CN1318855C - Optimal weighted value estimation method for optimum processing in airborne radar target detection - Google Patents

Abstract

The invention discloses an optimal weight estimation method for optimal processing in airborne radar target detection. Unknown Doppler parameters; (2) Obtain the Doppler distributed clutter model with definite parameters, and obtain the clutter covariance matrix R at the same time; (3) Obtain the optimal weight vector w _opt according to the clutter covariance matrix R . The invention converts the calculation problem of the optimal weight value into the parameter estimation problem of the DDC model, thereby utilizing the prior knowledge of the model, and significantly reducing the requirement of the optimal processing on the number of independent and identically distributed (iid) samples. In the step (1) of the present invention, a low-complexity non-linear energy operator is used to realize the estimation of the above parameters, and the theoretical analysis and simulation experiments show that the new method significantly reduces the requirement of iid sample numbers, and has the advantages of small amount of computation, easy realized advantages.

Description

An Optimal Weight Estimation Method for Optimal Processing in Airborne Radar Target Detection

technical field

The present invention relates to the radar field, and more specifically, the present invention relates to an optimal weight estimation method for optimal processing in airborne radar target detection.

Background technique

Airborne radar is carried by moving platforms such as early warning aircraft, reconnaissance aircraft or helicopters, which can effectively detect, track and image moving targets on the ground, low altitude or ultra-low altitude, and it also has all-weather, all-weather, penetrability, etc. It is widely used in civil and military fields such as navigation, surveying and mapping, reconnaissance, security, and fire control.

Airborne radar needs to suppress clutter as much as possible during the signal processing process of target detection. However, airborne radars often work in the downward-looking mode, and the ground clutter has a wide distribution range and high intensity. Especially in some cities and mountainous areas, the clutter intensity can reach 60-90dB; at the same time, due to the movement of the carrier aircraft, the clutter spectrum is significantly expanded, causing the target to be submerged in the clutter, which seriously affects the detection ability of the target (D.C.Schleher, "MTI and pulsed Doppler radar," Artech House Inc., London, 1991). The Adaptive Implemented Optimal Processing (AIOP) method based on the maximum output signal-to-interference ratio criterion can greatly suppress the clutter and significantly improve the detection performance of the target (Farina, F.A. Studer. "Application of Scram-Schmidt algorithm to optimal radar signal processing," IEE Proceeding-F, vol.134, no.2, pp139-145, 1984), and is widely used in the detection of many radars.

Here the concept of Adaptive Implementation of Airborne Radar Optimal Processing (AIOP) is given first. For radar target detection, the broadening of the clutter spectrum caused by the movement of the airborne radar platform is equivalent to broadband interference. Therefore, it is necessary to weight and sum each delayed pulse to compensate the effect of platform movement and achieve the best suppression of the interference environment. When airborne radar is actually working, due to the influence of platform motion and non-uniform background, the statistical characteristics of clutter are changing. In order to obtain the maximum improvement factor (IF), it is necessary to adaptively give a certain weight to the pulse sampling within a CPI (coherent processing interval), so as to track the change of the transient statistical characteristics of the clutter. As shown in Figure 1, x(t)=[x ₁ , x ₂ ,...,x _M ]T represents the M pulse samples of the airborne radar in one CPI, using the optimal weight vector w={ω _i }, i=1, 2, ... M, perform adaptive optimal processing on M pulse samples respectively, and finally output the processing results. This process of obtaining the optimal weight vector is also referred to as Adaptive Implemented Optimal Processing (AIOP). The weight vector of AIOP can be obtained from the optimal detection theory

w _opt =μR ^-1 s (1)

In the formula, R=E[xx ^H ] is the covariance matrix formed by the interference data vector, μ is a constant, and the known target signal vector s=a(f _r )=[1, e ^j2πfsΔ ,..., e ^{j2πft(M-1)Δ} ] ^T . In this way, the follow-up detector of AIOP can be described as

$\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; opt</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; ></span>\\ <span\; class="notranslate">\; <</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array},{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

That is to compare the output of AIOP with a set threshold. When the output value of AIOP is greater than the threshold, it is judged that there is a target, otherwise, there is no target. The judgment threshold is usually determined according to the constant false alarm criterion.

From the above description, we can see that in the AIOP process, the most critical part is how to obtain the optimal weight. Obviously, AIOP needs to estimate and invert the M×M clutter covariance matrix R in order to obtain adaptive weights. In the prior art, R generally needs to be estimated from L independent and identically distributed (i.i.d) interference samples. In practical applications, the sample covariance matrix is usually constructed using the data in L units near the distance unit to be detected as the estimate of R, where the maximum likelihood estimation (ML) of R

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In order that the loss of AIOP performance does not exceed 3dB, L≥2M is required. Therefore, it can be seen that when M increases, the requirement for the number of iid samples will increase significantly. In the specific implementation of AIOP, a large number of independent and identically distributed (iid) interference samples are needed to estimate the interference covariance matrix and obtain the optimal weight. However, since the airborne radar clutter environment is non-uniform and time-varying, it is difficult to satisfy the independent and identical distribution of samples. That is to say, when AIOP is implemented in an actual airborne radar, the number of iid samples is usually difficult to meet the requirements. Therefore, there is a need for a new method that can realize the estimation of the optimal weight under limited samples. in addition,The complexities estimated with R ^-1 are O[M ² ] and O[M ³ ], respectively, which increase exponentially with M. Therefore, it is required that the new method maintains an appropriate complexity.

The inventor proposed a "Doppler distributed clutter model for airborne radar" in the patent "A Modeled Clutter Doppler Parameter Estimation Method for Airborne Radar" with the Chinese patent application number "03160052.2" (DDC)", the clutter Doppler signal can be modeled by an incoherent distributed source model. Among them, the analytical expression of the covariance matrix of the Gaussian DDC model is as follows:

${<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">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;f</span>}\mathrm{<span\; class="notranslate">\; c\&Delta;</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;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><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

where M is the number of sampling points of the clutter signal, Δ is the pulse repetition interval of the radar, f _c and ρ _f are the Doppler center and Doppler spread parameters of the DDC model, and And σ _c ² and σ _v ² represent the scattering intensity of clutter and noise. The method provided by this patent can use the DDC model to obtain parameter estimates of [f _c , ρ _f , σ _c ² , σ _v ² ] in the model when the number of iid samples is small.

Contents of the invention

The purpose of the present invention is to carry out the estimation of optimal weight value by Doppler distributed clutter (DDC) model, reduce the requirement to i.i.d sample number by utilizing the prior knowledge of clutter contained in clutter model, Therefore, an optimal weight estimation method for optimal processing in airborne radar target detection is provided.

In order to achieve the above-mentioned purpose of the invention, the optimal weight estimation method for optimal processing in the airborne radar target detection of the present invention comprises the following steps:

(1) Estimate the unknown Doppler parameters in the Doppler distributed clutter model (DDC), the unknown Doppler parameters include Doppler center frequency f _c and Doppler spectral width expansion coefficient ρ _f , Scattering intensities σ _c ² and σ _v ² of clutter and noise;

For the estimation of unknown Doppler parameters, two methods can be used, one is the method of fitting sample data and model, including the following steps:

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

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

(c) 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 from the digitized received signal;

(d) The signal processing system estimates the unknown Doppler parameters in the clutter model through the interference covariance matrix of the samples and the Doppler distributed clutter model.

The unknown Doppler parameters can also be obtained directly from the sampling signal of the airborne radar, where,

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</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">\; 3</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; the\; angle</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</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">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2.355</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">\; 4</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; cos</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{<span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

x=[x ₁ , x ₂ , Λ, x _M ] ^T represents the interference sampling of M pulses in a coherent processing interval of the airborne radar, angle(*) represents the complex phase operator, Δ is the radar pulse repetition interval . In the airborne radar application with high clutter-to-noise ratio, the influence of σ _v ² can be ignored, and the effect of σ _c ² on the optimal weight can be summarized in μ, so in practical applications, only the Doppler parameter needs to be estimated to realize Calculation of optimal weights.

(2) according to the estimated Doppler parameter of step (1), obtain the Doppler distributed clutter model with definite parameter; Obtain the clutter covariance matrix R described by this model simultaneously;

(3) According to the clutter covariance matrix R, the optimal weight vector w _opt is obtained, and the optimal weight vector w _opt = μR ^-1 s, wherein R ^-1 is the inverse matrix of the clutter covariance matrix R, μ is a constant, and s is the target signal vector to be detected.

The invention converts the calculation problem of the optimal weight value into the parameter estimation problem of the DDC model, thereby utilizing the prior knowledge of the model and significantly reducing the requirement on the number of i.i.d. samples. The present invention uses a low-complexity nonlinear energy operator to realize the estimation of the above parameters. Theoretical analysis and simulation experiments show that the requirement of the new method for i.i.d. sample number is significantly reduced, and has the advantages of small calculation amount and easy implementation.

Description of drawings

Figure 1 is a functional block diagram of an airborne radar adaptive optimal processing (AIOP);

Figure 2 is a schematic structural diagram of the airborne radar;

Figure 3 is a schematic diagram of the work of the airborne radar;

Fig. 4 is the flowchart of the method provided by the present invention;

Figure 5(a) is the error comparison of R estimation using the three methods of NLOP, S-ESPRIT and ML under the same i.i.d sample number;

Figure 5(b) is the error comparison of R estimation using the three methods of NLOP, S-ESPRIT and ML under the same noise-to-noise ratio.

Figure 6 shows the improvement factor curves of three AIOP methods using NLOP, S-ESPRIT and ML.

Detailed ways

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

Fig. 2 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 receiving signal into a digital signal, and then processes the digital signal 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 3 shows the working schematic diagram of airborne radar. 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.

Fig. 4 shows the flow chart of the present invention, from which it can be seen that the present invention adopts a kind of Doppler distributed clutter (DDC) model describing clutter property in order to reduce the requirement to iid sample number, the present invention is in DDC model Based on this, a parameterized optimal processing method is proposed. Different from the existing methods, the new method converts the optimal weight calculation into the parameter estimation of the DDC model, that is, estimates the Doppler frequency center f _c and the Doppler frequency expansion coefficient ρ _f . As can be seen from Fig. 4, the method of the present invention is carried out through the following steps.

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

Step 2: The airborne radar receives the backscatter signal from the detection area through the antenna system and the receiver. The 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.

Step 3: Send the received signal of the airborne radar to the signal processing system after mixing and A/D conversion.

Step 4: The signal processing system uses the converted received signal to estimate the Doppler parameters in the clutter model. One method is to form the received signal into the interference covariance matrix of the samples, namely $\hat{R}={\mathrm{XX}}^h/N,$ The unknown Doppler parameters x=[f _c , ρ _f , σ _c ² , σ _v ² ] of the clutter model obtained above are jointly estimated according to the interference covariance matrix of the samples. The parameter estimation methods available here include methods based on covariance matrix approximation, methods based on subspace analysis of covariance matrix, and the like.

其与机载雷达及平台的运动参数有关，通过已知的参数可预估多普勒谱宽扩展系数ρ_f的范围，当ρ_f相对于脉冲重复频率较小时(如小于典型值0.2)，多普勒中心f_c和多普勒谱宽扩展系数ρ_f可以近似为2个多普勒频率分别为f₁和f₂的点信号的叠加。因此，可由The invention also provides a nonlinear energy operator (NLOP) method, which significantly reduces the computational complexity of the optimal weight. The NLOP is introduced below, and the Doppler spectral width expansion coefficient can be known from the DDC model

It is related to the motion parameters of the airborne radar and the platform. The range of the Doppler spectral width expansion coefficient ρ _f can be estimated by the known parameters. When ρ _f is relatively small relative to the pulse repetition frequency (such as less than the typical value of 0.2), The Doppler center f _c and the Doppler spectral width expansion coefficient ρ _f can be approximated as the superposition of two point signals with Doppler frequencies f ₁ and f ₂ respectively. Therefore, by

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

According to the above ideas, it is approximately extended to the sampling data of a single distance unit, and we get

Furthermore, for formula (7), using NLOP can directly get

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</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">\; 3</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; the\; angle</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</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">\; 8</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2.355</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">\; 4</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; cos</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{<span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</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">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, x=[x ₁ , x ₂ , . . . , x _M ] ^T represents the interference sampling of M pulses in the CPI, and angle(*) represents a complex phase operator. Through the closed-form solutions of (8) and (9), the estimation of the parameters of the DDC model can be obtained directly by simple operations (the complexity is O[M]). In the airborne radar application with high clutter-to-noise ratio, the influence of σ _v ² can be ignored, and the effect of σ _c ² on the optimal weight can be summarized in μ, so in practical applications, only the Doppler parameter needs to be estimated to realize Calculation of optimal weights.

Step 5: Bring the Doppler parameters of the DDC model obtained in Step 4 into the DDC model to obtain a DDC model with certain parameters, and at the same time obtain the clutter covariance matrix R described by the DDC model.

Step 6: Obtain the optimal weight vector w _opt according to the clutter covariance matrix R, and the optimal weight vector w _opt = μR ^-1 s, where R ^-1 is the inverse matrix of the clutter covariance matrix R, and μ is constant, s is the target signal vector to be detected.

The above optimal weight calculation method can reduce the requirements of AIOP on i.i.d samples to a very low level by introducing the parameterized prior information of the DDC model.

The following is a performance comparison of the three methods of NLOP, S-ESPRIT (extended rotation invariant signal parameter estimation method) and ML (maximum likelihood estimation) in terms of i.i.d sample number requirements, implementation complexity and improvement factor:

(1) i.i.d number of samples

It should be pointed out that in the above step 4, the estimation accuracy of f _c and ρ _f is related to the iid sample number. However, in the application of airborne radar with strong clutter background, using the prior knowledge of the structure of R, it is possible to complete the accurate estimation of R on a small number of or even a single range unit sampling vector, so it can significantly reduce the iid sampling volume requirements. Firstly, according to the radar parameters, a Doppler signal satisfying the Gaussian DDC model is generated, and then the three methods realize the estimation of R under the set simulation conditions under different iid sample numbers and noise-to-noise ratio (CNR) conditions (as shown in Figure 5 (a) and Figure 5(b)). Among them, the ML method uses formula (3) to directly calculate R; NLOP uses (8) and (9) to obtain DDC parameters, and then substitutes into (4) to get the estimate of R, and defines the root mean square error of the estimated covariance matrix as follows :

$\mathrm{<span\; class="notranslate">\; RMSE</span>}<span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Figure 5(a) is the performance curve of R estimation under different i.i.d sample numbers when CNR=35dB is set; Figure 5(b) is the estimation performance curve of different CNR in a single distance unit sampling. It can be seen from Figure 5 that although NLOP and S-ESPRIT are not asymptotically consistent estimates of R, their estimation performance based on a single range sample sampling data is better than that of the ML method "blind" to the R structure under large sample size (>2M) estimated performance. Therefore, based on the prior knowledge of the DDC model, the new method can minimize the i.i.d sample number requirement.

(2) Implementation complexity

Firstly, the implementation complexity of three methods is given as shown in Table 1. It can be seen that the overall complexity of the three methods is O[M ³ ], but in terms of estimating the complexity of R estimation, the NLOP method has an order of magnitude improvement compared with the traditional ML method.

Table 1 Comparison of complexity of three algorithms (M ₁ =9)

NLOP S-ESPRIT ML R estimated complexity O[M] O[M ₁ ³ ] O[M ² ] R ^-1 estimated complexity O[M ³ ] O[M ³ ] O[M ³ ] overall complexity O[M ³ ]+O[M] O[M ³ ]+O[M ₁ ³ ] O[M ³ ]+O[M ² ]

(3) AIOP performance

The following uses the signal-to-interference ratio improvement factor (IF) as an index to compare the performance of the above three methods in terms of airborne radar AIOP. The definition of IF is: the ratio of the output SIR _output to the input SIR _input ,

IF＝10log(SIR _onput /SIR _input ) (17)

Set the system's CNR = 35dB, NLOP and S-ESPRIT use the clutter vector of a single range unit to estimate the adaptive weight to realize AIOP; the ML method uses the clutter vector of 8 range units. The performance curves of the three methods are shown in Fig. 6. Among them, "optimal" means the performance curve obtained by directly using the optimal weight value obtained by the simulation set R to realize AIOP; it can be seen that the method of NLOP and S-ESPRIT can still approach the optimal processing well under the condition of a single i.i.d sample number ; and the ML method has a strong dependence on the number of i.i.d samples, so in the application of small samples, the performance is seriously deteriorated.

Claims (3)

1, a kind of optimum optimum weights method of estimation of handling of airborne radar target detection that is used for comprises the steps:

(1) by the unknown Doppler parameter in the distributed Clutter Model of clutter sample data estimating Doppler of record radar collection, the Doppler parameter of described the unknown comprises doppler centroid f _cWith Doppler's spectrum width spreading coefficient ρ _f

(2) according to the estimated Doppler parameter of step (1), the doppler distributed clutter (ddc) model that obtains having definite parameter; Obtain the clutter covariance matrix R of this model description simultaneously;

(3) obtain optimum weighted vector w according to clutter covariance matrix R _Opt, described optimum weighted vector w _Opt=μ R ^-1S, wherein, R ^-1Be the inverse matrix of clutter covariance matrix R, μ is a constant, and s is an echo signal vector to be detected.

2, optimum weights method of estimation according to claim 1 is characterized in that, the estimation of unknown Doppler parameter described in the step (1) obtains as follows:

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

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

(c) 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;

(d) signal processing system is estimated Doppler parameter unknown in this Clutter Model by the interference covariance matrix and the doppler distributed clutter (ddc) model of sample.

3, optimum weights method of estimation according to claim 1 is characterized in that, at Doppler's spectrum width spreading coefficient ρ _fLess than 0.2 o'clock, unknown Doppler parameter described in the step (1) can be directly sampled signal by airborne radar obtain,

$f_c=\frac{1}{2\mathrm{\&pi;}(M-3)\mathrm{\&Delta;}}\underset{k=1}{\overset{M-3}{\mathrm{\&Sigma;}}}\mathrm{angle}\left(\frac{x_{k+2}^2-x_{k+1}{x}_{k+3}}{x_{k+1}^2-x_k{x}_{k+2}}\right)$

${\mathrm{\&rho;}}_f=\frac{1}{2.355\mathrm{\&pi;}(M-4)\mathrm{\&Delta;}}\underset{k=1}{\overset{M-4}{\mathrm{\&Sigma;}}}{\cos }^{-1}\left(\frac{1}{2}\sqrt{\left|\frac{x_{k+2}^2-x_{k2}{x}_{k+1}}{x_{k+2}^2-x_{k+1}{x}_{k+3}}\right|}\right),$

Wherein, x=[x ₁, x ₂, Λ, x _M] ^TThe expression airborne radar is a relevant interference sample of handling M pulse in the interval, and angle (*) represents the phase position operator of plural number, and Δ is the radar pulse recurrence interval.

Images