A radar target coherent detection method based on binary quadratic programming global optimal solution

Abstract

The application discloses a radar target coherent detection method based on binary quadratic programming global optimal solution, belongs to the technical field of radar target detection, and particularly relates to a radar target detection method in a non-Gaussian and non-uniform clutter environment. The method converts the radar detection problem into a quadratic programming problem meeting a binary constraint, and judges whether a target signal exists or not by using a global optimal condition of the binary quadratic programming problem. Compared with the detection method mentioned in the technical background, the method does not depend on the statistical characteristics of the clutter, and has stronger generalization ability. Taking the detection probability as an evaluation performance index, simulation experiments show that the application has higher detection performance than the existing detection method in the non-Gaussian clutter environment, and has stronger robustness in a signal steering vector mismatching scene, and is suitable for practical application.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar target detection, and particularly relates to a radar target detection method in a non-Gaussian and non-uniform clutter environment. BACKGROUND

[0002] Radar target detection technology mainly uses radar to emit electromagnetic waves to irradiate a target and receive a return wave, and judges whether the return wave signal of the target return wave signal is "yes" or "no". Radar target detection plays an important role and has great value in the field of national security, such as sea, land and air target monitoring and early warning detection. The performance of radar detection is mainly limited by clutter, noise and other interference. In particular, when the radar transmitter scans the sea surface, the receiver will receive the backscattering return wave signal from the sea surface, i.e. sea clutter. Influenced by many factors such as radar parameters, weather, geography and the like, the characteristics of sea clutter are complex and changeable and are difficult to understand. Especially, the statistical characteristics of sea clutter deviate from the Gaussian distribution and show obvious non-Gaussian characteristics. At the same time, in high sea states or low grazing angles, sea spikes appear on the sea surface. The complex sea clutter environment greatly increases the difficulty of detecting targets on the sea surface, resulting in high clutter false alarms and target missing detection and the like. Therefore, it is very important to improve the radar target detection performance in a non-Gaussian clutter environment.

[0003] Many research institutions at home and abroad have carried out research on radar target detection methods under non-Gaussian clutter. For compound K-distributed clutter, the University of Naples Federico II in Italy proposed an asymptotically optimal detection method (E. Conte, M. Lops and G. Ricci, Asymptotically optimum radar detection in compound-Gaussian clutter, IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 2, pp. 617-625, Apr. 1995.). Xi'an University of Electronic Science and Technology modeled the amplitude statistical characteristics of sea clutter as compound Gaussian-generalized inverse Gaussian distribution, and then proposed an optimal and near-optimal detection method (S. Xu, Z. Wang, X. Bai and H. Zhou, "Optimum and near-optimum coherent CFAR detection of radar targets in compound-Gaussian clutter with generalized inverse Gaussian texture," IEEE Trans. Aerosp. Electron. Syst., Oct. 2021.). The above detection methods assume that the statistical characteristics of the clutter amplitude are known, and their performance is heavily dependent on the statistical characteristics of the clutter. In actual scenarios, when the preset statistical characteristics of the clutter do not match the actual clutter environment, the detection performance of the above methods will degrade seriously. Therefore, it is of great value to study the detection method under non-Gaussian clutter that does not depend on the statistical characteristics of the clutter in the field of radar target detection. SUMMARY

[0004] In order to solve the above problems, the present application provides a radar target coherent detection method based on binary quadratic programming global optimal solution suitable for non-Gaussian clutter environment. First, the binary hypothesis test problem is recast as a binary quadratic programming (BQP) problem, then the necessary and sufficient condition for the global optimal solution of the BQP problem is determined, and then the soft decision result is obtained, secondly, the detection statistics are obtained by accumulating multiple soft decision results, finally the detection statistics are compared with the threshold to judge whether the target signal exists or not, so as to realize target detection.

[0005] The technical scheme of the present application is as follows:

[0006] A radar target coherent detection method based on binary quadratic programming global optimal solution, the method comprising the following steps:

[0007] Step 1: model the target detection problem as a binary quadratic programming problem;

[0008] By introducing an auxiliary variable z, the radar target detection problem under non-Gaussian clutter is represented as:

[0009] y = zp + c

[0010] where y is the received echo signal vector, a reflects the target scattering and channel propagation effects, p is the steering vector, ap represents the target echo signal vector, c is the clutter vector, z takes values 0 and 1, representing the absence and presence of targets, respectively;

[0011] By maximizing the likelihood function, the target detection problem is converted into an estimation problem of the parameter z, represented as:

[0012]

[0013] where represents the estimated value of z, H = a diag(p), diag(p) represents the diagonal matrix composed of the vector p, and Ω = {z i |z i ∈ {0, 1} M , i = 0, 1} represents the feasible set of z, and M represents the number of pulses sent by the radar in one coherent processing interval. Each element of z can only take values 0 and 1, so the above problem is a binary constrained quadratic programming problem;

[0014] Step 2: Determine the global optimal solution condition of the binary quadratic programming problem;

[0015] For the estimation problem of the parameter z, the sufficient condition for the global optimal solution of the problem is represented as:

[0016]

[0017] where is composed of the real and imaginary parts of H, and represent the real and imaginary part operations, respectively, g ij is the i-th row and j-th column element of the matrix G, b i is the i-th element of the vector b, and represent the i-th and j-th values of , respectively, λ min (·) represents the minimum eigenvalue of the matrix;

[0018] Then determine the necessary condition for the global optimal solution of the problem, represented as:

[0019]

[0020] Based on the above sufficient and necessary conditions, the soft decision result of the binary quadratic programming problem is determined as follows:

[0021]

[0022] Where, p i and y i Let p and y represent the i-th elements respectively;

[0023] Step 3: Design the detection statistics;

[0024] The results of soft decision-making are accumulated to obtain the detection statistic, which is expressed as:

[0025]

[0026] Step 4: Detection and Judgment

[0027] Using the detection statistics designed above, a detector is constructed.

[0028]

[0029] The detection statistic T BQPS With the decision threshold η BQPS The comparison is performed. If the detection statistic is greater than the threshold, it is determined that the target exists in the current detection unit; otherwise, it is determined that the target does not exist.

[0030] This invention proposes a radar target coherent detection method based on the global optimal solution of binary quadratic programming. This method transforms the radar detection problem into a quadratic programming problem satisfying binary constraints, and uses the global optimal condition of the binary quadratic programming problem to determine the presence or absence of a target signal. Compared to the detection methods mentioned in the background, this method does not rely on clutter statistical characteristics and has stronger generalization ability. Using detection probability as the performance evaluation index, simulation experiments show that this invention has higher detection performance than existing detection methods in non-Gaussian clutter environments, and exhibits stronger robustness in signal steering vector mismatch scenarios, making it suitable for practical applications. Attached Figure Description

[0031] Figure 1 This is a flowchart of the radar target detection method based on BQP global optimal conditions.

[0032] Figure 2 The detection probability varies with the signal-to-clutter plus noise ratio (SCNR).

[0033] Figure 3 This is the ROC (Receiver Operating Characteristics) curve.

[0034] Figure 4 The curves show the probability of missed detection under different pulse numbers and reference distance units.

[0035] Figure 5 For signal steering vector mismatch cos 2 The detection probability curve at θ = 0.9784.

[0036] Figure 6 For signal steering vector mismatch cos 2 The detection probability curve at θ = 0.6964. Detailed Implementation

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0038] A radar target coherent detection method based on the global optimal solution of binary quadratic programming includes the following steps:

[0039] 1. Model the object detection problem as a BQP problem.

[0040] Assuming the radar operates at pulse repetition intervals T within a coherent processing interval. r Send M pulses and sample the radar received signal to obtain an M-dimensional vector form y = [y1, ..., y2]. M ] T Without loss of generality, the radar target detection problem can be represented by the following binary hypothesis testing model:

[0041]

[0042] Where α reflects the target scattering and channel propagation effects, and the steering vector p = [1, exp(j2πf d T r ),…,exp(j2π(M-1)f d T r )] T f d Let c be the target normalized Doppler frequency. c represents the clutter vector. It's worth noting that the composite Gaussian model is a commonly used model for modeling the amplitude characteristics of non-Gaussian clutter. By introducing an auxiliary variable z, taking values ​​of 0 and 1, the above binary hypothesis testing model can be expressed as...

[0043] y = Hz + c

[0044] Where H = αdiag(p), and

[0045]

[0046] By making the likelihood function p yMaximizing (yz), the above object detection problem can be transformed into an estimation problem of parameter z, equivalently represented as:

[0047]

[0048] in, Let z represent the feasible set, where each element of z can only take the values ​​0 and 1. The above problem is a quadratic programming problem that satisfies binary constraints.

[0049] 2. Determine the globally optimal solution to the above BQP problem.

[0050] The sufficient and necessary conditions for the global optimal solution to the above BQP problem are expressed as follows:

[0051]

[0052] and

[0053]

[0054] in

[0055]

[0056] Based on the characteristic form of matrix G, the necessary and sufficient conditions for the global optimal solution of the BQP problem can be integrated into a necessary and sufficient condition, expressed as follows:

[0057]

[0058] Among them, b i Let be the i-th element of vector b, and

[0059]

[0060] Based on the above conditions, the soft decision outcome of the BQP problem can be determined, expressed as:

[0061]

[0062] 3. Design of detection statistics

[0063] Accumulate the results of M soft decisions to obtain the detection statistic, denoted as:

[0064]

[0065] 4. Detection and Judgment

[0066] Using the detection statistics designed above, a detector is constructed.

[0067]

[0068] Where, ηBQPS This is the decision threshold. Based on the false alarm probability P... fa Size, execute 100 / P fa In this experiment, the detection statistics for the targetless case were calculated and sorted in descending order. The 100th detection statistic was taken as the decision threshold. The detection statistic T... BQPS With the decision threshold η BQPS We compare the results, and if the detection statistic is greater than the threshold, we determine that the target exists in the current detection unit; otherwise, we determine that the target does not exist.

[0069] Parameter settings: The number of pulses transmitted by the radar in one coherent processing interval is M=8, and the clutter amplitude statistical characteristics are modeled as a K-distribution, expressed as follows: Where τ is a random variable following a gamma distribution, and x is a random variable with zero mean and a covariance matrix of Σ=Σ0+I. M The complex Gaussian distribution is Σ0, and Σ0 is modeled in exponential form.

[0070]

[0071] Where ρ is the first-order delay correlation coefficient of clutter, set to ρ = 0.9; For noise ratio, set to 10dB; f dc The normalized Doppler frequency for clutter is set to 0.05.

[0072] Example 1:

[0073] Assume the signal-to-noise ratio (SCNR) is between -20dB and 20dB, and the false alarm probability is 0.01. Figure 2 This shows how the detection probability of existing technologies and this invention changes with SCNR. For example... Figure 2 As shown, the technology of the present invention has a higher detection probability and significantly improves the radar target detection performance in non-Gaussian clutter environments.

[0074] Example 2:

[0075] Assuming the false alarm probability is 10 -3 Up to 10 -1 The signal-to-noise ratio (SCNR) is set to 8dB and varies linearly within the range. Figure 3 The paper demonstrates how the detection probability of existing technologies and the present invention varies with the false alarm probability. The results show that the present invention significantly improves the detection probability under different false alarm probabilities.

[0076] Example 3:

[0077] Existing detection technologies rely on reference distance cells around the unit to be detected, and require that the number of reference cells N and the number of pulses M satisfy the relationship N≥2M. Figure 4The diagram illustrates the variation of the false alarm probability with the missed detection probability under four conditions: M=8, N=8, M=8, N=16, M=16, N=16, and M=16, N=32. The signal-to-noise ratio (SCNR) is set to 8 dB. Figure 4 As shown, the prior art exhibits significant fluctuations in the false negative probability under four conditions, reaching a false negative rate of 70% when the condition N≥2M is not met. In contrast, the false negative rate of this invention is lower, and the difference in false negative rates across the four conditions is relatively small. This invention is more suitable for scenarios where there is a limited amount of practically available reference unit data.

[0078] Example 4:

[0079] The actual target guidance vector p and the set target guidance vector Mismatch scenarios, definition

[0080]

[0081] Figure 5 and Figure 6 They showcased cosplay respectively. 2 θ = 0.9784 and cos 2 The detection probability at θ = 0.6964 varies with SCNR. As can be seen from the figure, both existing technologies and this invention show varying degrees of decrease in the target guidance vector mismatch scenario, and this decrease intensifies with increasing mismatch severity. In particular, existing technologies show a decrease in cos... 2 The method fails to function at θ = 0.6964, but compared to existing technologies, this invention can still effectively detect targets. Simulation results show that the radar target detection method for non-Gaussian clutter provided by this invention not only has good detection performance but also stronger robustness, verifying the correctness and effectiveness of the invention and making it suitable for practical applications.

Claims

1. A radar target coherent detection method based on the global optimal solution of binary quadratic programming, the method comprising the following steps: Step 1: Model the object detection problem as a binary quadratic programming problem; By introducing an auxiliary variable z, the radar target detection problem under non-Gaussian clutter can be expressed as: y = zαp + c Where y is the echo signal vector received by the radar receiver, α reflects the target scattering and channel propagation effects, p is the steering vector, αp represents the target echo signal vector, c is the clutter vector, and z takes values ​​of 0 and 1, representing the absence and presence of the target, respectively. By maximizing the likelihood function, the object detection problem is transformed into an estimation problem of the parameter z, expressed as: in, Let H = αdiag(p) ​​represent the estimated value of z, where diag(p) ​​represents the diagonal matrix consisting of vector p, and Ω = {z}. i |z i ∈{0,1} M Let {i = 0, 1} represent the feasible set of z, and M represent the number of pulses transmitted by the radar within a coherent processing interval. Each element of z can only take the values ​​0 and 1. Therefore, the above problem is a quadratic programming problem that satisfies binary constraints. Step 2: Determine the conditions for the global optimal solution to the binary quadratic programming problem; For the problem of estimating parameter z, the sufficient condition for the global optimal solution is expressed as: in It consists of the real and imaginary parts of H. and These represent the operations of extracting the real and imaginary parts, respectively. ij Let be the element in the i-th row and j-th column of matrix G. b i Let i be the i-th element of vector b. and They represent The i-th and j-th values, λ min (·) indicates taking the smallest eigenvalue of the matrix; Then, the necessary conditions for the global optimal solution to this problem are determined, expressed as: Based on the above sufficient and necessary conditions, the soft decision result of the binary quadratic programming problem is determined as follows: Where, p i and y i Let p and y represent the i-th elements respectively; Step 3: Design the detection statistics; The results of soft decision-making are accumulated to obtain the detection statistic, which is expressed as: Step 4: Detection and Judgment Using the detection statistics designed above, a detector is constructed. The detection statistic T BQPS With the decision threshold η BQPS The comparison is performed. If the detection statistic is greater than the threshold, it is determined that the target exists in the current detection unit; otherwise, it is determined that the target does not exist.

2. The radar target coherent detection method based on the global optimal solution of binary quadratic programming as described in claim 1, characterized in that, In step 1, diag(p) ​​is: Among them, f d To achieve the target normalized Doppler frequency, T r This is the pulse repetition interval.

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