CN1299123C - Parameter estimation method for modelling noise Doppler of airborne radar - Google Patents

Abstract

The invention discloses a modeled clutter Doppler parameter estimation method for airborne radar. The clutter model provided by the present invention is the Doppler distributed clutter model (DDC), and the clutter covariance matrix described by the model consists of Doppler center f _c , Doppler spectral width expansion coefficient ρ _f , clutter fluctuation The parameter σ _c ² and the noise fluctuation parameter σ _v ² are four parameters to be determined analytically. The parameter estimation of the clutter includes: 1) The airborne radar transmits the pulse signal and collects the echo data; 2) The interference covariance matrix of the sample is formed by the clutter data in the collected signal; 3) According to the interference covariance matrix of the sample Joint estimation of unknown parameters in DDC clutter models. The DDC model of the present invention simultaneously characterizes the change of Doppler center and spectral width of airborne radar clutter. Moreover, the joint parameter estimation method of the present invention can break through the Rayleigh limit and overcome the error propagation effect of sequential estimation, so its performance is better than the existing airborne radar clutter Doppler parameter estimation method.

Description

A Modeled Clutter Doppler Parameter Estimation Method for Airborne Radar

technical field

The present invention relates to radar, and more specifically, the present invention relates to a method for estimating clutter Doppler parameters of airborne radar.

Background technique

Airborne radar has excellent characteristics such as all-day, all-weather, and penetrating, and has a wide range of applications in civil and military fields such as navigation, surveying and mapping, reconnaissance, warning, and fire control. However, there are many unresolved technical problems in airborne radar signal processing, and many of them can be attributed to the clutter Doppler parameters (such as Doppler center, Doppler spectral width and Doppler Tuning frequency, etc.) estimation problem.

For example, in the moving target detection of airborne radar, the received signal usually includes target signal, clutter signal and noise signal. Since the airborne radar is usually in the downward-looking mode, the ground clutter is widely distributed and strong, especially in urban and mountainous areas, where the clutter intensity can reach 60-90dB; on the other hand, the platform movement causes the clutter Doppler spectral width f _B It is greatly expanded, causing the target to be submerged in the clutter, and the detection ability of the radar target is seriously affected (see literature [1]: DCSchleher, "MTI and pulsed Doppler radar", Artech House Inc., London, 1991). Therefore, airborne radar needs to adaptively estimate the distribution of clutter spectrum (including estimating parameters such as Doppler spectral width f _B , Doppler center f _c ) to distinguish and suppress clutter, so as to improve target detection performance.

Another example, in the high-resolution imaging of airborne synthetic aperture radar (SAR), it is necessary to accurately measure the attitude and motion parameters of the platform to achieve motion compensation for imaging (see literature [2]: JCCurlander, RNMcDonough.Synthetic Aperture Radar: System & Signal processing, John Wiley & Sons, New York, 1991). However, the current measurement equipment (such as inertial navigation, etc.) cannot meet the requirements of measurement accuracy due to hardware limitations. Therefore, it is necessary to extract relevant Doppler parameters (such as Doppler center f _c and Doppler modulation frequency) by analyzing the actually collected data (that is, clutter data) in order to realize accurate estimation and analysis of platform attitude and motion parameters. Inversion, and finally obtain a satisfactory imaging effect.

In the prior art, the estimation of the Doppler parameters of the clutter usually adopts the fast Fourier transform (FFT), and the power spectrum of the clutter is modeled in the frequency domain and the Doppler parameters are extracted (see literature [1]) . However, the spectral resolution of such methods is limited by the Rayleigh limit, ie, the resolution is larger than the inverse of the coherent processing interval (CPI). When pulse sampling is limited, this limitation will inevitably affect the accuracy of parameter estimation. In addition, its estimation of Doppler parameters generally adopts sequential estimation, for example, its estimation of f _B and Doppler frequency is based on f _c estimation, so the error of f _c parameter estimation is inevitably transmitted to Subsequent parameter estimation.

In a word, the accurate modeling and parameter estimation of clutter, as a core part of various engineering applications of airborne radar, has attracted extensive attention and research. In view of the deficiencies of the traditional methods, a new method for estimating Doppler parameters with higher precision is required.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the Doppler parameter estimation method in the prior art, and accurately describe the statistical characteristics of clutter by providing a clutter model that includes prior knowledge of clutter, thereby providing an airborne radar A modeled clutter Doppler parameter estimation method realizes accurate estimation of clutter Doppler parameters.

In order to achieve the above-mentioned purpose of the invention, a method for estimating a modeled clutter Doppler parameter of an airborne radar provided by the present invention comprises the following steps:

(1) set up clutter model in the signal processing system of airborne radar, described clutter model refers to the interference covariance matrix of clutter and noise:

${<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="c"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">c</figure-callout></span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; B</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; ;</span>$

where [R] _m,n is the (m,n)th element of the interference covariance matrix, M is the number of pulses in a coherent processing interval, σ _c ² is the clutter fluctuation parameter, σ _v ² is the noise fluctuation parameter , δ _mn is the Delta function, f is the Doppler frequency, α _l is the elevation angle of the clutter ring, Δ is the radar pulse repetition interval, f _max =2V/λ, f _min =-2V/λ, V is the carrier , λ is the wavelength of the radar carrier frequency; B ² (f, α _l ) is the two-way power pattern of the radar beam, including two undetermined parameters of the Doppler center f _c and the Doppler spectral width expansion coefficient ρ _f .

This clutter model may be referred to as a Doppler distributed clutter (DDC) model.

When B ² (f, α _l ) is a Gaussian bidirectional power pattern, the clutter model (DDC) can be simplified as:

${<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; .</span>$

The clutter model includes four undetermined parameters of Doppler center f _c , Doppler spectral width expansion coefficient ρ _f , clutter fluctuation parameter σ _c ² and noise fluctuation parameter σ _v ² . There is a simple linear relationship between the Doppler spectral width expansion coefficient ρ _f and the clutter Doppler spectral width f _B , and the specific form is related to the shape of the beam. When B ² (f, α _l ) is a Gaussian bidirectional power pattern, there is ${\mathrm{\&rho;}}_f=\frac{{2f}_B}{2.355}$ is established, so the estimate of f _B can be directly obtained through the estimated ρ _f .

(2) The airborne radar transmits pulse signals to the detection area through the transmitter and antenna system;

(3) The airborne radar receives the backscatter signal of the detection area through the antenna system and the receiver, and the backscatter signal includes target echo, clutter signal and system noise;

(4) The airborne radar sends the received signal to the signal processing system after frequency mixing and A/D conversion, and the signal processing system forms the interference covariance matrix of the sample with the digitized received signal;

(5) The signal processing system jointly estimates the unknown parameters [f _c , ρ _f , σ _c ² , σ _v ² ] through the interference covariance matrix of the sample and the analytical expression of the interference covariance matrix described in step (1).

Wherein, the method used to estimate the unknown parameters in step (5) is the maximum likelihood method, and the maximum likelihood method is the Newton search method. The method used for estimating unknown parameters in step (5) is a pseudo-subspace decomposition method, and the pseudo-subspace decomposition method includes distributed signal parameter estimator (DSPE), extended signal parameterized estimation (DISPARE), weighted subspace matching ( WSF). The method used to estimate the unknown parameters in step (5) is an approximation method based on the covariance matrix, and the approximation method based on the covariance matrix includes the extended rotation-invariant signal parameter estimation method (S-ESPRIT), the general rotation-invariant Variable signal parameter estimation method (G-ESPRIT).

The advantages of the present invention are:

1) The DDC model can describe the changes of the clutter Doppler spectral center and spectral width at the same time, and is especially suitable for describing the clutter Doppler broadening and spectral center shift caused by the movement of the airborne radar platform.

2) The existing clutter model focuses on describing the spectral characteristics in the frequency domain, while the DDC model describes the covariance matrix properties in the clutter time domain, so the sample covariance matrix can be directly obtained through the sample, thus avoiding the transformation domain processing .

3) The Doppler parameter estimation based on the DDC model usually adopts the time-domain joint estimation method based on covariance matrix analysis, which can break through the Rayleigh limit, so the performance is better than the traditional sequential estimation method.

4) Since the DDC model itself contains prior knowledge of the statistical characteristics of clutter, it can obtain higher-precision parameter estimation with a small number of samples.

Description of drawings

Figure 1 is a schematic structural diagram of an airborne radar;

Fig. 2 is a working diagram of a single-channel airborne radar system;

Fig. 3 is the flowchart of the modeled clutter Doppler parameter estimation method of the airborne radar of the present invention;

Figure 4(a) is the estimation performance comparison of Doppler angle frequency center parameters under different CNR conditions;

Figure 4(b) is the estimation performance comparison of Doppler angle frequency extension parameters under different CNR conditions;

Figure 5(a) is the estimation performance comparison of Doppler angular frequency center parameters under different angular spread conditions;

Fig. 5(b) is the estimation performance comparison of Doppler angular frequency extension parameters under different angular extension conditions;

Fig. 6(a) is the estimation performance comparison of Doppler angular frequency center parameter under different pulse number conditions;

Fig. 6(b) is the estimation performance comparison of Doppler angle frequency extension parameters under different pulse number conditions;

Figure 7 is the imaging result of the airborne radar measured data.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 shows a schematic structural diagram of a conventional airborne radar, which is mainly composed of a transceiver system 1, a signal processing system 2, and a terminal display system. The transceiver system is composed of transmitter, receiver and antenna system. The transmitter modulates a specific form of pulse signal onto a radio frequency carrier and transmits it into space through an antenna system. After the transmitted signal is reflected by the targets and ground objects in the detection area, the backscattered signal is received by the airborne radar antenna system, and the RF signal is mixed by the receiver to obtain an intermediate frequency signal, and the intermediate frequency signal is then subjected to multi-stage mixing After that, it is transformed into a signal suitable for acquisition, and then sent to the subsequent signal processing system.

The A/D converter of the signal processing system converts the analog received signal into a digital signal, and then the digital signal is processed by multiple DSP processing boards to realize various functions such as target detection, parameter estimation, and imaging recognition.

The terminal display system displays the processing results dynamically, interactively and intuitively through secondary processing (data processing), various forms of displays, and man-machine interfaces.

Figure 2 shows the working diagram of the airborne radar. The airborne radar usually adopts the pulse-Doppler system, that is, the detection or imaging of the target is realized by continuously transmitting and receiving coherent pulse signals. Among them, the Doppler signal of the airborne radar clutter is related to many factors such as the position of the clutter source, the moving speed of the platform, and the radar beam. Here  is the azimuth; u() represents the clutter unit corresponding to , V is the speed of the carrier aircraft; f _p and Δ=1/f _p represent the radar repetition frequency (PRF) and radar repetition interval (PRT) respectively; R _l and α _l are the radar slant distance and elevation angle corresponding to the l-th range ring respectively; F(, α _l ) is the bidirectional voltage pattern of the radar antenna.

In order to estimate the Doppler parameters of the clutter signals collected by the airborne radar, the modeled clutter Doppler parameter estimation method of the airborne radar provided by the present invention can be used, and the flow chart of the method is shown in FIG. 3 . The basis of the method of the present invention is to provide a Doppler distributed clutter model (DDC). Therefore, the DDC model of the airborne radar is first given through theoretical derivation here. Before deriving the DDC model, the following two assumptions are given:

1) Within a CPI (coherent processing interval), the relative geometric relationship between the radar and the clutter source remains unchanged, that is, the moving distance of the carrier aircraft is much smaller than the slant distance between the radar and the clutter;

2) The loader moves in a straight line at a uniform speed;

These two assumptions are generally established, and can be better satisfied by shortening the CPI in practical applications. Based on the above assumptions, the mth pulse sampling of the interference signal (clutter plus noise) received by the radar can be expressed in the following integral form

Among them, τ _m = (m-1)Δ, s _ (t) represents the scattering signal of clutter unit u(), and can be regarded as an independent random process; Represents the noise sampling of m pulses, M is the number of pulses in a coherent processing interval, they are usually Gaussian white noise in the time domain, and their cross-correlation E[v _m (t)v _n (t)]=σ _v ² δ _mn . Let the normalized Doppler angular frequency

Substitute it into (1) to get

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Here, s _f (t) represents the time-varying scattering signal caused by internal fluctuations of the scattering points in the clutter unit u([phi]). When the clutter is uniform in azimuth and its internal motion is negligible, there is s _f (t)=s _f , that is, the scattering function of the clutter unit degenerates into an independent and identically distributed (iid) random variable, and $\mathrm{E.}\left({\mathrm{the\; s}}_f{\mathrm{the\; s}}_{f\&prime;}\right)={{\widetilde{\mathrm{\&sigma;}}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">c</figure-callout>}}}^2{\mathrm{\&delta;}}_{{\mathrm{ff}}^{\&prime;}}.$ So far, the sampling vector of the interference is as follows

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Here x=[x ₁ (t), x ₂ (t), . . . , x _M (t)] ^T , v=[v ₁ (t), . . . , vM ₍ t)] ^T , a(f)= [1, e ^j2πfΔ , ..., e ^j2πf(M-1)Δ ] ^T . Then the (m, n)th element of the interference covariance matrix R=E(xx ^H ) can be expressed as

${<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="c"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">c</figure-callout></span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; B</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="v"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">v</figure-callout></span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, the above formula is the generalized DDC model of airborne radar clutter, and the "generalized" here means that the specific expressions of the covariance elements given by the above formula can vary according to the difference of B ² (f, α _l ). expression. A special case when B ² (f, α _l ) is Gaussian is given below. Assume that the airborne radar has a Gaussian bi-directional power pattern, namely

(其中指方位角，_c是波束的方位指向，ρ_是波束的扩展系数，α_l是距离环对应的高低角)，这在实际的单通道机载雷达中通常是满足的。可以证明当ρ_→0和_c→π/2，有下式成立

(where  refers to the azimuth angle,  _c is the azimuth pointing of the beam, ρ _ is the expansion coefficient of the beam, and α _l is the height angle corresponding to the range ring), which is usually satisfied in the actual single-channel airborne radar. It can be proved that when ρ _ →0 and  _c →π/2, the following formula holds

${\mathrm{<span\; class="notranslate">\; B</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">d</figure-callout></span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

here d is a constant determined by known parameters. (6) Explanation: In the case of narrow beam and small squint, the clutter Doppler spectrum of the airborne radar with Gaussian pattern is also Gaussian.

Substituting formula (6) into formula (5), using the property of Fourier transform, we have

${<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="v"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">v</figure-callout></span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in ${{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">c</figure-callout>}}}^2=d{{\widetilde{\mathrm{\&sigma;}}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">c</figure-callout>}}}^2.$ So far, the airborne radar clutter Gaussian DDC model is obtained as shown in (7).

Referring to Figure 3 again, the clutter Doppler parameters can be estimated according to the obtained DDC model, including the following steps:

(1) The airborne radar transmits pulse signals to the detection area through the transmitter and antenna system;

(2) The airborne radar receives the backscatter signal by the detection area through the antenna system and the receiver, and the described backscatter signal includes target echo, clutter signal and system noise; the airborne radar obtains independent N interference samples with the same distribution. The N interference samples form a vector X=[x(t ₁ ), . . . , x(t _N )]. In practical applications, X can be composed of sample vectors in N units near the distance unit to be processed.

(3) The received signal of the airborne radar is sent to the signal processing system after frequency mixing and A/D conversion, and the signal processing system forms the interference covariance matrix of the sample with the converted received signal, namely $\hat{R}={\mathrm{XX}}^h/N.$

(4) The signal processing system of the airborne radar jointly estimates the unknown parameters x=[f _c , ρ _f , σ _c ² , σ _v ² ] of the clutter model obtained above according to the interference covariance matrix of the samples. The present invention provides new methods for estimating three types of clutter Doppler parameters based on covariance matrix approximation, subspace analysis based on covariance matrix, and approximate model based on covariance matrix. These three types of methods can realize the unknown of DDC model Estimation of the parameter vector x, and they can achieve significantly better performance than traditional frequency domain methods for Doppler parameter estimation.

The first type of clutter Doppler parameter estimation method in the present invention is a method based on covariance matrix approximation, such as methods such as maximum likelihood estimation (ML), weighted least square matching (WLS), and the like. This manual uses the ML method (see literature [3]: T.Trump and B.Otterson.Estimation of nominal direction of arrival and angular spread using an array of sensors, Signal Processing, Vol.50, pp57～69, Apr.1996) as The implementation process is given as an example. The ML method for estimating clutter Doppler parameters needs to minimize the following negative log-likelihood function

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; log</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; tr</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Where |R| is the determinant of matrix R. The above 4-dimensional nonlinear minimization problem can be solved by a search method, for example, a Newton-type search algorithm (see literature [3]). The present invention provides the covariance matrix of the parameter estimation error vector obtained by the ML method

为估计的参数矢量，为Kronecker积。同时由(9)式得到的参数估计误差，即C_ML的对角矢量，也给出了各估计参数误差的Cramer-Rao(CRB)界。Where D=vecR ₀ /z ^T ,

is the estimated parameter vector,  is the Kronecker product. At the same time, the parameter estimation error obtained by (9), that is, the diagonal vector of C _ML , also gives the Cramer-Rao (CRB) bound of each estimated parameter error.

The second type of clutter Doppler parameter estimation method of the present invention is the method based on the subspace analysis of covariance matrix, as distributed signal parameter estimator (DSPE) (referring to literature [4]: S.Valaee, B.Champagne, P. Kabal, "Parametric localization of distributed sources," IEEE Tans.Signal Processing, vol.43, no.9, pp2144-2153, 1995), extended signal parameterization estimation (DISPARE) (see literature [5]: Y.Meng, P. Stoica, and K.M. Wong, "Estimation of the directions of arrival of spatially dispersed signals in array processing," Proc. Inst. Elect. Eng., Radar, Sonar, Navigat., vol.143, pp.1-9, Feb. .1996), Weighted Subspace Fitting (WSF) (see literature [6]: Bengtsson M, Ottersten B, "AGeneralization of Weighted Subspace Fitting to Full-Rank Models," IEEE Trans.SignalProcessing, vol.49, no.5, pp1002-1012, 2001) and other pseudo-subspace algorithms. This description takes the WSF method as an example to give its implementation process. First, decompose the singular value of the covariance matrix R into the following signal subspace and noise subspace

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

And the identifiable condition of DDC model parameter estimation is established, that is, the sufficient and necessary condition for the establishment of x=x ₀ is

span[U _s (x)]=span[U _s (x ₀ )] (11)

The distribution source parameter estimation using pseudo-signal subspace estimation and pseudo-subspace matching methods are respectively

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Where ‖‖ is the undetermined matrix norm. It can be seen that the unknown parameter vector x can be obtained by searching the criteria determined by (12) or (13). According to the identifiable conditions of parameter estimation of DDC model, when N is large enough, the estimates obtained from (12) and (13) are consistent estimates. Considering the weighted quadratic norm, the two algorithms are asymptotically equivalent, that is, corresponding to each weighted norm in formula (12), there is another weighted norm in formula (13), so that the parameters obtained by the two estimates have the same large-sample distribution, and vice versa. The covariance matrix of the parameter estimation error vector obtained by the WSF method is given here as

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; WSF</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

The third type of clutter Doppler parameter estimation method of the present invention is the approximation method based on the covariance matrix proposed for the application of small angle spread ρ _f , including S-ESPRIT (extended rotation-invariant signal parameter estimation method) (see literature [ 7]: Shahbazpanahi S, Valaee S, Bastani M, "Distributed source localization using ESPRIT algorithm," IEEE Trans.Signal Processing, vol.49, no.10, pp 2169-2178, 2001), G-ESPRIT (general rotation without variable signal parameter estimation method) (see literature [8]: J S Jeong, KSakaguchi, "Generalization of MUSIC Using Extended Array Mode Vector for JointEstimation of Instantaneous DOA and Angular Spread," IEICE Trans.Commun., E84-B, no.7 , pp1781-1789, 2001) and other low-complexity methods. Here, take S-ESPRIT as an example to give its realization process. According to the expression of the covariance matrix given by (5), it can be seen that under the condition of small angular expansion ρ _f , there are only a small number of large eigenvalues in the eigenvalue distribution of the covariance matrix. Therefore, through the second-order Taylor series expansion and first-order approximation of the perturbation component near the Doppler angular frequency center, it can be obtained that R _c ≈ AA ^H /2, where the matrix A=[a(f ₁ )a(f ₂ )]=[a( _fc - _σf )a( _fc + _σf )]. The effective rank of the signal covariance matrix is 2, and the clutter signal can be approximated as the superposition of two point signals whose Doppler frequencies are f ₁ and f ₂ respectively. Therefore, by

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Estimates of f _c and ρ _f are obtained. The S-ESPRIT method uses the characteristic that the rank of R _c is approximately 2 to decompose R _c into eigenvalues, namely

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&ap;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

Among them, the two column vectors of the matrix U _s of order M×2 are the eigenvectors corresponding to the two largest eigenvalues of R _c , and the diagonal elements of the diagonal matrix ∑s are the two largest eigenvalues of R _c , namely is an estimate of _f1 and _f2 .

So far, the present invention has obtained a DDC model and a new method for estimating three types of clutter Doppler parameters based on the DDC model. In order to verify the effectiveness of the new model and new method, the X-band airborne synthetic aperture radar (SAR) developed by China Electronics Technology Group East China Electronic Engineering Research Institute (ECRIEE) is used as a prototype to design a simulated airborne radar with parameters as shown in the table 1. In order to increase the Doppler dynamic range of detectable targets, this paper increases the PRF of the prototype from 700Hz to 2000Hz. The radar is set to work in the side-looking mode, that is, _fc fluctuates around 0; the number of pulses in the CPI is M=32. The main beam of the clutter corresponds to the clutter bandwidth f _B =2vβ/λ≈167.5Hz. From formula (6), it can be seen that the parameter ρ _f of the Gaussian DDC model corresponding to the radar clutter is ≈142.5Hz. In the following, the performance of various methods is compared from two aspects of simulation and measured data. In the following, the angular frequencies θ _c and ρ _θ of f _c and ρ _f are used as indicators for comparison.

Table 1 Airborne Radar System Parameters System parameters parameter value Flight Altitude Azimuth Beam Width Carrier Wavelength Signal Bandwidth Pulse Repetition Frequency Aircraft Velocity h=3000mβ=1.5°λ=0.03125mB=70MHzPRF=700/2000Hzv=100m/s

1) Simulation performance analysis

According to the set radar parameters, 500 Monte Carlo experiments of DDC parameter estimation are carried out using the three methods introduced above. _Figure 4(a) and Figure 4(b) show _the root mean square error ( RMSE). here $\mathrm{CNR}=10\log ({\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C0316005200141.png"\; state="\{\{state\}\}">c</figure-callout>}}^2/{\mathrm{\&sigma;}}_{\mathrm{no}}^2).$ It can be seen that 1) when the CNR is large, the performance of WSF is very close to ML; 2) due to the limitation of the Rayleigh limit based on the FFT method, there is a fixed deviation in the estimation of θ _c , that is, it is not consistent with the CNR. Figure 5(a) and Figure 5(b) show the RMSE of DDC parameter estimation obtained by the above three methods under the condition of signal-to-noise ratio CNR=35dB and different angular extension numbers. It can be seen that the errors of the three methods are proportional to the angular spread. Figure 6(a) and Figure 6(b) show the results obtained by the three methods under different pulse numbers. It can be seen that the errors of the three methods are inversely proportional to the number of pulses. All in all, it can be seen from Figures 4 to 6 that the performance of the ML and WSF methods based on the DDC model significantly exceeds the traditional FFT-based method.

2) Verification of measured data

Figure 7 is the imaging result of some data collected by the ECRIEE-SAR system on the Yellow River channel area in the first half of 2001. The image has been processed by four-view, and the resolution is about 3m×3m. The corresponding area is about 3 kilometers (longitudinal) × 10 kilometers (horizontal), in which the vertical direction of the image is the flight direction of the platform, and the horizontal direction is the radar slant range direction. The imaging scene contains rich types of ground objects. The left part of the image is the Yellow River, and the right part is mountains and plateaus. Area 1 (area1) and area 2 (area2) correspond to the water surface and the plateau flat area respectively, and the actual data from these two areas are respectively analyzed by the WSF method based on the DDC model provided by the present invention and the existing FFT-based method. The Doppler parameters were estimated for the data. Table 2 shows the Doppler parameter estimation results of the two methods. The values in the table are obtained by the two methods for the 100 adjacent distance cells in area 1 and area 2. statistical results. It can be seen from Table 2 that since the WSF algorithm is a super-resolution two-dimensional joint estimation, its estimated standard deviation (STD) is significantly smaller than that of the frequency domain method. Simultaneously Table 2 also illustrates that the model and method of the present invention are correct.

Table 2 Estimation results of Doppler parameters Estimated results in Region 1 (Hz) Estimated results in Region 2 (Hz) f _dc mean (FFT) 358.7 f _dc mean (WSF) 358.1 f _dc mean (FFT) 361.2 f _dc mean (WSF) 359.6 f _dc standard deviation (FFT) 5.7 f _dc standard deviation (WSF) 2.7 f _dc standard deviation (FFT) 6.3 f _dc standard deviation (WSF) 3.2 f _B mean (FFT) 171.0 f _B mean (WSF) 168.6 f _B mean (FFT) 173.6 f _B mean (WSF) 169.5 f _B standard deviation (FFT) 6.6 f _B standard deviation (WSF) 3.3 f _B standard deviation (FFT) 8.7 f _B standard deviation (WSF) 4.1

Claims (8)

1, a kind of modelling clutter Doppler parameter method of estimation of airborne radar comprises the steps:

(1) set up Clutter Model in the signal processing system of airborne radar, described Clutter Model is meant clutter and interference of noise covariance matrix:

${\left[R\right]}_{m,n=1}^M={{\mathrm{\&sigma;}}_c}^2{\&Integral;}_{f_{\min }}^{f_{\max }}{B}^2(f,{\mathrm{\&alpha;}}_l)e^{j2\mathrm{\&pi;f}(m-n)\mathrm{\&Delta;}}\mathrm{df}+{{\mathrm{\&sigma;}}_v}^2{\mathrm{\&delta;}}_{\mathrm{mn}};$

Wherein, [R] _{M, n}Be interference covariance matrix the (m, n) element, M are relevant pulse numbers in handling at interval, σ _c ²Be the clutter roughness parameter, σ _v ²Be the noise bounce parameter, δ _MnBe the Delta function, f is a Doppler frequency, α _lBe the angular altitude of clutter ring, Δ is the radar pulse recurrence interval, f _Max=2V/ λ, f _Min=-2V/ λ, V are the speed of carrier aircraft, and λ is the wavelength of radar carrier frequency; B ²(f, α _l) be the bidirectional power directional diagram of radar beam, comprise Doppler center f _cWith Doppler's spectrum width spreading coefficient ρ _fTwo parameters undetermined;

Described Clutter Model comprises Doppler center f _c, Doppler's spectrum width spreading coefficient ρ _f, clutter roughness parameter σ _c ²With noise bounce parameter σ _v ²Four undetermined parameters;

(2) airborne radar by transmitter and antenna system to search coverage transponder pulse signal;

(3) airborne radar receives backscatter signal by search coverage by antenna system and receiver, and described backscatter signal comprises target echo, noise signal and system noise;

(4) airborne radar is sent into signal processing system with received signal after mixing and A/D conversion, and signal processing system constitutes digitized received signal the interference covariance matrix of sample;

(5) signal processing system is united estimation unknown parameter [f by the interference covariance matrix of sample and the analytical expression of the interference covariance matrix described in the step (1) _c, ρ _f, σ _c ², σ _v ²].

2, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 1 is characterized in that, works as B ²(f, α _l) when being Gaussian bidirectional power directional diagram, described interference covariance matrix is reduced to:

${\left[R\right]}_{m,n=1}^M={\mathrm{\&sigma;}}_c^2{e}^{j2\mathrm{\&pi;}{f}_c\mathrm{\&Delta;}}{e}^{(-\frac{{\left(2\mathrm{\&pi;}(m-n){\mathrm{\&rho;}}_f\mathrm{\&Delta;}\right)}^2}{2})}+{{\mathrm{\&sigma;}}_v}^2{\mathrm{\&delta;}}_{\mathrm{mn}}.$

3, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 1 is characterized in that, estimates in the step (5) that the method that unknown parameter adopts is a maximum likelihood method.

4, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 3 is characterized in that described maximum likelihood method is newton's search procedure.

5, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 1 is characterized in that, estimates in the step (5) that the method that unknown parameter adopts is pseudo-Subspace Decomposition method.

6, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 5, it is characterized in that described pseudo-Subspace Decomposition method comprises that distribution signal parameter estimation, spread signal parametrization estimate, add weight subspace and mate three class methods.

7, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 1 is characterized in that, the method for estimating the unknown parameter employing in the step (5) is the approximation method based on covariance matrix.

8, the modelling clutter Doppler parameter method of estimation of airborne radar according to claim 7, it is characterized in that described approximation method based on covariance matrix comprises the invariable rotary signal parameter estimation technique of expansion, the general invariable rotary signal parameter estimation technique two class methods.

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