A design method for adaptive target detector capable of suppressing mismatch signals

Abstract

The present invention discloses a design method for an adaptive target detector capable of suppressing mismatch signals, comprising the following steps: 1) receiving to-be-detected and auxiliary data collected by a uniform sonar line array and constructing a binary hypothesis testing problem; 2) introducing latent variables to obtain a linear Gaussian model of the observed data matrix; 3) solving for the unknown parameters in the probability density function using the EM method; and 4) substituting the estimated results into the posterior probability to obtain a final EM-ABORT detector, thereby achieving adaptive target detection capable of suppressing mismatch signals. By introducing latent variables to construct a linear Gaussian model, the present invention effectively integrates information under various hypotheses, obtaining more accurate parameter estimation results. While achieving a high detection probability, it can effectively suppress interference signals with large mismatches, thereby improving the detector's signal selectivity.

Description

Technical Field

[0001] The invention belongs to the technical field of sonar, and in particular relates to a design method of an adaptive target detector capable of suppressing mismatch signals. Background Art

[0002] Active sonar performs underwater detection, identification, and tracking by transmitting acoustic signals and receiving echoes reflected from scatterers. It is an important means of underwater information acquisition. In shallow waters, reverberation, resulting from the irregular scattering and superposition of the sea surface, seabed, and water column, is a major interference to active sonar. To address the spatiotemporal coupling of shallow water reverberation, underwater space-time adaptive detection (STAD) technology, based on two-dimensional space-time joint processing, has emerged. This technology effectively combats spatiotemporal coupled reverberation and improves the efficiency of active sonar. In recent years, adaptive target detection in unknown Gaussian backgrounds has attracted widespread attention, and a large number of adaptive detection algorithms have been proposed, such as the generalized likelihood ratio (GLRT) detector, adaptive matched filter (AMF), adaptive correlation estimator (ACE), and Rao detector. Recently, researchers have explored the problem of adaptive target detection from the perspective of maximizing a posteriori probability (MAP). By introducing latent variables to construct a linear Gaussian model, information under various assumptions is effectively integrated. The expectation maximization method (EM) is then used to obtain more accurate estimates of the unknown parameters. The posterior distribution of the received data is then used to design the detection statistic, ultimately resulting in the EM-GMAP detector. In the matched case, where the true target direction is assumed to be consistent with the beam pointing angle, the EM-GMAP detector has a high detection probability. However, in practical applications, factors such as antenna calibration errors, beam pointing errors, and electromagnetic wave multipath effects can cause deviations between the target's direction of arrival (AoA) and the sonar pointing direction, resulting in mismatch. Even with significant mismatch, the EM-GMAP detector still has a high detection probability, failing to effectively suppress signals with significant mismatches and exhibiting poor signal selectivity.

[0003] To effectively suppress signals with large mismatches, the Adaptive Beamforming Orthogonality Rejection Test (ABORT) was proposed. ABORT modifies the null hypothesis in binary hypothesis testing problems by introducing a virtual signal that is orthogonal to the true target in the whitened space. This modification makes the detector more likely to judge the null hypothesis as true in cases of large mismatches, thereby improving its selectivity for mismatched signals. However, the ABORT detector performs poorly in matched conditions and is inferior to EM-GMAP. Summary of the Invention

[0004] The existing MAP-based EM-GMAP detector still has a high detection probability when the mismatch is large, and cannot effectively suppress signals with large mismatches, resulting in poor signal selection capability. The ABORT detector introduced to improve signal selection capability has poor detection performance under matching conditions. The purpose of the present invention is to overcome the above-mentioned defects of the prior art by combining the EM-MAP method with the ABORT method to propose an adaptive target detector that can suppress mismatched signals, thereby achieving good detection performance while effectively suppressing interference signals with large mismatches.

[0005] In view of this, the present invention proposes a design method for an adaptive target detector capable of suppressing mismatch signals, comprising:

[0006] Step 1) receiving the data to be tested and auxiliary data collected by the uniform sonar line array, and constructing a binary hypothesis testing problem;

[0007] Step 2) introduce latent variables to obtain a linear Gaussian model of the observation data matrix;

[0008] Step 3) Solve the unknown parameters in the probability density function by EM method;

[0009] Step 4) Substitute the estimated result into the posterior probability to obtain the final EM-ABOT detector, realizing adaptive target detection that can suppress mismatch signals.

[0010] Preferably, the step 1) comprises:

[0011] The array is composed of N array elements with an equally spaced uniform linear array. The array element spacing is d = λ / 2, where λ is the operating wavelength. The received echo data is processed to form an N-dimensional complex vector Where z represents the echo data of the unit to be detected, is auxiliary data, z k represents the kth auxiliary data located near the main data, K represents a total of K auxiliary data, represents a complex domain;

[0012] Construct a binary hypothesis test problem, using H0 and H1 to represent the hypothesis of no target signal and the hypothesis of target signal, respectively, satisfying the following formula:

[0013]

[0014] Among them, n,n k , k=1,…,K is the independent and identically distributed interference component, which has a mean of 0 and a covariance matrix of Gaussian distribution; α is the unknown complex amplitude of the target; v is the target guidance vector; v ⊥ Orthogonal to v in the whitening space, that is, v⊥ M -1 v=0,let Represents the data matrix.

[0015] Preferably, the step 2) comprises:

[0016] Introduce a latent variable c representing the existence of the target, where c = 0 means that the H0 hypothesis is true, c = 1 means that the H1 hypothesis is true, and the probability mass function of c is P(c = t) = p t , t=0,1 and p0+p1=1, then the probability density function of Z satisfies the following linear Gaussian model:

[0017] f(Z;M,α,v ⊥ )=p0f0(Z;M,v ⊥ )+p1f1(Z;M,α)

[0018] Among them, f0(Z;M,v ⊥ ) and f1(Z;M,α) represent the probability density functions of Z under the H0 and H1 assumptions, respectively.

[0019] Preferably, the step 3) comprises:

[0020] Introducing the adjustable parameter η, we can obtain the adjustable false alarm probability P fa , design the EM-ABORT detector with the test statistic satisfying the following formula:

[0021]

[0022] in, and are p0, p1, M, α and v respectively ⊥ After l max The final estimation result after iteration;

[0023] The unknown parameters p={p0,p1} and θ={M,v ⊥ ,α}.

[0024] Preferably, the parameter p={p0, p1} in step 3) is obtained according to the following steps:

[0025] Step S1) The result of the first iteration of p for:

[0026]

[0027] Among them, the superscript (l-1) represents the (l-1)th iteration result, and They are respectively expressed as the posterior distribution of Z under the H0 and H1 assumptions, satisfying the following formula:

[0028]

[0029] Step S2) solve the optimization problem:

[0030]

[0031] Step S3) Use Lagrange multiplier method to get the estimated values ​​of p0 and p1 and

[0032]

[0033] Preferably, the parameter θ in step 3) is ⊥ ,α} is obtained according to the following steps:

[0034] Step T1) The lth iteration result of θ (l) for:

[0035]

[0036] Step T2) solve the optimization problem:

[0037]

[0038] Step T3) v ⊥ Make an estimate and transform the optimization problem into:

[0039]

[0040] Get v ⊥ The lth iteration result for:

[0041]

[0042] Step T4) Get the lth iteration result of α for:

[0043]

[0044] Step T5) converts the and step T4) Substitute into the optimization problem of step T2) and get the lth iteration result of α for:

[0045]

[0046] in, is the projection matrix of supplement.

[0047] Preferably, the final EM-ABOT detector in step 4) satisfies the following formula:

[0048]

[0049] Compared with the prior art, the advantages of the present invention are:

[0050] 1. The present invention constructs a linear Gaussian model by introducing latent variables, effectively integrating the information under various assumptions, and obtaining more accurate parameter estimation results, thereby achieving optimal detection performance under matching conditions.

[0051] 2. While achieving a high detection probability, the present invention can effectively suppress interference signals with a large degree of mismatch, thereby improving the detector's ability to select signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 shows the relationship between the residual mean and the number of iterations l for 1000 independent Monte Carlo tests under different N and K conditions. Figure 1(a) shows the relationship between the residual mean and the number of iterations l under the H0 hypothesis, and Figure 1(b) shows the relationship between the residual mean and the number of iterations l under the H1 hypothesis.

[0053] Figure 2 shows the detection performance curve of the algorithm in the case of complete matching, where Figure 2(a) shows the relationship between the detection probability and SRNR when N=8 and K=16, and Figure 2(b) shows the relationship between the detection probability and SRNR when N=16 and K=32.

[0054] Figure 3 shows the curve of false alarm probability changing with RNR and ρ, where Figure 3(a) shows the curve of false alarm probability changing with ρ, and Figure 3(b) shows the curve of false alarm probability changing with RNR.

[0055] FIG4 is a contour map under mismatch conditions, wherein FIG4(a) is a contour map under the condition of N=8, K=16, and FIG4(b) is a contour map under the condition of N=16;

[0056] Figure 5 This is a flow chart of a design method of an adaptive target detector capable of suppressing mismatch signals according to the present invention. DETAILED DESCRIPTION

[0057] To address these issues, we combined the design concepts of EM-MAP and ABORT detectors to propose an EM-ABORT detector design approach. This approach achieves superior detection performance in matched conditions while effectively suppressing interference signals with significant mismatches, improving detector selectivity.

[0058] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0059] Example

[0060] An embodiment of the present invention proposes a design method for an adaptive target detector capable of suppressing mismatch signals.

[0061] 1. Problem Modeling

[0062] Consider a sonar system equipped with N array elements. The receiving array is a uniform linear array with an element spacing of d = λ2, where λ is the operating wavelength. The sonar system receives echo data from the unit under test (CUT) and the auxiliary unit, and performs appropriate processing to form an N-dimensional complex vector Where z represents the echo data of CUT, is auxiliary data. In order to determine whether there is a target in the CUT, a binary hypothesis test problem is established as shown in the following formula. Under the H0 hypothesis, a virtual signal orthogonal to the target guidance vector is introduced to improve the system's ability to suppress signals with a large mismatch degree:

[0063]

[0064] Among them, n,n k , k=1,…,K is the independent and identically distributed interference component, which has a mean of 0 and a covariance matrix of Gaussian distribution; α is the unknown complex amplitude of the target; v is the target guidance vector; v ⊥ Orthogonal to v in the whitening space, that is, v ⊥ M -1 v = 0. Let Represents the data matrix, then the probability density function (PDF) of Z under the H0 and H1 assumptions are:

[0065]

[0066] in

[0067] Next, we introduce a latent variable c representing the existence of the target, where c = 0 means that the H0 hypothesis is true, and c = 1 means that the H1 hypothesis is true. The probability mass function (PMF) of c is P(c = t) = p t , t=0,1 and p0+p1=1. Based on this, the PDF of Z can be rewritten as the following linear Gaussian model:

[0068] f(Z;M,α,v ⊥ )=p0f0(Z;M,v ⊥ )+p1f1(Z;M,α) (4)

[0069] Next, we use the EM method to solve the unknown parameters M, α and v ⊥Specifically, the EM algorithm iterates through the E step and the M step. In the first iteration, the E step can be expressed as the posterior distribution of Z under the H0 and H1 assumptions, that is,

[0070]

[0071]

[0072] in, p0, p1, M, v respectively ⊥ , the estimated results of the l-1th iteration of α. In the M step, we solve p0, p1, M, v through the following optimization problem ⊥ , the result of the lth iteration of α.

[0073]

[0074] 2. Algorithm Process

[0075] From the above analysis, we can know that the E step is the posterior distribution of Z under the H0 and H1 assumptions, which can be used to evaluate whether the data is more consistent with the H0 hypothesis or the H1 hypothesis given Z. Therefore, we can derive the corresponding decision criterion as follows:

[0076]

[0077] Among them, l max To ensure the upper limit of the number of iterations to converge. However, the above detection threshold is constant, which does not allow us to calculate the false alarm probability (P fa ) to adjust. Therefore, we modify the above formula by introducing the adjustable parameter η to obtain the adjustable P fa , the final test statistic is as follows:

[0078]

[0079] The detector shown in the above equation is called EM-ABORT detector, where the unknown parameters can be estimated by the row-wise EM method. Specifically, consider the optimization problem shown in equation (7), where the parameters p = {p0, p1} and θ = {M, v ⊥ ,α} are independent of each other, so the l-th iteration results of p and θ can be written as:

[0080]

[0081] First, solve the optimization problem shown in formula (10):

[0082]

[0083] Using the Lagrange multiplier method, we can get:

[0084]

[0085] The optimization problem shown in formula (11) can be rewritten as:

[0086]

[0087] First, v ⊥ Make an estimate, and the optimization problem is transformed into:

[0088]

[0089] Therefore, v ⊥ The result of the lth iteration is

[0090]

[0091] Next, solve for α and we get

[0092]

[0093] Substituting the results of (16) and (17) into (14), the optimization problem of M is:

[0094]

[0095] in is the projection matrix The complement. Then, by taking the derivative of the matrix M, we can get:

[0096]

[0097] Further simplification, left-multiplying and right-multiplying by M respectively can get:

[0098]

[0099] in Observed Therefore, multiply (20) by Right multiplication We can get:

[0100]

[0101] Substitute the above result into And simplifying it, we can get:

[0102]

[0103] Finally you can get

[0104]

[0105] In progress max After iterations, the above estimation results are substituted into formula (9) to obtain the final EM-ABOT detector:

[0106]

[0107] 3. Performance Analysis

[0108] Next, we analyze the performance of the algorithm. First, assume that the interference covariance matrix is:

[0109]

[0110] Among them, σ 2 I is the noise term, σ 2 =1 is the noise power, is the reverberation power, and its value can be obtained by the reverberation-to-noise ratio (RNR), that is, Unless otherwise specified, we assume RNR = 30dB. c The (i,j)th element of can be generated by the following formula:

[0111] M c (i,j)=ρ i-j (26)

[0112] Where ρ = 0.9. In addition, the signal-to-noise ratio is defined as follows:

[0113]

[0114] v t is the actual target orientation vector. In the complete matching scenario, v t Equal to v. Next, we initialize the EM iterative method,

[0115] We first evaluate the iterative convergence of the algorithm. To this end, the objective function is defined as follows:

[0116]

[0117] θ={p0,p1,M,α,v ⊥} is the unknown parameter set. Let θ (l) is the l-th iteration result of θ, then the residual between the l-th iteration and the l-1-th iteration is:

[0118]

[0119] Figure 1 shows the relationship between the mean residual and the number of iterations l for 1000 independent Monte Carlo tests under the assumptions H0 and H1, with different N and K values. Figure 1(a) shows the relationship between the mean residual and the number of iterations l under the assumption H0, and Figure 1(b) shows the relationship between the mean residual and the number of iterations l under the assumption H1. It can be seen from the figure that the residual decreases monotonically with the increase of the number of iterations. And under the condition of a given number of iterations, as N and K increase, the residual gradually decreases. This is because the larger the values ​​of N and K, the more accurate the estimation of the unknown parameters. In addition, when l ≥ 6, the residuals under the assumptions H0 and H1 are less than 10 -4 Therefore, we select l max =6, the convergence of the algorithm can be guaranteed.

[0120] In this section, we verify the detection performance of the algorithm under the condition of perfect matching, as shown in Figure 2. To ensure the constant false alarm (CFAR) probability, let P fa =10 -4 And run 100 / P fa The detection threshold is determined by performing independent Monte Carlo experiments. Figure 2(a) shows the relationship between the detection probability and the SRNR for the case of N = 8 and K = 16. As can be seen from the figure, the proposed EM-ABORT detector achieves the best detection performance among all detectors. Compared to EM-GMAP, the detection probability of EM-ABORT improves significantly at small SRNR values. When SRNR = 18dB, the detection probabilities of EM-ABORT and EM-GMAP converge to 1, resulting in a 2dB performance improvement over the GLRT, ABORT, and AMF detectors. This is because the EM-based detector integrates information under various hypotheses through latent variables, thereby statistically representing the received data. Traditional methods, on the other hand, simply discard hypotheses that may not conform to the received data model, resulting in certain errors. Therefore, compared with traditional methods, the EM-based detector achieves better detection performance. Figure 2(b) shows the relationship between the detection probability and the SRNR for the case of N = 16 and K = 32. The superiority of the EM-ABORT and EM-GMAP detectors is further verified. At the same time, compared with Figure 2(a), it can be seen that the performance of each detector has improved. This is because the larger the values ​​of N and K, the more accurate the estimation of the unknown parameters, and accordingly the better the detection performance.

[0121] Next, we verify the CFAR characteristics of the algorithm. First, in P fa =10 -4 , N=8,K=16,ρ=0.9,RNR=30dB, determine the detection threshold. Next, run 10 6The Monte Carlo experiment calculates the true false alarm probability under different RNR and ρ values, and draws the curves as shown in Figure 3. Figure 3(a) is the curve of false alarm probability changing with ρ, and Figure 3(b) is the curve of false alarm probability changing with RNR. It can be seen from the figure that with the change of RNR and ρ values, the false alarm probability is around the preset value P. fa =10 -4 Therefore, the algorithm has the CFAR property.

[0122] In this section, we consider the case of mismatch, where the true steering vector v t The suppression performance of the algorithm when there is a deviation from v. To this end, the mismatch angle φ is used to evaluate v t The degree of deviation from v is defined as:

[0123]

[0124] observe It can be concluded that cos 2 φ=1 corresponds to the perfect match, while cos 2 φ=0 means v t It is orthogonal to v in the whitened space, corresponding to the complete mismatch scenario. Figure 4 shows the constant detection probability P of each detector under mismatch conditions. d Figure 4(a) shows the contour plot for N = 8 and K = 16, while Figure 4(b) shows the contour plot for N = 16. As can be seen from the figures, compared to EM-GMAP, the EM-ABORT detector has a lower detection probability when the signal mismatch is large, effectively suppressing interfering signals with large mismatches and exhibiting better selectivity.

[0125] like Figure 5 The figure shows a flow chart of the method of the present invention, and the table below shows a specific algorithm flow.

[0126] Table 1 Algorithm flow

[0127]

[0128] In summary, the EM-ABORT detector integrates information from various hypotheses by introducing latent variables, achieving optimal detection performance under matching conditions. Furthermore, the introduction of the AOBRT method improves the ability to suppress signals with large mismatches.

[0129] This invention integrates the design concepts of both the EM-GMAP detector and the ABORT detector. By introducing latent variables, it effectively integrates information from various hypotheses and achieves more accurate parameter estimation through the expectation maximization method. This method offers superior detection performance compared to traditional adaptive detection methods. Furthermore, the incorporation of the ABORT detector design further enhances the ability to suppress interfering signals with significant mismatches.

[0130] Invention point:

[0131] 1) The present invention introduces a virtual steering vector orthogonal to the target steering vector in the whitening space to improve the ability to suppress interference signals with a large degree of mismatch.

[0132] 2) The present invention obtains a linear Gaussian model by introducing latent variables, thereby achieving effective integration of various hypothesis information.

[0133] 3) The present invention obtains accurate parameter estimation through the EM method, thereby achieving better detection performance.

[0134] 4) The present invention utilizes the maximization of the posterior probability to design an adaptive detector, thereby obtaining a higher detection probability.

[0135] The present invention combines the EM method with the AOBRT detector. On the one hand, in the case of mismatch, it has better selectivity than EM-GMAP and improves the ability to suppress interference signals with a large degree of mismatch; on the other hand, in the case of matching, it has better detection performance than ABORT.

[0136] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention and are intended to be encompassed by the claims of the present invention.

Claims

1. A design method for an adaptive target detector capable of suppressing mismatch signals, comprising: Step 1) Receive the data to be detected and the auxiliary data collected by the uniform sonar line array, and construct a binary hypothesis testing problem, including: using H0 and H1 to represent the hypothesis of no target signal and the hypothesis of target signal, respectively, to satisfy the following formula: Among them, n and n k is an independent and identically distributed interference component with a mean of 0 and a covariance matrix of Gaussian distribution; α is the unknown complex amplitude of the target; v is the target guidance vector; v ⊥ Orthogonal to v in the whitening space, v ⊥ M -1 v=0,let represents the data matrix; z represents the echo data of the unit to be detected; z k represents the kth auxiliary data; K represents the total number of auxiliary data; represents a complex domain; step 2) introducing a latent variable to obtain a linear Gaussian model of the observation data matrix, including: introducing a latent variable c representing the existence of the target, where c=0 indicates that the H0 hypothesis is true, and c=1 indicates that the H1 hypothesis is true; The probability density function of Z satisfies the following linear Gaussian model: f(Z;M,α,v ⊥ )=p0f0(Z;M,v ⊥ )+p1f1(Z;M,α) Among them, f0(Z;M,v ⊥ ) and f1(Z;M,α) represent the probability density functions of Z under the H0 and H1 assumptions, respectively; Step 3) Solve the unknown parameters in the probability density function by EM method; Step 4) Substitute the estimated result into the posterior probability to obtain the final EM-ABORT detector, thereby achieving adaptive target detection that can suppress mismatch signals; wherein the final EM-ABORT detector satisfies the following formula: in, and are p0, p1, α and v respectively ⊥ After l max The final estimation result after iterations, η is an adjustable parameter.

2. The design method of an adaptive target detector capable of suppressing mismatch signals according to claim 1, characterized in that: The step 1) comprises: The array is composed of N array elements with equal spacing. The array element spacing is d = λ / 2, where λ is the working wavelength. The received echo data is processed to form 3. The design method of an adaptive target detector capable of suppressing mismatch signals according to claim 2, characterized in that: The step 2) comprises: The probability mass function of the latent variable c is P(c=t)=p t ,t=0,1;where p0+p1=1.

4. The design method of an adaptive target detector capable of suppressing mismatch signals according to claim 2, characterized in that: The step 3) comprises: Introducing the adjustable parameter η, we can obtain the adjustable false alarm probability P fa , design the EM-ABORT detector with the test statistic satisfying the following formula: in, and are p0, p1, M, α and v respectively ⊥ After l max The final estimation result after iterations; The unknown parameters p={p0,p1} and θ={M,v ⊥ ,α}.

5. The design method of an adaptive target detector capable of suppressing mismatch signals according to claim 4, characterized in that: The parameter p={p0, p1} in step 3) is obtained according to the following steps: Step S1) The result of the first iteration of p for: in, and They are respectively expressed as the posterior distribution of Z under the H0 and H1 assumptions, satisfying the following formula: Step S2) solve the optimization problem: Step S3) Use Lagrange multiplier method to get the estimated values ​​of p0 and p1 and 6. The design method of an adaptive target detector capable of suppressing mismatch signals according to claim 5, characterized in that: The parameter θ in step 3) is ⊥ ,α} is obtained according to the following steps: The result of the first iteration of step T1)θ is: Step T2) solve the optimization problem: Step T3) v ⊥ Make an estimate and transform the optimization problem into: Get v ⊥ The lth iteration result for: Step T4) Get the lth iteration result of α for: Step T5) converts the and step T4) Substitute into the optimization problem of step T2) and get the lth iteration result of M for: in, is the projection matrix of supplement.

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