Self-adaptive target detection method under non-Gaussian clutter and data loss

Abstract

The invention discloses a self-adaptive target detection method under non-Gaussian clutter and data missing, which belongs to the field of radar signal processing and comprises the following steps of: determining a selection matrix according to positions of missing channels in a unit to be detected and a reference unit; estimating a divergence matrix by using an EM algorithm according to the selection matrix and the auxiliary data; setting adaptive test statistics according to the test criterion and the EM estimation of the divergence matrix; adopting a Monte Carlo method to calculate accurate estimation of a threshold in an off-line manner, and establishing an observation dimension-threshold table; in a target detection process, according to a channel missing condition, quickly determining a threshold by querying the table, and if the adaptive test statistic is greater than the corresponding threshold, judging that an interested target exists; otherwise, determining that the target does not exist. When the method is used for coping with different data missing situations and complex non-Gaussian clutters, the false alarm probability can be effectively controlled, the excellent detection performance is kept, and the method has good engineering application value and popularization potential.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and particularly to a radar adaptive target detection method under non-Gaussian clutter and data missing, which can control the Constant False Alarm Rate (CFAR) under certain conditions. Background Art

[0002] In radar signal processing, most target detection methods are designed based on ideal assumptions, that is, it is assumed that all data of the array output are complete and available. However, in practical applications, due to the influence of various factors, radar systems often face the problem of data missing. The main reasons for data missing include: intermittent failures of sensors in the radar array caused by pulse noise interference, analog-to-digital converter failures, material aging, solder joint failures, chip cracks, and environmental condition changes such as temperature and humidity; in a distributed radar system, failures of receivers or communication links may cause data transmission interruptions; some radar systems adopt switched array technology and dynamically select some channels for observation, so only partial data can be obtained for each observation; the interference of range-ambiguous echoes may affect the sampling integrity of useful signals; in the time domain, the received signal may be affected by sporadic radio frequency interference, resulting in the loss of some slow-time sampling points in specific range cells.

[0003] On the other hand, in scenarios with high range resolution, low grazing angle, and rapid terrain changes (such as the land-sea boundary area), the statistical characteristics of radar clutter are often difficult to accurately describe by traditional Gaussian distribution models. Measured data analysis shows that the composite Gaussian clutter model is more suitable for clutter modeling in complex environments.

[0004] In the face of data missing and non-Gaussian clutter, existing signal detection methods are usually difficult to be directly applied. A commonly used processing scheme is a two-step method: first, use data interpolation technology to complete the missing data; then, use existing target detection methods for detection. However, this method has obvious deficiencies: it cannot guarantee CFAR, and at the same time, the target detection ability is significantly reduced. Currently, there is no adaptive CFAR detection method that can simultaneously cope with data missing and non-Gaussian clutter interference. Summary of the Invention

[0005] The present invention aims to overcome the limitations of existing detection methods, design an adaptive target detection method applicable to non-Gaussian clutter and data missing situations. Compared with the method of first completing and then detecting, it can effectively control the false alarm rate and obtain better adaptability and higher detection probability. To achieve the above technical objectives, the present invention designs a generalized likelihood ratio detector based on the Expectation Maximum (EM) algorithm and a method for quickly determining the threshold depending on the observation dimension, and specifically adopts the following technical solutions to achieve it.

[0006] 1) If the total number of channels of the radar system is N, according to the data missing situation of the radar system, considering that the {v i} i＝1,…,N-p th observed value of the data to be detected is missing, determine the selection matrix E ∈ R p×N (p is a positive integer, representing the observation dimension of the unit to be detected), and E is expressed as the N×N-dimensional identity matrix I N after deleting the {v i} i＝1,…,N-p th row, which is the missing data selection matrix. E reflects the position of the missing channel, thereby establishing the corresponding relationship x = Er between the complete data r and the (data missing situation) observed data x; similarly, the selection matrix of the kth auxiliary data unit can be determined (p k is an integer, representing the observation dimension of the kth auxiliary data unit), and define p′ = min{p k} k＝1,…,K as the minimum observation dimension of the auxiliary data.

[0007] 2) When the divergence matrix R of the compound Gaussian distribution clutter is known, based on common test criteria (such as generalized likelihood ratio test, Rao test, Wald test, etc.), according to the selection matrix E, design the test statistic T.

[0008] 3) According to the (data missing situation) observed data, use the EM algorithm to iteratively estimate the divergence matrix R of the compound Gaussian distribution clutter. The iterative process consists of an expectation (E) step and a maximization (M) step to obtain the EM estimate of the divergence matrix R Substitute it into the test statistic T designed in 2) to obtain the adaptive test statistic T EM .

[0009] 4) Under the condition of fixed observation dimension p and {p k}, the designed detector T k＝1,…,K has the CFAR property for the changes of the clutter texture component and the divergence matrix, where the set {p EM} k} k＝1,…,KThe order of the elements in does not affect the CFAR property. However, according to the "repeated combination number", all possible {p k} k＝1,…,K combinations are In the actual operation of the radar system, considering the storage limitation and fast calculation requirements of the system, the present invention proposes an offline calculation method for the T EM threshold:

[0010] a) Fix p and p′. Under the conditions of no target, white Gaussian clutter, and p k = p″, use the Monte Carlo method to obtain the empirical distribution P EM (T P,p′ ) and store it. EM )

[0011] b) According to the preset false alarm rate P fa , calculate the (1 - P p,p′ )(T EM ) quantile of the empirical distribution P fa ), denoted as γ p′ (p) (i.e., the threshold of T EM ).

[0012] For different observation dimensions p and p′, calculate the threshold γ p′ (p) offline, so as to establish an "observation dimension - threshold" table.

[0013] 5) In different clutter environments, according to the radar (with missing data) observation data, calculate the value of the detection statistic T EM , quickly retrieve the threshold γ p′ (p) by looking up the "observation dimension - threshold" table, and compare the sizes of T EM and γ p′ (p) to determine whether the target of interest exists.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] □ The present invention proposes a detector in a non - Gaussian clutter environment, which can ensure that the detector has the upper - bound CFAR property in the case of missing data in the data to be detected and the training data.

[0016] □ According to the variation range of the available channel number, calculate the "dimension - threshold" table offline, realize the adaptability to different data missing situations, and the fast retrieval of the threshold. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 FIG. is a flowchart of an EM algorithm provided for a specific embodiment of the present invention.

[0018] Figure 2A flowchart for offline calculation of the "observation dimension - threshold" table provided by a specific embodiment of the present invention.

[0019] Figure 3 A flowchart for an adaptive upper - bound CFAR detection method provided by a specific embodiment of the present invention.

[0020] Figure 4 A comparison chart of the detection performance between a specific embodiment of the present invention and a detector based on linear interpolation.

[0021] Figure 5 Showing the empirical distribution P p,p′ (T EM ) in a specific embodiment of the present invention is affected by p'.

[0022] Figure 6 A simulation verification chart of the bounded CFAR property of the method of the present invention. Detailed implementation manners

[0023] It should be noted that relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variant thereof are intended to cover non - exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including an..." does not exclude the existence of another identical element in the process, method, article or device including the said element.

[0024] The present invention proposes an adaptive detector for non - Gaussian clutter and data - missing environments, and provides an offline calculation method for the threshold. This detector has the upper - bound CFAR property, and specifically includes the following steps:

[0025] Step 1: For an ideal observation situation (no data missing), for complete data to be detected and training data, according to information such as the total number of radar channels N, the distance, elevation angle, azimuth angle, Doppler frequency, etc. of the target of interest, determine the target signal steering vector p ∈ X N . Let the complete echo data of the cell to be detected be r ∈ X N , and the radar collects K complete auxiliary data r k , k = 1, …, K near the target to be detected. In this case, for this ideal target detection problem, the following hypothesis - testing model can be established:

[0026]

[0027] where α is the unknown target amplitude, and the clutter c and c k are independent of each other and follow a complex Gaussian distribution

[0028] c ∼ CN(0, τR), c k ∼ CN(0, τ k R),

[0029] The divergence matrix R is an unknown positive definite matrix, and τ, τ k are non - negative texture components.

[0030] Step 2: According to the positions {v i} i＝1,…,N-p of the missing channels in the cell under test, remove the {v N} i th rows from the identity matrix I i＝1,…,N-p to obtain the selection matrix E ∈ R p×N . Similarly, and can be obtained, and they represent the indices of the positions of the missing data in each reference cell. According to the selection matrices E and E , establish the relationship between the (missing - data - containing) observed data and the complete data: k x = Er, …, x

[0031] = E k r k r k , … i = 1, …, K,

[0032] where the vectors r and r k represent the complete data, while x and x k represent the (missing - data - containing) observed data. The observation dimensions p and p k respectively reflect the number of available channels in the cell under test and the reference cell, and are consistent with the dimensions of the corresponding observation vectors x and x k . Define p′ = min{p k}, and p′ represents the minimum observation dimension of the auxiliary data. k＝1,…,K According to the above - mentioned observation model, the target - detection problem with missing data can be transformed into the following hypothesis - testing problem:

[0033] Let X = [x, x1, …, x

[0034]

[0035] , where the dimensions of x and x K may not be the same, but for the convenience of representation, still use the matrix - like form X to represent all the observed data in the cell under test and the reference cell. k

[0036]

[0036] Step 3: Refer to the appendixFigure 1 For the process of the given selection matrix E k and the auxiliary data x k , use the EM algorithm to estimate the divergence matrix R.

[0037] Given the initial iteration value I of the divergence matrix N . The EM algorithm iteratively calculates the expectation (E) step and the maximization (M) step, continuously updating the estimate of R until convergence. Specifically, in the t-th iteration, it is necessary to calculate:

[0038] ● E step: Calculate the conditional expectation of the log-likelihood function of the complete data

[0039]

[0040] where represents the conditional expectation

[0041]

[0042] represents E k 's complementary matrix (obtained by deleting the p N rows in I k corresponding to the selection matrix E k ).

[0043] ● M step: Maximize the function in the E step.

[0044]

[0045] where the calculation of R (t) needs to be obtained through iterative calculation. By continuously updating the estimate of R until R (t) converges, and the convergence point is denoted as

[0046] Step 4: According to the existing test criteria (generalized likelihood ratio test, Rao test, Wald test, etc.), design a detector when the divergence matrix R is known, and use the EM estimate of the divergence matrix obtained in Step 3 to replace R and obtain the adaptive test statistic T EM (X)

[0047]

[0048] Step 5: When determining the training sample size K and the total number of channels N, for the available channels p of the unit to be tested and the minimum available channels p′ of the auxiliary data, use the Monte Carlo method to obtain an accurate estimate of the threshold.

[0049] First, for the minimum preset false alarm rate Random Generation independent complete data matrix Y (1) ,…,Y (MC) ∈X N×(K+1) ,in,

[0050]

[0051] Secondly, given the observation data dimensions p and p′, a selection matrix E∈P is randomly generated for each distance unit p×N , E k ∈Ρ p′×N Then, based on the selection matrix, the observed data in the case of missing data is generated

[0052]

[0053] On this basis, the statistic T is calculated EM (X (j) ).

[0054] Finally, according to the independent and identically distributed samples {T EM (X (1) ),…,T EM (X (MC) )}, get T EM The empirical distribution P p,p′ (T EM ), store P p,p′ (T EM ). For the preset false alarm rate P fa , calculate the empirical distribution P p,p′ (T EM ) of (1-P fa ) quantile, denoted as γ p′ (p), as the adaptive test statistic T EM threshold.

[0055] It is worth noting that for p k ≥p′, the threshold γ p′ (p) can ensure that the actual false alarm rate is no greater than the preset P fa , that is, γ p′ (p) is a conservative threshold.

[0056] Step 6: Process reference attachment Figure 2 , for different observation data dimensions p and p′, use step 5 to calculate the corresponding detection threshold γ p′ (p), establish an "observation dimension-threshold" table. Since the above table can be calculated and stored offline, it will not increase the online calculation complexity of the detection method.

[0057] Step 7: The complete operation process of the adaptive upper bound CFAR detection method is referred to in Appendix Figure 3 . Specific process: According to Steps 1 to 4, obtain the value of the adaptive test statistic T EM (X), and determine the threshold γ p′ (p) by querying the "observation dimension - threshold" table established in Step 6. If T EM (X) is greater than the corresponding threshold, it is determined that the target of interest exists; otherwise, it is determined that the target does not exist.

[0058] The effects of the present invention will be further described below in conjunction with simulation experiments.

[0059] Refer to Figure 4 . As shown in the figure, this figure is a comparison chart of the radar target detection probability under t-distributed clutter interference, showing the detection performance of the method of the present invention and the existing method under different Signal to Interference plus Noise Ratio (SINR). For simplicity of calculation, assume that the number of channels of the radar system N = 10, the number of auxiliary samples K = 30, the shape parameter ν of the t-distribution = 2.1, the observation dimension p of the data to be detected = 7, the minimum observation dimension p' of the training data = 8, the power of the thermal noise is The clutter covariance matrix is The covariance matrix of uncorrelated narrowband interference is where

[0060]

[0061] represents the steering vector of the l-th interference source in the direction θ l , then is the power of the l-th interference source. In the simulation experiment, the specific parameter settings are as follows: The directions of the interference sources (θ1, θ2) = (-10°, 15°), the interference source to noise ratio is The preset false alarm probability P fa = 10 -3 . Define where,

[0062] The detector proposed by the present invention is called GLRT2S-EM. The detection method based on linear interpolation is called GLRT2S-LI. In addition, a two-step GLRT detector using complete data (substituting Tyler-M estimation) is used as a comparison benchmark. Analysis Figure 4 It can be seen that the method proposed by the present invention has significant performance advantages compared with GLRT2S-LI.

[0063] Refer to Figure 5As shown, under the original hypothesis H0, for the case where the observation dimension p of the data to be tested is determined, the empirical distribution P EM proposed by the present invention p,p′ (T EM ) is affected by p'. Analysis Figure 5 shows that an increase in the minimum observation dimension p' of the training data will increase the tail probability of P p，p′ (T EM ). This phenomenon verifies that T EM has an upper bound false alarm rate.

[0064] Referring to Figure 6 shown, for a nominal false alarm rate of 10 -3 , under the simulation conditions of Figure 4 , for the changes in the correlation coefficient ρ of the exponential divergence matrix and the shape parameter ν of the K-distributed clutter, the method proposed by the present invention effectively controls the true false alarm rate.

[0065] The above are only some specific embodiments of the present invention. Specific content or common knowledge well known in the solution is not described in detail here (including but not limited to abbreviations, contractions, units commonly used in the art). It should be noted that the above embodiments do not limit the present invention in any way. For those skilled in the art, any technical solutions obtained by means of equivalent replacement or equivalent transformation fall within the protection scope of the present invention. The protection scope required by this application should be subject to the content of its claims, and the specific implementation manners in the specification and the like can be used to interpret the content of the claims.

Claims

1. An adaptive target detection method under non-Gaussian clutter and data loss, characterized in that: Adaptive detection is achieved by using a generalized likelihood ratio detector based on the EM algorithm and an "observation dimension-threshold" table. The method specifically includes the following steps: No data missing: For complete data to be detected and training data, the target signal steering vector p∈X is determined according to the total number of radar channels N, the distance, pitch angle, azimuth, and Doppler frequency information of the target of interest. N , set the complete echo data of the unit to be tested to r∈X N , K complete auxiliary data r of the radar in the reference unit k ,k=1,…,K, construct the signal detection model of complete data; There is missing data: According to the position of the missing channel in the unit to be tested {v i } i＝-,…,N-p , from the identity matrix I N Remove the first {v i } i＝1,…,N-p Row, get the selection matrix E∈R p×N ; In this way, the selection matrix E representing each reference unit is obtained k , establish the corresponding relationship between missing observation data and complete data; According to the selection matrix E k and the observed auxiliary data x k , use the EM algorithm to estimate the unknown clutter divergence matrix R; According to the test criterion and the EM estimate of the scatter matrix R, set the adaptive test statistic T EM (X); When the training sample size K and the total number of channels N are determined, random data are generated using white Gaussian distribution. When the number of available channels of the unit to be inspected is p and the number of available channels of auxiliary data is p′, the threshold γ is obtained using the Monte Carlo method. p′ (p) is accurately estimated; for different observation data dimensions p and p′, the corresponding detection thresholds are obtained respectively, and an "observation dimension-threshold" table is established; By analyzing the radar observation data, the number of available channels p of the unit to be inspected and the minimum number of available channels p' of the auxiliary data are determined. By querying the "observation dimension-threshold" table, the corresponding threshold is determined. If T EM If (X) is greater than the threshold, the target of interest is determined to exist; otherwise, the target is determined not to exist.

2. The adaptive target detection method under non-Gaussian clutter and data loss according to claim 1, characterized in that: The relationship between the missing observation data and the complete data is: x=Is,…,x k =E k r k ,…i=1,…,K, Among them, vectors r and r k represents the complete data, while x and x k This means there are missing observations, and the observation dimensions p and p k are the number of available channels in the test unit and the reference unit, respectively, and the corresponding observation vectors x and x k The dimension is consistent, set p ′ =min{p k } k＝1,…,K , p ′ Represents the minimum observation dimension of auxiliary data.

3. The adaptive target detection method under non-Gaussian clutter and data loss according to claim 2, characterized in that: According to the relationship between missing observation data and complete data, the target detection model of observation data is:

4. The adaptive target detection method under non-Gaussian clutter and data loss according to claim 2, characterized in that: The target detection model for the complete data is: Among them, α is the unknown target amplitude, clutter c and c k Independent of each other, obeying a compound Gaussian distribution: c~CN(0,τR),c k ~CN(0,τ k R), The divergence matrix R is an unknown positive definite matrix, τ, τ k is the unknown non-negative texture component.

5. The adaptive target detection method under non-Gaussian clutter and data loss according to claim 1, characterized in that: The test criteria include generalized likelihood ratio test, Rao test and Wald test.

6. The method for adaptive target detection under non-Gaussian clutter and data loss according to claim 1, characterized in that: The method of using the EM algorithm to estimate the divergence matrix R includes: according to the iterative initial value I of R N ,The EM algorithm iteratively calculates the expected E step and the maximum M step, and continuously updates the estimate of R until convergence.

7. The adaptive target detection method under non-Gaussian clutter and data loss according to claim 6, characterized in that: The expected E step includes the following steps: In the tth iteration, the conditional expectation of the log-likelihood function of the complete data is calculated: in, Represents conditional expectation Indicates E k The complementary matrix, By deleting I N corresponds to the selection matrix E k p k Line obtained.

8. The adaptive target detection method under non-Gaussian clutter and data loss according to claim 6, characterized in that: The maximum M step comprises the following steps: In the tth iteration, maximize the E step function: Among them, R (t) The calculation of needs to be obtained through iterative calculation; by continuously updating the estimate of R until R (t) Convergence, the convergence point is recorded as 9. The method for adaptive target detection under non-Gaussian clutter and data loss according to claim 1, characterized in that: The adaptive test statistic T EM (X):

10. The method for adaptive target detection under non-Gaussian clutter and data loss according to claim 1, characterized in that: The Monte Carlo method for obtaining an accurate estimate of the threshold comprises the following steps: For the minimum preset false alarm rate Random Generation independent complete data matrix Y (1) ,…,Y (MC) ∈X N×(K+1) ,in, Given the observation data dimensions p and p ′ Under the condition of randomly generating the selection matrix E∈Ρ for each distance unit p×N , E k ∈Ρ p′×N ; Generate observations with missing data based on the selection matrix: Calculate the statistic T EM (X (j) ); According to the independent and identically distributed samples {T EM (X (1) ),…,T EM (X (MC) )}, get T EM The empirical distribution P p,p′ (T EM ), store P p,p′ (T EM );For the preset false alarm rate P fa , calculate the empirical distribution P p,p′ (T EM ) of (1-P fa ) quantile, denoted as γ p′ (p), as the adaptive test statistic T EM threshold.

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