters objects or targets, such as the sea floor, submarines, divers, fish, or other underwater features, or land features. When the original wave hits a target 108, it is reflected towards the sonar system 110. The characteristics of this reflected wave (echo) exhibit change in relation to the original wave 106, based on the target's size, shape, composition, and relative motion. The sonar system's receiver 102 (which might be the same transducer used for transmission in a monostatic sonar, or a separate one in bistatic or multi-static arrangements as described above) measures the reflected waves. This received signal 22 contains echoes from various targets. The target 108 is any object or feature that reflects the sonar waves back to the receiver. By analysing the echoes, information about the target, such as its distance, size, speed, and direction, can be inferred. The methods and systems of the present disclosure are particularly concerned with detection (in terms of range and velocity) of moving targets, as will become clear from the following description. The received signal 22 is analysed by the signal processing pipeline 10, which will be described in further detail with respect to FIG. 2.

[27] FIG. 2 show a schematic of a signal processing pipeline 10 in accordance with embodiments of the present disclosure. According to the signal processing pipeline 10, a receive signal 22 is demodulated to baseband data 24 (which is a transformed version of the receive signal 22) and split up in short time segments (not shown), over which the Doppler shift is assumed to be negligible, thereby simplifying the subsequent processing steps. In other words, the split up short time segments are selected such that target velocity is assumed to be negligible. A short-time matched filter 14 (STMF) results in STMF data 26 corresponding to a signal model for targets in range-time, in which the ambiguity function of a transmit waveform (not shown) comes back (i.e. models the STMF response). A range-time image (or matrix form) based on the STMF data 26 can be analysed and interfering signals from static targets (clutter) can be filtered out by a clutter filter 16 to provide clutter filtered data 28. Coherent integration 20 is applied to the clutter filtered data 28 (which is a decluttered form of the STMF filtered data 26) to arrive at estimated range and velocity data 30 for the moving target. In embodiments, a Radon-Fourier transform (RFT) is applied for the coherent integration 20.

[28] The baseband demodulation 12 is performed on the receive signal 22 to yield (complex-valued) baseband data 24, which removes redundancy in the received data, thereby increasing processing speed. A linear bandpass filter (not shown) may be used to reduce noise outside the frequency band of the sonar system in the receive signal 22 in advance of the baseband demodulation 12. [29] The present inventors have realized that over a short period of time, motion is negligible, and all the signal contributions can be approximated as coming from static targets. This approach is only matched to the moving target for a short period of time by the short-time matched filter 14, but signal information is maintained. Apart from the target, there are also other echoes coming from non-moving reflectors (clutter interference), which are filtered out in the stage of the clutter filter 16. What remains is ideally only the signal contributions from the moving target plus random noise. Coherent integration 20 is performed in an efficient manner from the pulse/short-time correlation results (STMF filtered data 26) given by the short-time matched filter 14, e.g., by using a Radon-Fourier transform (RFT), evaluated at the target delays corresponding to a set of constant velocities.

[30] The signal processing pipeline 10 provides an algorithm that extends the detection capabilities of a sonar system by an increase in processing gain. This improves the maximum detection range of the sonar system, which is of special interest to an operator who wants to detect the incoming target as early as possible. The processing pipeline 10 may be embodied in a moving target detection sonar. Prior sonar processing schemes correlate a single transmit pulse with the received data, which limits the achievable processing gain and thus the maximum detection range of such a system. The moving target detection algorithm of the signal processing pipeline 10 addresses this problem, in part, by coherent integration 20 over multiple pulses/extended time and is generalized for arbitrary (including pulsed and continuous) transmit signals.

[31] The transmit signal corresponding to the original wave 106 in FIG. 1 may be a Continuous Wave (CW) sonar signals such as Pseudo Random Noise Continuous Wave (PRN CW): This type of signal involves continuously transmitting a pseudo-random acoustic signal. The randomness in frequency or phase characteristics of the signal helps in distinguishing between multiple simultaneous transmissions and improves resolution. In other embodiments, the transmit signal may be a pulsed sonar signal. For example, Frequency Modulated (FM) pulses may be utilized. In one embodiment, the pluses are Linear Frequency Modulation (LFM) pluses, which increase or decrease in frequency over time, forming a linear relationship between frequency and time. LFM pulses are particularly useful for distinguishing targets that are close together. In other embodiments, Hyperbolic Frequency Modulation (HFM) pulses are used in which the frequency of the pulses vary in a hyperbolic manner. PRN CW can be difficult to use in a Clutter dominated environment due to poor peak-to-sidelobe level and overlapping echoes. In such environments, using pulses might be advantageous due to non-overlapping clutter and target reflections. PRN CW is however (maximally) Doppler sensitive, which means that Doppler shifted version is maximally different from the non-Doppler shifted version. This may facilitate differentiation of clutter and target using a CW waveform. Using LFM/HFM is mainly advantageous for its high peak-to-sidelobe. Since LFM/HFM is a Doppler tolerant waveform, a Doppler shift results in a range displacement. This property is maximized for HFM (which LFM approximates under narrowband conditions). Therefore, unmodelled Doppler does not result in correlation loss but in range displacement. The present disclosure is developed based on realizing that range and velocity can only be (unambiguously) determined using multiple such pulses. Range resolution is similar for PRN and FM: both inversely proportional to the bandwidth: dr = c/2B. Therefore, using PRN and HFM with same bandwidth gives similar range resolution. One benefit of use of PRW CN in the present systems and methods is improved SNR as compared to using pulses (because of higher total signal energy).

[32] Other examples for the transmit signal include Chirp Signals, which are a form of FM pulse. Chirp signals sweep through a range of frequencies during the pulse duration. The long pulse length of chirps allows for high energy transmission, enhancing detection capabilities, especially for distant or weak targets. Phase-Coded pulses could be used in which the pulses modulate the phase of the transmitted signal according to a predefined code. Phase coding can improve the signal-to-noise ratio and is useful in multi-user environments to prevent signal interference. The centre frequency of the transmit signal may be in the low frequency range (1 to 10 kHz) or in the low to medium frequency range (10 to 30 kHz) with a bandwidth typically in the range of5% to 100% of the center frequency. The use of low and low to medium frequency transmit signals allows for lower absorption and thus improved long range detection of moving targets.

[33] Referring to FIG. 2, the signal processing pipeline 10 allows for detecting a low SNR moving target. In order to avoid requiring an accurate kinematic model of a moving target, which could be difficult to obtain as the motion of the target is generally unknown, an assumption has been made by the present inventors in which, over a sufficiently short period of time, the target’s motion can be accurately modelled with a constant radial velocity towards (positive velocity) or away from (negative velocity) the receiver 102. As described herein, determination of the velocity of a moving target includes positive and negative values. The trajectory of the target over this interval can then be described by two parameters: initial range (r₀) and velocity (v), which is the ultimate output of the signal processing pipeline 10.

[34] In the stage of baseband demodulation 12, echoes reflected from targets in the form of received signal 22 are provided as an input. These signals are typically at the same frequency as the transmitted signal, which is in the kilohertz range for the sonar system 110 as described above. The received high-frequency signal is mixed with a reference signal of the same frequency as the transmitter. This process generates two new signals: the sum and difference of the original and reference frequencies. The higher frequency sum signal is filtered out, leaving only the lower frequency difference signal, known as the baseband signal. The baseband signal represents the original received signal but shifted down to near- zero frequency. This signal retains the information present in the original high-frequency signal, including phase and amplitude changes caused by the target and is output from the stage of baseband demodulation 12 in the form of baseband data 24. Baseband demodulation may include down sampling the measured data representing the receive signal 22 at a rate of at least the bandwidth, instead of nyquist: 2*(fc+B/2).A low pass filter may be applied to the baseband data 24 after baseband demodulation 12 or before any down sampling of the baseband data 24 for anti-aliasing.

[35] The baseband data 24 is segmented into intervals corresponding to fast-time and arranged in a matrix format. This may be performed as part of the stage of short-time matched filter 14 as described further below with respect to FIG. 7. In pulsed systems, fasttime is the time interval within each pulse. Fast-time data is directly related to the range or distance to the target because the time delay of the echo within a pulse corresponds to how far the sound travelled. The matrix is created by sampling the received echoes for each pulse. Each row of the matrix corresponds to one pulse, and the columns within that row represent different time samples within the pulse's duration. Slow-time represents the progression of time across the sequence of pulses. Slow-time (or the column of the matrix) is indexed by the pulse number. For example, the first pulse is indexed as 0, the second as 1, and so on. Each subsequent pulse (row in the matrix) may carry new information about the target or the environment, showing changes over time. The columns across rows show the same time instance within each pulse, tracking the evolution of the echo signature over time. For Continuous Wave (CW) systems, the fast-time concept is adapted by dividing the ongoing signal into artificial segments or windows, mimicking the pulse duration used in pulsed systems. These segments are used to simulate the range analysis as in pulsed systems. The slow-time in CW systems can be represented by sequential segments. The matrix is then formed with rows representing the artificial time segments, and columns representing points in time within those segments. That is, for pulsed systems, each row represents a different point in time within the duration of a single pulse whereas for continuous systems, the continuous signal is artificially segmented into intervals or 'artificial pulses' and each row in the matrix then represents a different point in time within these artificial segments, mimicking the fast-time analysis in pulsed systems. For both pulsed and continuous systems, each column in the matrix represents the same point in time but across different pulses (or artificial segments in the case of CW systems).

[36] Accordingly, the baseband data 24 representing the receive signal 22 is provided to the short-time matched filter 14 in the form of a fast versus slow-time matrix or is generated in that form as part of the algorithm of the short-time matched filter 14 as described below with respect to FIG. 7. [37] The short-time matched filter 14 is applied to the baseband data 14 under an assumption of a moving target acting as a static target in fast-time. In the following, a baseband signal model of a moving target is derived, which is subsequently used to derive the short-time matched filter for a moving target.

[38] The transmit waveform of the transmit signal 102 is given by the real part of the complex envelope g(t) modulated by a carrier at frequency fc, which provides: s_T(t) = Re[g(t)e^j27rf^ct], 0 < t < T (equation 1) for a transmission of length T (in seconds). If this transmission is reflected from a point target at range ro, the delay of its echo is given by T = 2ro/c T = 2r₀/c. Writing the received signal 22 as a scaled and delayed version of the transmission then gives: (equation 2)

The complex baseband signal is obtained by multiplying the complex signal:

(equation 3) writing f_cz =

where A is the wavelength of the carrier, gives the received signal 22 in complex baseband for a static target:

(equation 4)

From equation 4, it is seen that in baseband, a delayed signal is a time shifted version of the baseband signal g(t) with an additional phase shift of the carrier.

[39] Under the supposition that there is a moving target whose range is given by its initial range ro and constant radial velocity v towards the sensors, as r(t) = r₀ - vt, 0 < t < T.

The echo delay T can be found as a function of time by realising that a signal received at time t is reflected from the moving target at time t - 1. Then -r(t) is found by solving for the two- way propagation distance, which has been found to be approximated by:

(equation 5) under the condition that the target radial velocity is low compared to the medium velocity v/c « 1 , which is assumed in the following derivations. Substituting equation 5 into equation 3, leads to the following expression for the received signal 22 (equation 6)

and its baseband representation: (equation 7)

[40] From equations 6 and 7, it can be seen that the received signal is a copy of the transmit signal with a time dilation or compression and a frequency shift, due to the

Doppler effect. The exponential in the baseband expression can be written as the product of a time-varying phase shift and a constant = f

_D is the Doppler frequency of the carrier. Including the phase and attenuation constants in a new (complex-valued) constant a gives: (equation 8)

[41] As described previously, the baseband data 24 has the received signal 22 split into fast-time and slow-time. In pulsed sonar systems, the measured signal is split up in fast-time (time within one pulse duration) and slow-time (from pulse to pulse). For a continuous wave system, the measured signal is split into fast-time (within one artificial pulse duration) and slow-time (from pulse to pulse for an artificial pulse). Adopting this method, fast time is defined as t' = t - mT_w with t' e [0, T_w], such that -r(t) = (t' + mT_w), where m = 0,1,2 ... M - 1 is slow-time. The baseband signal can thus be written as:

[42] The time length of a window T_w is chosen such that the radial displacement of the target within the duration of the window is below the range resolution: | vT_w | « AR. It is thus assumed that over a short period of time (fast-time) the target is static. However, the target’s movement over multiple of such windows (slow-time) cannot be neglected. Under the assumption that the target is static in fast-time, the time dilation of the complex envelope in fast-time can be neglected:

(equation 10)

[43] This means that in fast-time the received baseband signal is a delayed version of the transmit baseband signal with z(m) = -^- - —mT_w, scaled with a complex-valued constant, and multiplied with the phase term e^{j2nfc c}

The short-time matched filter 14 is, therefore, applied over fast-time (which is translated to range) for each slow-time sample (giving time) to obtain a range-time image.

[44] The signal processing pipeline 10 is applicable to continuous transmit waveforms (such as Pseudo Random Noise (PRN)) as well as pulsed wave systems. Continuous wave systems may allow for more flexibility in the processing, as any window length Tw may be chosen and may be a user settable parameter through a user interface of the sonar system.

[45] The short-time matched filter 14 for static targets is applied to each fast-time window. This approach is ‘matched’ over a short period of time, during which the motion of the target is assumed to be negligible. Under these assumptions, the present inventors have derived the following function representing the matched filter output of the short-time matched filter 14, which is generalized to both pulse and continuous transmit waveforms: s_MF(t',m) = ae^}2nfDmTwXg_miNB t' - T(m),f_D) (equation 11) [46] Equation 11 reveals the narrowband ambiguity function x_gm,NB(t' ~

X(gm

and the short-time matched filter 14 performs a cross-correlation represented by the narrowband ambiguity function. This means that the output of the matched filter in baseband for a short-time window m is approximated by the narrowband ambiguity function of that transmit window, under the made assumption that the target velocity is relatively low v/c « 1.

[47] The ambiguity function measures how well the received signal 22 (in a given fasttime window) matches the transmit signal at a specific delay r(m) and Doppler frequency fo. This function is essentially performing a cross-correlation between the received signal and a set of reference signals shifted in time and frequency, yielding a measure of similarity at various ranges (delays) and velocities (Doppler shifts). The ambiguity function operates on the baseband data 24 within each fast-time window, correlating it with a theoretical signal model to produce a one-dimensional slice of the two-dimensional ambiguity function. This process effectively isolates the range information of the target in each fast-time window.

[48] From equation 11 , the output of the matched filter in baseband represents a slice of the two-dimensional ambiguity function of that short-time segment at a specific Doppler frequency fD, multiplied with a phase term that changes in slow-time, corresponding to the Doppler shift of the carrier.

[49] r(m) and /D represent the unknown range and Doppler frequency of the target 108, respectively. r(m) indicates the delay corresponding to the target's range in the mth slowtime window, while /D reflects the Doppler shift due to the target's velocity. The short-time matched filter 14 performs a cross-correlation process that scans through fast-time (f), which is the time within each pulse or artificial pulse duration. If the target's signal is strong enough to rise above the noise level, it appears at a delay

in the fast-time dimension. This process essentially provides a one-dimensional slice of the two-dimensional narrowband ambiguity function at a specific Doppler frequency, capturing range information for the target.

[50] In some traditional sonar systems, both range and Doppler are processed for each fast-time window. However, the short-time matched filter 14 initially focuses only on range by correlating the received signal with a non-Doppler shifted version of the transmit signal, essentially slicing the ambiguity function in f = fo. The Doppler component ( b) is not actively swept or varied during the process of the short-time matched filter 14. Instead, it arises as a result of the correlation with the received signal, which may have a Doppler shift due to the target's motion. [51] Equation 11 represents the short-time matched filter output, where a is a complex constant incorporating phase and attenuation. This equation gives a range-time representation where each row (fast-time window) correlates to the range, initially disregarding the Doppler effect. The Doppler effect is subsequently accounted for in the step of coherent integration 20, where the Doppler frequency component becomes significant. This approach to sonar signal processing separates the initial range estimation (via short- time matched filter 14 in fast-time) from the later Doppler analysis (in slow-time), refining the target detection and characterization process.

[52] In FIG. 7, an exemplary method 700 of short-time matched filtering as implemented by the short-time matched filter 14 is illustrated in accordance with exemplary embodiments. The method 700 of FIG. 7 illustrates a manner by which a continuous wave signal can be divided into fast-time windows by introducing the concept of a definable transmit signal correlation time window. In addition, the transmit signal correlation time window can be applied to pulsed waveforms having relatively long pulses (for increased SNR, which may facilitate extended detection range) that need to be divided into smaller segments so that the assumption made herein of treating the moving target as stationary over a sufficiently short transmit signal correlation time window (which can be considered as akin to the previously described CW PRN processing).

[53] In step 702, the inputs are initialized. That is, the transmit signal (tx(t)) is obtained and the receive signal 22 is received. A maximum target velocity (v_max) is defined, which specifies the highest velocity of targets that the system is expected to detect. This velocity is used to ensure that the time window is appropriate for capturing the necessary data from moving targets without significant loss of information due to their motion. The maximum target velocity may be a user settable parameter through a user interface. A maximum detection range (R_max) is defined, which is the furthest distance at which the system is expected to detect targets. It is used in defining the length of the receive signal correlation window. The range determines how long the system should listen for echoes after transmitting a pulse or continuous wave signal, based on the time it takes for sound to travel to the maximum range and back. The maximum detection range may be a user settable parameter through a user interface.

[54] In step 704, the transmit signal correlation time window length (T_w) is computed. T_w, the correlation time window, is the duration over which the transmit signal (tx(t)) and the received signal (rx(t)) will be compared or correlated. The formula for Tw is T_w < — - — , fc^vmax where: c is the speed of sound in the medium (e.g., water or air), f_c is the carrier frequency of the transmit signal. This formula ensures that the time window is short enough to capture the necessary details from a target moving at the maximum expected velocity whilst still meeting the underlying assumption of the short-time matched filter 14 that the time window is short enough to allow the moving target to be treated as stationary. For practical and operational

0 1-c effectiveness, it is suggested to use a smaller time window: T_w « — — , which has been fc^vmax found to provide enhanced performance.

[55] In step 706, the receive signal correlation window length is computed. This step determines the time duration T_r for which the received signal rx(t) should be analysed in each correlation operation. This duration directly relates to the furthest distance at which the sonar system is expected to detect targets, known as the maximum detection range R_max. The time

2 window is calculated by the formula T_r = - • R_max. The factor of 2 in the formula accounts for the round-trip travel time of the sonar signal. The calculated T_r determines how long after transmitting a pulse the sonar system should listen for echoes. This ensures that echoes from targets at the edge of the maximum detection range are included in the analysis.

[56] In step 708, the number of transmit windows is calculated. This step involves calculating the number of transmit windows (N_windows) in the short-time matched filter process by dividing the entire duration of the transmit signal into smaller, discrete segments or windows. Each of these segments will be used in the matched filtering process. The formula for determining the number of windows is N_windows

The

Tv number of windows indicates how many individual segments the transmit signal will be broken down into for the purpose of matched filtering. Each window represents a distinct portion of the transmit signal that will be correlated with the corresponding part of the received signal.

[57] In step 710, a stopping criterion for the subsequent iterative steps 712 to 718. This step controls the short-time matched filter process to iterate over each transmit window or segment that was previously defined in step 704. The iteration is set to run from m = 0 to m = Nwindows - 1 , where Nwindows is the total number of transmit windows calculated in step 708. Each iteration index m represents a specific transmit window or segment. In this context, m serves as an index for slow-time bins. The loop will start at m = 0, which corresponds to the first transmit window, and proceed sequentially through each window. For each value of m, the corresponding segment of the transmit signal (tx(t)) and the received signal (rx(t)) will be processed as per the matched filter algorithm. By iterating over each window, the algorithm ensures that the entire duration of the transmit signal is analysed.

[58] In step 712, the start and end times for the transmit and receive windows are defined. This step involves setting up the specific time intervals to be used in each iteration of the short-time matched filter. A starting point of a current time window is determined by t₀ = m • T_w and applies to both receive and transmit windows, m is the index for the current iteration in the slow-time dimension. T_w is the correlation time window as determined in step 704 and corresponds to the length of each fast-time window. As m increases, to shifts forward in time, moving to the next segment of the signal. An end point of the current fasttime window in the transmit signal is determined by t_Wiend = t₀ + T_w. An end point of the current time window in the received signal is determined by t_riend = t₀ + T_r. Since T_r is typically longer than T_w, the end time of the received signal window t_r,_end extends beyond that of the transmit signal window t_w,_end. In this case: adjacent receive windows overlap in data, as the (longer) receive window of length T_r shifts by a (small) amount T_w per iteration.

[59] In step 714, the transmit window segment is defined. This step selecting a segment of the transmit signal tx(t) for the current window based on the formula a = tx[t₀: t_{w end}] , The notation tx[t₀: t_{w end}] means taking a slice of the transmit signal from to to t(_W,_end). a is the variable that holds this segment of the transmit signal.

[60] In step 716, the receive window segment is defined. This step selects a segment of the received signal rx(t) for analysis based on the formula b = rx[t₀: t_{r end}] , The notation rx[t₀: t_{r end}] means taking a slice of the received signal from to to t(_r,_end). b is the variable assigned to this segment of the received signal.

[61] In step 718, temporal correlation is performed based on the formula s_MF(m, t') = (b * a)(t'). This step involves performing temporal correlation between the selected segments of the transmit and receive signals from steps 714, 716. The symbol * denotes the operation of temporal correlation. Temporal correlation is a signal processing technique where one signal (in this case, a , the segment of the transmit signal) is slid over another signal (b, the segment of the receive signal) to measure the similarity as a function of the time shift. The result of this correlation gives an indication of how similar a and b are at different shifts, providing information about the time delay and, consequently, the range to the target. The correlation result of step 718 is stored as s_MF(t', m)for each slow-time bin m. t’ represents the time shift variable in the correlation. It varies over the range of possible shifts and essentially explores different alignments of a and b.

[62] Each correlation step provides a row of range data, and each iteration m corresponds to a different row in the slow-time versus range STMF filtered data 24. That is, the outcome of this correlation for each time shift t' provides information about the similarity between a and b at that particular shift. The result of this correlation for a given m is a set of values representing how the received signal aligns with the transmitted signal over different ranges. This creates a profile of range data for that specific time window. The index m runs through different slow-time windows, essentially moving through the received signal over time. For each m, the process repeats, and a new correlation is performed with a new segment of the transmit and receive signals. The result of the correlation for each constitutes a separate row in the resulting data matrix of the STMF filtered data 26. Each row represents the range profile at a different point in time. The complete set of these correlations, across all values of m, forms the matrix, which is output as STMF filtered data 26 in step 720. Rows in this matrix represent different time windows (slow-time), and columns represent range information derived from the correlation at different time shifts t'. This matrix can be visualized as a range-time image as shown in FIGS. 3(a) to 3(d), where each row shows how the echoes received at a specific time relate to different ranges, and moving down the rows shows how this relationship changes over time.

[63] The process of FIG. 7 includes adaptive transmit and receive windows that may be user set through a user interface during use of the sonar system 110 or set as a design parameter. In traditional pulse-based systems, the fast time and slow-time windows are intrinsically linked to the pulse duration and the pulse repetition interval (PRI), respectively. With adaptive windows as allowed by the systems and methods of the present disclosure, the fast and slow-time windows are not constrained by fixed pulse characteristics. This allows for more versatile processing and extends the signal processing pipeline 10 to continuous waveforms or long pulsed waves.

[64] An exemplary output of the short-time matched filter 14 in the form of an image of the STMF filtered data 26 is illustrated in FIG. 3(a). The STMF filtered data 26 is provided in the form of a matrix of slow-time versus range, which can be visualized on a display device of the sonar system 110 as an image of slow-time versus range. In the image of FIG. 3(a), vertical lines can be seen representing stationary targets. Further, a skewed line can be seen, which represents a moving target changing in range over slow-time. Already from this image, a moving target is identifiable, and the velocity and initial range of the moving target can be detected (where the angle of the skewed line corresponds to velocity). However, there may be situations where noise and other clutter will obscure the moving target. The stages of clutter filter 16 and coherent integration 20 allows the moving target to be more readily identified and the initial range and velocity of moving targets to be determined.

[65] Continuing to refer to FIG. 2, the STMF filtered data 26 is processed through a clutter filter 16 to remove various forms of clutter that do not correspond to moving targets of relevance. The clutter filter 16 may be an optional feature in some environments where clutter is less of an issue. A variety of filters could be used as the clutter filter 16, although the present inventors have found that a Moving Target Indication (MTI) filter and a CLEAN filter (described further below) are particularly effective in the present signal processing pipeline 10.

[66] Examples of suitable clutter filters are described in the following before describing the preferred MTI and CLEAN filters. An adaptive clutter filter may be employed, which adjust its parameters based on the characteristics of the clutter in the received signal. Exemplary adaptive filters include Least Mean Squares (LMS) and Recursive Least Squares (RLS) filters. A high-pass filters may be used for removing slow-moving or stationary clutter by allowing only high-frequency components associated with faster-moving targets to pass through. A doppler filter may be utilized to separate targets based on their velocity. They can be tuned to ignore clutter that does not match the Doppler shift characteristics of moving targets of interest. The MTI filter described below fits into the category of doppler filter. Wavelet transform filtering may be used to decompose the STMF filtered data into various scales or frequencies, allowing for the selective removal of clutter components. A constant false alarm rate (CFAR) filter provides an algorithm that adjusts the detection threshold dynamically to maintain a constant rate of false alarms over varying clutter conditions.

[67] In some embodiments, an MTI filter, also called a pulse canceller, is used as the clutter filter 16 to suppress the static components in the pulsed compressed echoes. This filter is used in conjunction with pulsed transmit signals and may also be used in conjunction with continuous wave transmit signals such as PRN. Even though a PRN (or other continuous) signal is continuous, it can be artificially segmented into 'pseudo-pulses' or windows for analysis. Indeed, the baseband data 24 is already divided into pseudo pulses before applying the short-time matched filter 14, as described above. It should be appreciated, however, that the MTI filter has been found by the present inventors to be more effective in clutter filtering with respect to (repetitive) pulsed transmit waveforms. The MTI filter works by comparing successive segments (or pseudo-pulses) to detect phase shifts indicative of movement. It is assumed that the measured signal corresponding to the receive signal 22 is a superposition of echoes from the clutter and from the moving target. The clutter signal is expected to be the same for two consecutive echoes, however, the signal of the moving target has undergone a phase shift over one pulse repetition interval (or pseudo pulse repetition interval). A two-pulse canceller may be used, which takes the difference of the matched filter output s_MF(t',m) over two successive slow-time samples. The transfer function H(z) = 1 - z^-1 of the MTI filter utilizes the concept of pulse repetition interval to cancel out echoes that are unchanged over one pulse repetition interval, effectively suppressing static clutter. The frequency response of the MTI filter, \H(f) | = \2sin(nfT_w')\, indicates its high-pass behavior. It suppresses signals at zero frequency (static clutter) and allows through signals with frequency corresponding to moving targets. If the transmit signal is identical for each pulse (as in the case of chirps or HFM pulses), an MTI filter can be implemented before pulse compression. For varying transmit signals like PRN, the MTI filter may beapplied after pulse compression to effectively filter out the main lobe of the clutter. FIG. 3(b) illustrates decluttering of the STMF filtered data 26 after application of the MTI filter in the clutter filter 16 in which the signal from the moving target can be more distinctly identified with vertical lines from stationary or near stationary sources removed. However, there is still some general background noise caused by sidelobes.

[68] CLEAN is a deconvolution algorithm that is adapted by the present inventors for removing clutter interference in sonar systems as the clutter filter 16. In this section CLEAN is implemented in time-domain as a serial subtraction of estimated clutter signals. It is assumed that the clutter signal can be represented as a delayed and attenuated version of the transmitted signal. By finding the highest peaks in the matched filter for static targets, the clutter filtering method estimates the delay at which these signals are received and subtracts them from the measured signal. Since the moving target will not correlate at one single range, the target signal will be likely not affected.

[69] The algorithm can be summarized by a series of subtractions in time-domain, giving one iteration of CLEAN for the received signal y(n) as:

(equation 12) given a transmit signal x(n), where the amplitude A_T corresponds to the signal component at delay T in the cross-correlation: r_yx(r) = Sn=o y (n)x(n - T). This amplitude can be estimated by the correlation amplitude if it is assumed that this was the only component contributing to the correlation: r_yx =

(n). However, if there are multiple signals at different delays, then the signal will have contributed only partly so that scaling 0 < a < 1 is applied:

[70] The procedure is repeated until an appropriate stopping-criteria is met, for example, stop after the energy in the CLEAN signal is not significantly decreasing anymore per iteration. In the context of our signal model, y(n) is a sampled version of the receive signal 22 s_t(t) and x(n) a sampled version of the transmit signal s_T(t).

[71] The CLEAN algorithm has been specifically adapted for sonar systems in the present disclosure and is described in further detail with respect to FIG. 6, which provides a flow chart representing steps of the method 600 of the CLEAN algorithm for clutter filtering, in accordance with embodiments of the present disclosure.

[72] Generally, the method 600 of clutter filtering incorporates cross-correlation as a matched filter for reflectors that do not move in range and are thus considered static. Moving targets will produce a signal that over time loses its correlation due to the displacement of the target. However, for some short period of time the target appears static. The resolution in Doppler (translated to target velocity) for continuous wave noise is approximated by that of a continuous wave sinusoid and is given by:

Av « — (equation 14) f_CT

[73] For example, provided a carrier of f_c= 15 kHz and c=1500 m/s c Av=0.1/T, gives the mainlobe resolution a signal of duration T seconds. If the target moves at vT=1.0 m/s, correlation may be performed over short enough segments: T<0.1 s to maintain correlation gain with the target signal. Conversely, if correlation is performed over longer segments, correlation gain is lost with the target, but not with the (near) static clutter. This principle is leveraged in the CLEAN algorithm embodied by method 600 to separate the target signal from the clutter interference in an iterative estimation and subtraction of the interference. Furthermore, the clutter can be separated from the target in range if a target above a certain range is detected. This is important since clutter can be non-static (and can even overlap in Doppler with the target), for example due to surface reflections, which for continuous wave PRN produce sidelobes over the entire range and can mask a weak target at a long range. These surface reflections are removed in the method 600 by correlating over short segments and removing all the contributions at selected ranges. The method 600 takes a portion of the transmit signal, with a window length corresponding to a cut-off in Doppler, and correlates over a set of lags corresponding to a range of interest, to enable filtering in range and Doppler.

[74] An exemplary method 600 exploiting these concepts is described with reference to FIG. 6. It should be appreciated that whilst the clutter filtering method 600 of FIG. 6 is described with reference to the exemplary signal processing line 10 of FIG. 2, the clutter filtering method 600 is more generally applicable. For example, in some moving target detection pipelines, beamforming may be used as a first step in signal processing to focus on signals from a specific direction. After beamforming, the clutter filtering method 600 can be applied to the beamformed data to remove clutter while preserving the moving target's signal. In another example, where Doppler processing is used to determine the velocity of targets, clutter filtering can be applied after Doppler analysis but before a target tracking stage. In pulse-Doppler systems, which may be used in sonar for moving target detection, the clutter filtering method 600 can be applied after the pulse-Doppler processing. In systems that generate range-Doppler maps, clutter filtering can be applied to these maps to refine the target information. In certain cases, the clutter filtering method 600 can be sequentially combined with other filtering techniques, such as CFAR (Constant False Alarm Rate) or adaptive filters, to provide a multi-stage approach to clutter mitigation and target enhancement. As such, whilst the clutter filtering method 600 is described with reference to the signal processing pipeline 10 of FIG. 2, the clutter filtering method 600 can be applied in a number of other sonar system signal processing pipelines to declutter the receive signal with respect to stationary targets and other interference that do not correspond to moving targets of potential interest.

[75] Referring to FIG. 6, the method 600 includes a step 602 of receiving the transmit signal tx(t) and the receive signal 22 rx(t). The receive signal 22 is measured by the receiver 102 whilst the transmit signal is known from the signal that directs the transmitter to output the original wave 106. In step 604, further inputs are received including the doppler cut-off velocity v_cutoff and the clutter filtering range clean_range. In some embodiments, the number of iterations for the cleaning algorithm is set as N_iterations. further input is a scaling factor e (e: constant close to 1). The Doppler cut-off velocity sets a threshold for Doppler velocities that the clutter filtering method 600 considers relevant. It is used to define a window length for correlation in terms of Doppler shift. Signals with Doppler shifts higher than ^vcutoff ^are considered part of the target signal, while lower shifts are likely to be clutter. The clutter filtering range specifies a maximum range within which the clutter is expected to be present. It determines a window length for correlating the received signal, focusing the algorithm’s attention to a specific range where clutter is likely to be found. The number of iterations (N_iterations) defines how many times the method 600 will iterate its process of clutter estimation and subtraction. More iterations allow for more thorough clutter removal but increase computation time. The scaling factor (e) is a constant close to, but smaller than,1 for which 0.98 is a typically used value, used in scaling an amplitude of the estimated clutter signal. It accounts for the fact that the clutter signal may not be the only component contributing to the correlation peak, especially in cases where multiple signals are present.

[76] In some embodiments, the doppler cut-off velocity and the clutter filtering range are user settable parameters. In other embodiments, the doppler cut-off velocity and the clutter filtering range are algorithmically set. With reference to FIG. 4(a), a slow-time versus range image is illustrated as a representation of the STMF filtered data 26 output from the short- time matched filter 14 of FIG. 2. In this example, crosstalk interference is shown at a range of around 0m as a strongest signal. Sidelobes (background level) mask a target. A slow-time versus range image as in FIG. 4(a) may be presented to a user via a user interface to allow a range of relevance for clutter filtering to be readily identified. A Doppler cut-off velocity can be set based on a user’s experience and knowledge of the likely clutter source. In FIG. 4(a), the clutter filtering range is set by a user as -0.5m to 0.5m and the velocity is set as 0.1 m/s corresponding to crosstalk. The number of iterations may also be a user settable parameter in some embodiments.

[77] In step 606, the transmit window length (in time) and the receive window length (in time) are computed. The transmit window length and the receive window length refer to the specific durations of the transmit and receive signals that are analysed at each step of the algorithm. The transmit window length (T_w) is the duration over which the transmitted signal is considered for correlation with the received signal. It is calculated based on the Doppler cut-off velocity (v_cutOff) and the carrier frequency (f_c ) of the transmitted signal. The formula used is T_w = — - — , where c is the speed of sound in water (approximately 1500 m/s). The fc ^vcutoff purpose of this calculation is to set a window length that aligns with the expected Doppler shifts caused by target movements. The Doppler cut-off velocity helps in differentiating between the clutter and the target based on their relative velocities. The receive window length is the duration over which the received signal is analysed for each transmit window. It is determined by the maximum range (clean_range) within which clutter is to be identified 2 and removed. The formula for calculating the receive window length is T_r = - • clean_range.

This calculation ensures that the receive window encompasses the time it takes for the signal to travel to the maximum range and back. It effectively sets the focus of the algorithm on the specific range where clutter is expected to be present. These window lengths are utilized for subsequent temporal correlation, where sections of the transmit signal are correlated with corresponding sections of the receive signal to identify clutter. The window lengths help in isolating the parts of the signals where clutter is likely to be found, based on the expected Doppler shifts and range of interest.

[78] In step 608, the number of transmit windows 608 is determined. Step 608 determines how many segments or windows the transmit signal should be divided into for processing. This division is based on the transmit window length, T_w, which has already been calculated in step 606. As such, the transmit signal is divided into smaller, manageable pieces or 'windows' for correlation with the received signal. Each window represents a portion of the transmit signal over a specific duration (T_w). The total duration of the transmit signal is the overall length of the transmit signal being considered for the clutter filtering process. The number of windows N_windows =

- - — is the formula used. It

Tv calculates how many of these transmit windows fit into the total duration of the transmit signal being analysed by a given signal processing pipeline. It divides the entire duration of the transmit signal by the length of one window (T_w) to find out the total number of such windows.

[79] In step 610, a condition is assessed as to whether n (an iteration count) has reached N-1. Step 610 is a loop construct to specify a number of iterations for the loop, dictating how many times the operations of steps 612 to 624 within the loop will be repeated. The loop starts with n set to 0 and the loop continues to execute as long as n is less than N_windows. This condition ensures that the loop iterates over each transmit window. After each iteration, n is incremented by 1 , moving the loop to the next transmit window. N_windows - 1 represents the final window in the transmit signal. Other conditions may be used to determine whether a sufficient number of iterations have been performed such as determining whether a clutter signal is lower than a predetermined minimum amplitude or whether a current version of a decluttered receive signal minus a previous iteration of the decluttered receive signal is lower than a threshold.

[80] In step 612, the start and end times for the current transmit and receive windows are defined. t₀ is the start time of the current transmit window, n is the current iteration index of the loop (indicating which window is being processed), T_wis the transmit window length calculated in step 606. Multiplying n by T_w gives the start time of the nth transmit window. As n increases, t₀ shifts forward in time, starting each new window T_w seconds after the previous one. t_end is the end time of the current transmit window. It is calculated by adding the window length to the start time: t_end = t₀ + T_w. This defines a window of length T_w. in the transmit signal, starting at t₀ and ending at t_end. t'_end is the end time of the corresponding window in the received signal. T_r is the receive signal correlation window length, determined based on the maximum range (clean_range). In some embodiments, clean_range can correspond to a maximum value or a minimum value or both (i.e. a range). The end time of the receive signal is calculated by t'_end = t₀ + T_r which defines the corresponding interval in the received signal to be correlated. This step ensures that the received signal segment being analysed matches the range where clutter is expected, as determined by the clean_range. Step 612 aligns the transmit and receive signal windows for temporal correlation. By adjusting these windows as the loop progresses, method 600 systematically processes the entire transmit signal, correlating each segment with the appropriate part of the received signal to identify and remove clutter.

[81] In step 614, a cross-correlation of the current windows of the transmit and receive signals is performed. That is step 614 performs the step y(t) = tx(t₀: t_end) * rx(t₀: t_e'_nd) represents the process of temporally correlating segments of the transmit signal with corresponding segments of the received signal. A current transmit segment (tx(t₀: t_end)) defined by the start and end times of the transmit signal as determined in step 612 is crosscorrelated with a current receive segment (rx(t₀: t_e'_nd)) defined by the start and end times of the receive signal as determined in step 612. The symbol * denotes temporal correlation, a process where these two signal segments are compared to each other in time to identify how similar they are at different lags. Temporal correlation involves sliding one signal (e.g., tx ) across the other (e.g., rx) and calculating the degree of similarity at each point. This similarity is measured as a function of time t. y(t) is the output of the correlation process. It is a function of time that represents how well the transmit signal segment aligns with the received signal segment at different points in time. Peaks in y(t) indicate strong similarities or matches between the two signal segments, suggesting potential points where clutter reflections are present in the received signal. By finding these correlations, the algorithm can estimate the characteristics of the clutter (like its amplitude and delay) and subsequently remove it from the received signal.

[82] In step 616, a maximum peak of the correlation result of step 614 is found. Step 614 finds the time at which the correlation between the transmit and receive signal segments is the strongest. This point is indicative of the most significant clutter echo in the current window. Accordingly step 614 evaluates t_max = arg max |y(t) I where argmax stands for "argument of the maximum". In this context, it is used to find the value of t where y(t) (cross correlation result) reaches its maximum value. It identifies the time point at which the correlation is the strongest, suggesting the most likely position of a clutter echo. [83] In step 618, the clutter signal amplitude is calculated. This step evaluates A = e |y(t_max) I / || tx(t₀: tend) 11², which calculates the amplitude of the clutter signal that needs to be subtracted from the received signal. The scaling factor e slightly adjusts the amplitude of the estimated clutter signal, which may be necessary to avoid over-subtraction, which might remove parts of the target signal or introduce artifacts. y(t_max) is the magnitude of the correlation output at the time t_max , which is the point of strongest correlation identified in step 616. This value represents the strength of the clutter signal at the delay t_max.

| | tx(t₀: t_end)l l² is the squared Euclidean norm of the transmit signal segment from the start to the end of current transmit window. The Euclidean norm of a signal is a measure of its total energy or power, calculated as the sum of the squared signal values. This norm gives the signal energy of the transmit signal in the current window. The formula divides the magnitude of the clutter signal by the squared norm of the transmit signal segment. This division normalizes the clutter signal strength relative to the power of the transmit signal, providing a more accurate estimate of the clutter's relative amplitude. The result, A, is the estimated amplitude of the clutter signal that is to be subtracted from the received signal. It represents how strong the clutter signal is, in comparison to the transmit signal, adjusted by the factor e.

[84] In step 620, the clutter signal is determined. This step evaluates x_ciutter(t) = A • tx(t₀: t_end). x_ciutter(f) represents the estimated clutter signal at time t. This is an approximation of the actual clutter signal present in the received signal. A is the calculated amplitude of the clutter signal from step 618. The estimated clutter signal is obtained by multiplying the amplitude A with the current transmit signal segment. This multiplication scales the transmit signal segment to the level that is believed to represent the clutter in the received signal. By creating x_ciutter(t), the algorithm synthesizes a signal that approximates the clutter present in the received signal.

[85] In step 622, the clutter signal is shifted by t_max seconds to obtain x' _ciuter t), which involves time-shifting the estimated clutter signal to align it with the actual position of the clutter echo in the received signal. x_ciuter(t~) is the estimated clutter signal created in step 620. t_max is the time delay at which the peak correlation was observed between the transmit signal segment and the received signal in step 616. This time delay represents the position in time where the clutter echo is most prominent in the received signal. x_ciutter(t) is shifted by tmax seconds, which means adjusting the timing of the estimated clutter signal so that its peak aligns with the clutter echo in the received signal, x' _ciutter(A) is the resulting clutter signal after it has been shifted. The time shift is necessary because the estimated clutter signal initially has no time delay relative to the start of the transmit signal segment. The actual clutter echo in the received signal, however, occurs at a delay corresponding to t_max. [86] In step 624, the scaled and shifted clutter signal is subtracted from the receive signal. In step 624, the following function is evaluated: rx(t) = rx(t) - x' _ciutter(f) which represents the received signal at time t. This signal includes both the echoes from targets (including moving targets, which are of interest) and clutter (unwanted echoes from stationary objects, surface reflections, etc.). x' _ciutter(f) is the estimated clutter signal that has been time-shifted and scaled in steps 620 and 622. The scaled and shifted clutter signal is subtracted from the received signal. This operation is intended to remove the clutter component from the received signal. The result of this subtraction is a modified version of the received signal where the influence of the estimated clutter has been reduced or eliminated. The clutter signal, represented by x' _ciutter(t) is estimated over a specific window of the transmit and receive signals. Although the clutter signal is estimated based on a specific window, the subtraction is applied to the corresponding segment of the full received signal. The algorithm will typically repeat these steps 612 to 624 for all windows across the transmit and receive signals. This ensures that clutter is identified and removed throughout the entire duration of the received signal.

[87] In step 626, the clutter filtered data is output after all N-1 iterations (or some other end criterion is met) to a next stage in a signal processing pipeline. One or more further clutter filters may be applied after the CLEAN clutter filter that has been described with respect to FIG. 6.

[88] The iterative process of clutter filtering method 600 may be applied in more than one stage to remove different types of clutter. Referring to FIG. 4(b), a slow-time versus range image is illustrated after a first stage of clutter filtering by method 600 with the crosstalk 406 depicted in FIG. 4(a) filtered out. FIG. 4(b) may be displayed to a user through a user interface and shows a surface reflection 402 and a potential moving target 404. The user may input new parameters to the CLEAN algorithm of the method 600. In this specific example, the surface reflections can be identified based on the image of FIG. 4(b) as being in the range of 0 to 10m (low to mid-range) and a velocity (high Doppler) of the surface reflections of around 1.0m/s may be estimated by the user. Method 600 is performed based on these new parameters for the Doppler cut-off velocity and the clutter filtering range, which results in an image as shown in FIG. 4(c) with the surface wave reflections filtered out. As a result, the target 404 can be clearly seen plus some remaining clutter 408. The further clutter is recognized by the user as being in the range of 5 to 100m (long range) and having low doppler, which is identified by the user as being 0.2m/s. The user enters these new parameters for the Doppler cut-off velocity and the clutter filter range, which results in the image of FIG. 4(d) in which static clutter and other clutter is removed resulting in a clearly identifiable target 404. [89] Applying an MTI filter after the CLEAN procedure could help remove any remaining clutter main-lobes, which is verified in the example shown in FIGS. 3(b) to 3(d) where the combination of CLEAN and MIT provides optimal performance. As such, a combination of MTI and CLEAN filters may be used as the clutter filter 16.

[90] Referring back to FIG. 3, the clutter filtered data 16 (which is still in the form of a matrix of range versus slow-time) from the clutter filter 16 is provided to a stage of coherent integration 20. The coherent integration combines the outputs of the short-time matched filter (STMF filtered data 26 after clutter filtering) over a trajectory in range-time space, corresponding to a model of a target's constant velocity, thus achieving higher Doppler resolution and improved target detection capabilities. A moving target will have a skewed trajectory (a line segment) relative to vertical in the range versus slow-time domain where the angle corresponds to a particular velocity. Coherent integration is performed over more than one slow-time bin (i.e. a combination of slow-time bins/indicecs) that have been selected to follow the angled line segment. The coherent integration is performed for a set of potential velocities for moving targets of interest which correspond to different angles for the line segment and thus different combinations of the slow-time windows are selected corresponding to the different angled line segments. If a moving target is present, one of those line segment will result in a strong coherent integration response such that the corresponding velocity is taken as the velocity of the moving target.

[91] The short-time matched filter operates on short-time intervals in which the target appears static. Aside from the simplifications caused by the assumption that v « c and

| vT_w | « AR (range resolution), the output of the short-time matched filter 14 contains all the information of the moving target signal. The coherent integration 20 performs long time coherent integration of the target by integrating over the output of the short-time matched filter 14.

[92] The time delay of an echo from a moving target with a constant radial velocity v_T and initial range r₀, is -r(t) = ²⁽-^r°~^VTt This generates a straight line in range-time, under an angle that corresponds to the velocity of the target and an initial range at t = 0. Furthermore, the Doppler shift of the signal reflecting from a target is also dependent on its’ velocity. Therefore, there is a coupling in range-time between the angle and the Doppler phase shift of the straight line, which is exploited by the coherent integration 20 described herein. If a traditional Fourier transform is used to extract the Doppler, the Doppler resolution is limited by the time the target spends in one range resolution cell. However, the coherent integration 20 of the present disclosure is applied over a line under the right angle (Radon transform), such that the integration time and thus resolution is increased.

[93] The coherent integration 20 uses the coupling between the Doppler induced phaseshift and the range migration to express both in terms of the velocity of the target. More e

the target speed v_T. Combining the integration over a line-segment while compensating for the phase (Fourier) term, gives the so-called Radon-Fourier transform (RFT). The RFT is written as a function of the short-time matched filter, giving: s_RFT r,v) = f_mTw=o ^sMF (r_s(m),m)e~^j27l~^fcmTw dm (equation 15)

[94] where T_s(m) = - - -mT_w is the search delay, for which initial range r and a search velocity v for a constant velocity model. In some embodiments, the search is extended to include acceleration (e.g., by substituting v’ = v + a(mT_w)). Using the expression for s_MF(t' , m), the RFT method is ‘matched’:

(equation 16)

[95] as the peak amplitude in s_RFT(r, v) is observed at initial range r = r₀ and v = v_T, which maximises the ambiguity function for -r_s(m) = -r(m) and cancels the complex exponential. As seen from equation 16, the amplitude of the RFT peak is given by integrating the short-time ambiguity functions over m, evaluated at their peaks:

amplitude of the peak of the RFT method will then be: |s_RFT(r₀, v_T)| = (x_gm,_NB (0,0)) |, gives the loss due to the

assumption that Doppler is negligible within one segment. The RFT is mathematically formulated to integrate the STMF filtered data 26 over a line corresponding to a specific initial range (r) and target velocity (v). The peak amplitude in the RFT output will be observed at the actual initial range and velocity of the target, maximizing the ambiguity function and effectively cancelling out the complex exponential.

[96] The process of the coherent integration 20 will be further described, particularly with respect to a practical algorithm and parameterization of the Radon-Fourier Transform (RFT). The RFT is applied over a chosen number of slow-time bins, denoted as N. This number corresponds to a period during which the target's velocity is assumed to be constant. N is a design parameter; a larger N increases the integration time, potentially enhancing the signal response from a moving target and improving detectability. However, if N is so large that the target is not actually moving with a constant velocity within those N slow-time bins, performance will deteriorate. Coherent integration begins by selecting an initial time (To) in slow-time and an initial range. This selection serves as a starting point for the coherent integration 20. The coherent integration 20 then proceeds along a trajectory in the slow-time- range bins, determined by the assumed constant velocity of the target. The coherent integration 20 is carried out over N slow-time bins, following a trajectory that represents the target's assumed constant velocity and initial position. This trajectory forms an angle in the range-time space, corresponding to the target's velocity. The algorithm repeats this coherent integration process for all possible combinations of initial times (To), initial ranges, and target velocities. A predetermined set of target velocities may be used including a minimum velocity, a maximum velocity, and a distribution of velocity steps between the minimum and maximum velocities. The set of initial ranges and initial times may be defined by the resolution in range and slow-time of the STMF filtered data 28. If a moving target is present, one of these combinations will yield a strong signal (integration) response, indicating the detection of the moving target. The set of initial range and velocity corresponding to the peak signal response of the coherent integration 20 is output as the range and velocity data 30 for the moving target. The coherent integration 20 is a significant improvement over traditional Fourier transform techniques to extract Doppler information, which are limited in resolution by the time a target spends within one range cell whereas the coherent integration 20 integrates over more than 1 (N) slow-time bins that have been selected to correspond to an angle in range-time corresponding to a potential velocity.

[97] The coherent integration 20 over multiple slow-time bins increases the SNR (compared to sonar where only a single pulse/slow-time-interval is processed) of the target signal after the coherent integration 20. As such, systems and method described herein detect target signals that are too weak to detect using known sonar processing algorithms for moving targets. As a result, systems and methods described herein extend the range at which a target can be detected.

[98] The coherent integration 20 results in the range and velocity data 30 starting from an initial time, TO (from where the coherent integration path starts) that has been chosen. The signal processing pipeline 10 may repeat the RFT process for each initial time instance TO by looping over TO.

[99] Referring to FIG. 3(e), an image of the output of the coherent integration 20 can be seen. The coherent integration has transformed the slow-time versus time data from of the outputs of the short-time matched filter 14 and the clutter filter 16 to range and velocity data 30 (and additionally slow-time (not shown) in a third dimension of the matrix of range and velocity data 30. A target can be identified at approximately initial range ro = 2 meter and target velocity VT = 0.1 m/s.

[100] The range and velocity data 30 may be provided to a detection algorithm (not shown) for identification and characterization of moving targets. A standard detection algorithm in the context of sonar signal processing, particularly following coherent integration that provides range versus velocity data, performs several key functions to identify and characterize targets. The detection algorithm may utilize thresholding to distinguish between noise and potential target signals. Once potential targets are isolated based on the thresholding, the detection algorithm identifies these signals as targets. This identification may be based on specific characteristics such as signal strength, continuity over time, and consistency with expected target profiles. The detection algorithm may analyse the data to determine the range and velocity of detected targets. Since the input data is already in the form of range versus velocity, this step involves interpreting these values to estimate the distance and speed of each target. The detection algorithm may track the trajectory of each identified target over time. This involves analysing the change in range and velocity across successive data frames to predict the target's path and future position. The detection algorithm may also include a classification step, where identified targets are categorized based on their characteristics. For example, differentiating between small and large vessels, or distinguishing between surface and submerged objects. The detection algorithm may generate alerts or notifications for targets that meet certain criteria, such as proximity to a protected zone or exhibiting behaviour that suggests a threat.

[101] With reference to Figure 5, a computing device or system suitable for carrying out the methods described herein will now be described. Figure 5 shows a block diagram of one implementation of a processing system 500 in the form of a computing device within which a set of instructions for causing the computing device to perform any one or more of the methodologies discussed herein, may be executed. In alternative implementations, the computing device may be connected (e.g., networked) to other machines in a Local Area Network (LAN), an intranet, an extranet, or the Internet. The computing device may operate in the capacity of a server or a client machine in a client-server network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The computing device may be a personal computer (PC), a tablet computer, a set-top box (STB), a Personal Digital Assistant (PDA), a cellular telephone, a web appliance, a server, a network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine. Further, while only a single computing device is illustrated, the term “computing device” shall also be taken to include any collection of machines (e.g., computers) that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein.

[102] The example processing system 500 includes a processor 502, a main memory 504 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM) or Rambus DRAM (RDRAM), etc.), a static memory 506 (e.g., flash memory, static random access memory (SRAM), etc.), and a secondary memory (e.g., a data storage device 418), which communicate with each other via a bus 530. [103] Processor 502 represents one or more general-purpose processors such as a microprocessor, central processing unit, or the like. More particularly, the processor 502 may be a complex instruction set computing (CISC) microprocessor, reduced instruction set computing (RISC) microprocessor, very long instruction word (VLIW) microprocessor, processor implementing other instruction sets, or processors implementing a combination of instruction sets. Processor 402 may also be one or more special-purpose processors such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), network processor, or the like. Processor 502 is configured to execute the processing logic (instructions 522) for performing the operations and steps of the methods discussed herein.

[104] The processing system 500 may further include a network interface device 508. The processing system 500 also may include a video display unit 510 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device 512 (e.g., a keyboard or touchscreen), a cursor control device 514 (e.g., a mouse or touchscreen), and an audio device 516 (e.g., a speaker). The display 510 allows images generated by the signal processing pipeline 10 of FIG. 2 to be presented to a user. That is, the various images of FIGS. 3(a) to 3(e) may be presented to a user on the display 510. Further, the input device 512 allows a user to set parameters such as the slow-time window length with respect to the short-time matched filter 14, the Doppler cut-off velocity, the clutter filtering range and the number of iterations N with respect to FIG. 6 and the number of bins N with respect to the coherent integration 20. That is, any outputs along the signal processing pipeline 10 may be presented to the user through the display 510 and any user settable inputs that have been described herein may be entered through the input device 512. The display 510 and the input device 512 have been collectively referred to in the foregoing as a user interface.

[105] It will be apparent that some features of the processing system 500 shown in Figure 5 may be absent. For example, the processing system 500 may have no need for display device 510 (or any associated adapters). This may be the case, for example, for particular server-side computer apparatuses which are used only for their processing capabilities and do not need to display information to users. Similarly, user input device 512 may not be required. In its simplest form, processing system 500 comprises processor 502 and main memory 504.

[106] The data storage device 518 may include one or more machine-readable storage media (or more specifically one or more non-transitory computer-readable storage media) 528 on which is stored one or more sets of instructions 522 embodying any one or more of the methodologies or functions described herein. The instructions 522 may also reside, completely or at least partially, within the main memory 504 and/or within the processor 502 during execution thereof by the processing system 500, the main memory 504 and the processor 502 also constituting computer-readable storage media 528. [107] The various methods described above may be implemented by a computer program. The computer program may include computer code arranged to instruct a computer to perform the functions of one or more of the various methods described above. The computer program and/or the code for performing such methods may be provided to an apparatus, such as a computer, on one or more computer readable media or, more generally, a computer program product. The computer readable media may be transitory or non-transitory. The one or more computer readable media could be, for example, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, or a propagation medium for data transmission, for example for downloading the code over the Internet. Alternatively, the one or more computer readable media could take the form of one or more physical computer readable media such as semiconductor or solid-state memory, magnetic tape, a removable computer diskette, a random-access memory (RAM), a read-only memory (ROM), a rigid magnetic disc, and an optical disk, such as a CD-ROM, CD-R/W or DVD.

[108] The computer program is executable by the processor 502 to perform functions of the systems and methods described herein.

[109] In an implementation, the modules, components, and other features described herein can be implemented as discrete components or integrated in the functionality of hardware components such as ASICS, FPGAs, DSPs, or similar devices.

[110] A “hardware component” is a tangible (e.g., non-transitory) physical component (e.g., a set of one or more processors) capable of performing certain operations and may be configured or arranged in a certain physical manner. A hardware component may include dedicated circuitry or logic that is permanently configured to perform certain operations. A hardware component may be or include a special-purpose processor, such as a field programmable gate array (FPGA) or an ASIC. A hardware component may also include programmable logic or circuitry that is temporarily configured by software to perform certain operations.

[111] Accordingly, the phrase “hardware component” should be understood to encompass a tangible entity that may be physically constructed, permanently configured (e.g., hardwired), or temporarily configured (e.g., programmed) to operate in a certain manner or to perform certain operations described herein.

[112] In addition, the modules and components can be implemented as firmware or functional circuitry within hardware devices. Further, the modules and components can be implemented in any combination of hardware devices and software components, or only in software (e.g., code stored or otherwise embodied in a machine-readable medium or in a transmission medium).

[113] Unless specifically stated otherwise, as apparent from the following discussion, it is appreciated that throughout the description, discussions utilizing terms such as "receiving”, “determining”, “comparing”, “enabling”, “maintaining,” “identifying,”, “receiving”, “providing” or the like, refer to the actions and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices.

[114] The preceding detailed description is merely exemplary in nature and is not intended to limit the disclosure and its uses. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, overview, or the detailed description.

[115] Examples of the present disclosure may be described herein in terms of functional and/or logical block components and various processing steps. It should be appreciated that such block components may be realised by any number of hardware, software, and/or firmware components configured to perform the specified functions. For example, an example of the present disclosure may employ various integrated circuit components, e.g., memory elements, digital signal processing elements, logic elements, look-up tables, or the like, which may carry out a variety of functions under the control of one or more microprocessors or other control devices. In addition, those skilled in the art will appreciate that examples of the present disclosure may be practised in conjunction with any number of systems, and that the systems described herein are merely exemplary implementations of the present disclosure.

[116] For the sake of brevity, conventional techniques compared to signal processing, data transmission, signalling, control and other functional aspects of the systems (and the individual operating components of the systems) may not be described in detail herein. Furthermore, the connecting lines shown in the various figures contained herein are intended to represent example functional relationships and/or physical couplings between the various elements. It should be noted that many alternative or additional functional relationships or physical connection may be present in an example of the present disclosure.

[117] The term “apparatus” as used herein may refer to either a single apparatus or plural apparatus and should not be understood as being particularly limited to either a single discrete apparatus or a plurality of discrete apparatus unless a particular apparatus is further described as such.

[118] Those skilled in the art will recognise that a wide variety of modifications, alterations, and combinations can be made with respect to the above-described examples without departing from the scope of the disclosed concepts, and that such modifications, alterations, and combinations are to be viewed as being within the ambit of the disclosed concepts.

[119] Those skilled in the art will also recognise that the scope of the invention is not limited by the examples described herein but is instead defined by the appended claims.

Claims

1. A method of clutter filtering a receive signal using a sonar system, the method comprising: generating a transmit signal using the sonar system; measuring the receive signal using the sonar system; determining transmit windows of the transmit signal based on a desired velocity representing estimated velocity of objects of interest for clutter filtering; determining receive windows of the receive signal based on a desired range representing estimated range of objects of interest for clutter filtering; performing temporal cross correlation of each transmit window of the transmit signal with a corresponding receive window of the receive signal to identify correlation peaks; temporally shifting and scaling the transmit windows based on the correlation peaks to provide modelled clutter; and subtracting the modelled clutter from the receive signal.

2. The method of claim 1 , comprising: receiving a doppler cut-off velocity and a clutter filtering range; determining a time length of the transmit windows based on the doppler cut-off velocity, wherein the transmit signal is divided into N transmit windows; determining a time length of the receive windows based on the clutter filtering range.

3. The method of claim 2, wherein the doppler cut-off velocity and the clutter filtering range are provided by user inputs through a user interface.

4. The method of claim 1 , 2 or 3, wherein the steps of performing temporal cross correlation, temporal shifting and scaling and subtracting are performed iteratively for a predetermined number of iterations or until a convergence criterion is reached.

5. The method of any preceding claim, wherein there are N temporal windows making up the transmit signal and the method includes, for n=0 to N-1 determining a start of a current transmit window based on n multiplied by the time length of the transmit windows and an end of the current transmit window based on the start of the current transmit window and the time length of the transmit windows; determining a start of a current receive window based on the start of the current transmit window and the time length of the receive windows; cross correlating the current transmit window and the current receive window to provide a correlation result; finding the correlation peak time based on the correlation result; scaling the current transmit window based on an amplitude of the correlation result; temporally shifting the scaled current transmit window based on the correlation peak time to provide the modelled clutter; and subtracting the modelled clutter from the receive signal.

6. The method of any preceding claim, wherein the transmit signal is a continuous wave signal.

7. The method of any preceding claim, wherein the transmit signal is a continuous wave pseudo random noise signal.

8. The method of any preceding claim, comprising, prior to performing temporal cross correlation, temporally shifting and scaling, and subtracting the modelled clutter from the transmit signal: performing baseband demodulation on the measured receive signal to provide baseband data; segmenting the baseband data into a fast-time versus slow-time matrix of fast and slow time windows; and applying a matched filter to each fast time window to provide slow-time versus range data.

9. The method of claim 8, comprising applying coherent integration to the output of the clutter filter using a Radon Fourier Transform to obtain range and velocity data for moving targets.

10. The method of claim 9, wherein the applying coherent integration comprises: assuming a velocity from a predetermined set of potential velocities, an initial range and an initial slow-time, wherein the initial range corresponds to an initial range bin and the slow-time corresponds to an initial slow-time bin; selecting N slow-time bins of the matrix of slow-time bins and fast-time bins including the initial range bin based on the velocity; coherent integrating over the N slow-time bins; repeating the assuming, selecting and integrating steps over all combinations of range bins, slow-time bins and potential velocities to determine an integration response; and determining the range data and the velocity data for the moving target based on the integration response.

11 . The method of claim 9 or 10, comprising generating the range data and velocity data in the form of a matrix including velocity and range bins.

12. The method of any preceding claim, comprising generating a range time image on a user interface based on the receive signal and receiving a desired velocity and a desired range from a user that has been estimated based on the time range image.

13. The method of claim 12, comprising generating a time range image on the user interface based on a decluttered receive signal that is determined by subtracting the modelled clutter from the receive signal, receiving a second, different, desired velocity and a second, different, desired range from a user that has been estimated based on the time range image and repeating the steps of determining transmit windows, determining receive windows, performing temporal correlation, temporally shifting and scaling, and subtracting the modelled clutter.

14. A sonar system comprising: one or more processors; one or more memories having stored thereon computer readable instructions configured to cause the one or more processors to perform operations comprising the method of any of the preceding claims.

15. One or more computer readable media comprising instructions, that, when executed by a processor, cause the processor to perform operations comprising the method of any of claims 1 to 13.