Design method of adaptive target detector capable of suppressing mismatch signal

Abstract

The invention discloses a design method of a self-adaptive target detector capable of suppressing mismatch signals, which comprises the following steps of: 1) receiving to-be-detected and auxiliary data acquired by a uniform sonar linear array, and constructing a binary hypothesis test problem, and 2) introducing a latent variable to obtain a linear Gaussian model of an observation data matrix; 3) respectively solving unknown parameters in the probability density function through an EM method; and 4) substituting an estimation result into a posterior probability to obtain a final EM-ABOT detector, and realizing adaptive target detection capable of suppressing mismatch signals. According to the method, the linear Gaussian model is constructed by introducing the latent variables, the information under each hypothesis is effectively integrated, a more accurate parameter estimation result is obtained, the high detection probability is obtained, meanwhile, interference signals with the large mismatch degree can be effectively restrained, and the signal selection capacity of a detector is improved.

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 sends acoustic signals and receives echoes reflected by scatterers to complete underwater detection, identification, tracking and other tasks. It is an important means of underwater information acquisition. In shallow sea environments, reverberation caused by irregular scattering and superposition of the sea surface, seabed and water body is the main interference of active sonar. In the process of suppressing reverberation, in order to cope with the space-time coupling of shallow sea reverberation, underwater space-time adaptive detection (STAD) technology based on space-time two-dimensional joint processing came into being, which can effectively combat space-time coupled reverberation and improve the working efficiency of active sonar. In recent years, adaptive target detection technology under unknown Gaussian background has received widespread attention, and a large number of adaptive detection algorithms have been proposed. Such as generalized likelihood ratio (GLRT) detector, adaptive matched filter (AMF), adaptive correlation estimator (ACE), Rao detector, etc. Recently, scholars 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, the information under each hypothesis is effectively integrated, and a more accurate unknown parameter estimation result is obtained through the expectation maximization method (EM). Then, the detection statistic is designed using the posterior distribution of the received data, and the EM-GMAP detector is finally obtained. In the matching case, that is, when the true target direction is considered to be consistent with the beam pointing angle, the EM-GMAP detector has a higher detection probability. However, in actual application scenarios, factors such as antenna calibration error, beam pointing error, and electromagnetic wave propagation multipath effect may cause deviations between the target incoming wave direction (AoA) and the sonar pointing direction, resulting in mismatch problems. When the degree of mismatch is large, the EM-GMAP detector still has a high detection probability, cannot effectively suppress signals with a large degree of mismatch, and has poor signal selection ability.

[0003] In order to effectively suppress signals with a large degree of mismatch, Adaptive Beamforming Orthogonal Suppression Test (ABORT) was proposed. ABORT modifies the null hypothesis in the binary hypothesis test problem and introduces a virtual signal that is orthogonal to the real target in the whitening space. Through such a correction, the detector is more inclined to judge that the null hypothesis is true when the degree of mismatch is large, thereby improving the ability to select mismatched signals. However, the detection performance of the ABORT detector is not ideal in the matching situation, and its detection performance is poor compared to EM-GMAP. Summary of the invention

[0004] For the existing EM-GMAP detector based on MAP, when the mismatch degree is large, the detector still has a high detection probability, cannot effectively suppress the signal with a large mismatch degree, and has poor signal selection ability. The ABORT detector introduced to improve the signal selection ability has poor detection performance under matching conditions. The purpose of the present invention is to overcome the above-mentioned defects of the prior art, combine the EM-MAP method with the ABORT method, and propose an adaptive target detector that can suppress mismatch signals, so as to obtain good detection performance and effectively suppress interference signals with a large mismatch degree.

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

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

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

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

[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 equal spacing. The array element spacing is d = λ / 2, where λ is the working 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 an 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 a 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 assumptions H0 and H1, respectively.

[0019] Preferably, the step 3) comprises:

[0020] Introducing an adjustable parameter η, we can obtain an 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] The superscript (l-1) indicates the result of the (l-1)th iteration. 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 is 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 result of the first iteration 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 The 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 integrates the information under various assumptions, obtains more accurate parameter estimation results, and thus achieves the best detection performance under matching conditions.

[0051] 2. While obtaining a high detection probability, the present invention can effectively suppress interference signals with a large mismatch degree and improve 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, where 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] FIG2 is a detection performance curve of the algorithm under the condition of complete matching, wherein FIG2(a) shows the relationship between the detection probability and the SRNR under the condition of N=8 and K=16, and FIG2(b) shows the relationship between the detection probability and the SRNR under the condition of N=16 and K=32;

[0054] Figure 3 is a curve showing the variation of false alarm probability with RNR and ρ, where Figure 3(a) is a curve showing the variation of false alarm probability with ρ, and Figure 3(b) is a curve showing the variation of false alarm probability 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 It is a flow chart of the design method of the adaptive target detector capable of suppressing mismatch signals of the present invention. DETAILED DESCRIPTION

[0057] In response to the above problems, we comprehensively considered the design ideas of EM-MAP detector and ABORT detector and proposed the design method of EM-ABORT detector. On the one hand, we obtained better detection performance in the matching situation, and on the other hand, we effectively suppressed the interference signal with a large mismatch degree in the mismatch situation, thus improving the selectivity of the detector.

[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 of 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 an equally spaced uniform linear array with an array element spacing of d = λ2, where λ is the working wavelength. The sonar system receives echo data from the unit to be detected (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-oriented 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 an 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 lth 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, They are p0, p1, M, and v respectively. ⊥ , the estimated result 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 step E is the posterior distribution of Z under the H0 and H1 assumptions, which can 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 ensure iterative convergence. 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 an 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, ⊥ The result of the lth iteration is

[0090]

[0091] Next, solve for α and we get

[0092]

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

[0094]

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

[0096]

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

[0098]

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

[0100]

[0101] Substituting 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 equation (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, If there is no special explanation, we set RNR = 30dB. Reverberation covariance matrix M 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-oriented vector. In the complete matching scenario, v t is 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 result of the lth iteration of θ, then the residual between the lth iteration and the l-1th 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 for different N and K conditions. 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 both less than 10 -4 Therefore, we choose 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 complete 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 an independent Monte Carlo experiment. Figure 2(a) shows the relationship between the detection probability and SRNR when N=8 and K=16. It can be seen from the figure that the proposed EM-ABORT detector has the best detection performance among all detectors. Compared with EM-GMAP, the detection probability of EM-ABORT is significantly improved under small SRNR values, and when SRNR=18dB, the detection probabilities of EM-ABORT and EM-GMAP converge to 1, which is 2dB better than the GLRT, ABORT and AMF detectors. This is because the detector based on the EM method integrates the information under each hypothesis through latent variables, thereby statistically expressing the received data. The traditional method directly discards the hypothesis that may not conform to the received data model roughly, resulting in a certain error. Therefore, compared with the traditional method, the detector based on the EM method has better detection performance. Figure 2(b) shows the relationship between the detection probability and SRNR when N=16 and K=32. Among them, the superiority of EM-ABORT and EM-GMAP detectors is verified again. At the same time, by comparing with Figure 2(a), it can be seen that the performance of each detector has been improved. This is because the larger the values ​​of N and K, the more accurate the estimation of the unknown parameters, and the better the detection performance accordingly.

[0121] Next, we verify the CFAR properties of the algorithm. fa =10 -4 , N = 8, K = 16, ρ = 0.9, RNR = 30dB to determine the detection threshold. Next, run 10 6The Monte Carlo experiment calculates the true false alarm probability under different RNR and ρ values, and the curves are 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 changes with 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 algorithm’s suppression performance when there is a mismatch between v and 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 The formula can be obtained, cos 2 φ=1 corresponds to a perfect match, while cos 2 φ=0 means v t 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) is the contour map when N=8, K=16, and Figure 4(b) is the contour map when N=16. It can be seen from the figure that compared with EM-GMAP, the EM-ABORT detector has a lower detection probability when the signal mismatch is large, can effectively suppress the interference signal with a large mismatch, and has 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 the information under various assumptions by introducing latent variables, thereby achieving the best detection performance under matching conditions. At the same time, by introducing the AOBRT method, the ability to suppress signals with large mismatches is improved.

[0129] The present invention comprehensively considers the design ideas of the EM-GMAP detector and the ABORT detector. On the one hand, by introducing latent variables, the information under each hypothesis is effectively integrated, and more accurate parameter estimation is achieved through the expectation maximization method. Compared with the traditional adaptive detection method, it has better detection performance. On the other hand, the introduction of the design idea of ​​the ABORT detector further improves the ability to suppress interference signals with a large degree of mismatch.

[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 maximum a posteriori 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 only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A design method for an adaptive target detector capable of suppressing mismatch signals, comprising: Step 1) receiving the data to be detected and the auxiliary data collected by the uniform sonar line array, and constructing a binary hypothesis testing problem; Step 2) introducing latent variables to obtain a linear Gaussian model of the observation data matrix; Step 3) Solving the unknown parameters in the probability density function by EM method respectively; 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.

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 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; 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: Among them, n,n k , k=1,…,K is an 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 a data matrix.

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: 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: 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 assumptions H0 and H1, respectively.

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 an adjustable parameter η, we can obtain an 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 iteration; The unknown parameters p={p0,p1} and θ={M,v ⊥ ,α}.

5. The adaptive target detection method capable of suppressing mismatch signals according to claim 4, characterized in that: The parameter p={p0, p1} of step 3) is obtained according to the following steps: Step S1) The result of the first iteration of p for: The superscript (l-1) indicates the result of the (l-1)th iteration. 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 4, characterized in that: The parameters of step 3) are θ={M,v ⊥ ,α} is obtained according to the following steps: Step T1) The lth iteration result of θ is θ (l) for: Step T2) Solve the optimization problem: Step T3) v ⊥ Make an estimate and transform the optimization problem into: Get v ⊥ The result of the first iteration 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 α for: in, is the projection matrix The supplement.

7. The design method of an adaptive target detector capable of suppressing mismatch signals according to claim 6, characterized in that: The final EM-ABOT detector in step 4) satisfies the following formula:

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