A two-order tunable space-time adaptive detection method

Abstract

The present invention discloses a two-order tunable space-time adaptive detection method, the method comprising: receiving the data to be detected collected by a uniform sonar line array to obtain an observation data matrix; designing a two-order tunable space-time adaptive detector, and respectively calculating the corresponding detection statistics, the two-order tunable space-time adaptive detector comprising a first-order AMF detector and a second-order EnRAO detector; according to the false alarm probability, determining the threshold pair that the two-order tunable space-time adaptive detector meets the robustness and interference suppression requirements; comparing the threshold pair with the detection statistic, if it meets the requirements, it is judged that the target to be detected exists, otherwise the target to be detected does not exist. The method of the present invention solves the problem of poor interference suppression capability in the case of target mismatch, achieves a balance between robustness and interference suppression capability, and effectively improves the interference suppression capability of the system.

Description

Technical Field

[0001] The invention relates to the field of sonar technology, and in particular to a two-order tunable space-time adaptive detection method. Background Art

[0002] In the problem of adaptive signal detection, the design of the detector usually needs to have two properties: one is the robustness of the corresponding target signal, and the other is the suppression of interference signals. Usually a single detector cannot balance the two properties.

[0003] Since the actual application scenarios are relatively complex, it is hoped that the designed detector can balance the two performances. Steering vector mismatch is one of the important factors affecting adaptive detection. When the actual steering vector is inconsistent with the nominal steering vector, a mismatch occurs. Mismatch will lead to a decrease in detection performance, and in severe cases, the detector may not work properly. Steering vector mismatch is usually caused by a variety of reasons, such as array element consistency deviation, array installation error, transmission waveform distortion, and channel distortion.

[0004] Therefore, in order to be able to conveniently choose between the two performances or obtain a certain balance state, based on the tunable method, the threshold is used to adjust the balance between the robustness and interference suppression of the detector, that is, to allow the detector to have a smaller loss in the matching situation and provide better suppression capability for mismatched interference signals.

[0005] In adaptive signal detection, traditional methods mostly use first-order detectors, which cannot take into account both robustness and interference suppression performance. The existing implementation scheme is a second-order tunable space-time adaptive AMF-RAO detector, which selects a first-order AMF detector and a second-order RAO detector. This method has good detection performance when the steering vector matches, but has relatively poor interference suppression ability when the steering vector mismatches. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and propose a two-order tunable space-time adaptive detection method to adjust the balance between the robustness of the detector and the interference suppression performance.

[0007] The present invention proposes a two-order tunable space-time adaptive detection method, the method comprising:

[0008] Step 1) receiving the data to be detected collected by the uniform sonar line array to obtain an observation data matrix;

[0009] Step 2) designing a two-order tunable space-time adaptive detector and calculating corresponding detection statistics respectively, wherein the two-order tunable space-time adaptive detector includes a first-order AMF detector and a second-order EnRAO detector;

[0010] Step 3) determining a threshold pair that meets the robustness and interference suppression requirements of the two-order tunable space-time adaptive detector according to the false alarm probability;

[0011] Step 4) compare the threshold pair with the detection statistic. If the requirements are met, it is determined that the target to be detected exists; otherwise, the target to be detected does not exist.

[0012] As an improvement of the above method, the step 1) specifically includes:

[0013] A uniform sonar line array is composed of N array elements, using an N×1 dimensional vector Indicates the main data to be detected received by the array. z k represents the kth auxiliary data located near the main data, K represents a total of K auxiliary data, represents a complex domain;

[0014] Based on the binary hypothesis test, H0 and H1 are used to represent the hypothesis of no target signal and the hypothesis of target signal, respectively, satisfying the following formula:

[0015]

[0016] in, n,n k Respectively represent the background noise data in the data to be detected and the auxiliary data, both of which obey independent and identically distributed Gaussian random distributions with zero mean and the same covariance matrix; represents the unit-normalized main lobe target steering vector, and v0 represents the nominal steering vector; a represents the unknown complex amplitude scalar parameter of the received signal, which represents the reflection characteristics of the target and the channel fading properties; Z = [z1, z2, …, z k , …, z K ], k = 1, ..., K, Z represents a set of auxiliary data used to estimate the covariance matrix M, then

[0017]

[0018] Among them, E[·] represents the expectation, Represents the conjugate transpose operation.

[0019] As an improvement of the above method, the step 2) specifically includes:

[0020] The detection statistic t of the first-order AMF detector is calculated according to the following formula: AMF :

[0021]

[0022] The detection statistic t of the second-order EnRAO detector is calculated according to the following formula:EnRAO :

[0023]

[0024] Among them, β is a random variable that satisfies the following formula:

[0025]

[0026]

[0027] is a random variable that satisfies the following formula:

[0028]

[0029] As an improvement of the above method, the step 3) specifically includes:

[0030] The false alarm probability P of the two-order tunable space-time adaptive detector is obtained according to the following formula: fa Regarding the threshold pair (η A , η E ) function, with constant false alarm characteristics:

[0031]

[0032] Among them, F0(·) represents the random variable given β under the H0 hypothesis. The cumulative probability distribution function of p0(·) is The probability density function of the distribution model, u represents a random variable belonging to [0, ∞], which is used for integration operations;

[0033] According to the above formula, the false alarm probability P fa The contour plot under the condition of fa The threshold that meets the requirements is (η A , η E ).

[0034] As an improvement of the above method, the step 4) specifically includes:

[0035] The detection statistic and the threshold are matched (η A , η E ) is compared with, if the detection statistic t of the first-order AMF detector AMF >η A And the detection statistic t of the second-order EnRAO detector EnRAO >η E , then the target to be detected exists, if t AMF <η A or EnRAO<η E , the target to be detected does not exist.

[0036] Compared with the prior art, the advantages of the present invention are:

[0037] The present invention studies a multi-channel point target detection method under Gaussian reverberation background in the case of guidance vector mismatch, and proposes a two-order space-time adaptive AMF-EnRAO detector, which solves the problem of poor interference suppression capability in the case of target mismatch, balances robustness and interference suppression capability, and effectively improves the interference suppression capability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of a two-order tunable space-time adaptive detection method of the present invention;

[0039] Figure 2 The AMF-EnRAO detector P of the present invention fa =1e-4, 1e-3, 1e-2, 1e-1 contour plot;

[0040] FIG3 is a performance comparison of the AMF-EnRAO detector of the present invention and the existing AMF detector, wherein FIG3(a) is a P d With the SNR change curve; Figure 3 (b) is P d With SNR and cos 2 The variation curve of θ;

[0041] FIG4 is a performance comparison of the AMF-EnRAO detector of the present invention and the existing AMF-RAO detector, wherein FIG4(a) is P d With the SNR change curve; Figure 4 (b) is P d With SNR and cos 2 Variation curve of θ. DETAILED DESCRIPTION

[0042] Based on the tunable method, the present invention designs a two-order tunable space-time adaptive detection method. Specifically, the method is composed of a first-order AMF detector with good robustness and a second-order Enhanced RAO (EnRAO) detector with good interference suppression performance. The false alarm probability P of the new detector is derived fa and the detection probability P d The closed-form expression of . The new method has a constant false alarm characteristic for the background covariance matrix. By adjusting the threshold pair parameters of the tunable detector, its performance can be freely selected between the AMF and EnhancedRAO detectors, and a two-order tunable adaptive detector with both robustness and interference suppression capability is obtained.

[0043] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0044] Example 1

[0045] Embodiment 1 of the present invention provides a two-order tunable space-time adaptive detection method. The method comprises:

[0046] Step 1) receiving the data to be detected collected by the uniform sonar line array to obtain an observation data matrix;

[0047] Step 2) designing a two-order tunable space-time adaptive detector and calculating corresponding detection statistics respectively, wherein the two-order tunable space-time adaptive detector includes a first-order AMF detector and a second-order EnRAO detector;

[0048] Step 3) determining a threshold pair that meets the robustness and interference suppression requirements of the two-order tunable space-time adaptive detector according to the false alarm probability;

[0049] Step 4) compare the threshold pair with the detection statistic. If the requirements are met, it is determined that the target to be detected exists; otherwise, the target to be detected does not exist.

[0050] 1 Theoretical approach

[0051] Consider a linear receiving array consisting of N array elements, using an N×1 dimensional vector To represent the main data to be detected received by the array, Represents K auxiliary data located near the main data. For the binary hypothesis test problem, H0 and H1 are used to represent the hypothesis of no target signal and the hypothesis of target signal respectively. Then the problem can be expressed as:

[0052]

[0053] in,

[0054] (1)n, They represent the background noise data in the main and auxiliary data respectively, which obey the independent and identically distributed Gaussian random distribution with zero mean and the same covariance matrix.

[0055] (2) Represents the unit-normalized mainlobe target steering vector. Usually we can use v0 to represent the nominal steering vector.

[0056] (3) a represents the unknown complex amplitude scalar parameter of the received signal, which characterizes the reflection characteristics of the target and the fading properties of the channel.

[0057] (4) Z = [z1, z2, ..., z k ], k = 1,…, K represents a set of auxiliary data used to estimate the covariance matrix.

[0058] Its covariance matrix is ​​denoted as M. Then we have

[0059]

[0060] Among them, E[·] represents the expectation, Represents the conjugate transpose operation.

[0061] AMF detection statistic t EnRAO It can be expressed as

[0062]

[0063] EnRAO's detection statistics

[0064]

[0065] Among them, t K Represents Kelly's GLRT test statistic

[0066]

[0067]

[0068]

[0069] The AMF-EnRAO two-stage tunable detector structure can be expressed as follows

[0070]

[0071] Among them, η A and η E They represent the thresholds of the first-order AMF and the second-order Enhanced RAO detector in the newly formed two-order detector. The two thresholds can be recorded as (η A , η E ) form a threshold pair of the new detector, corresponding to the same P fa There are an infinite number of threshold pair combinations possible.

[0072] 2 Performance Evaluation

[0073] Here, closed expressions for the detection probability and false alarm probability of the new two-order space-time detector are given.

[0074] 2.1 False Alarm Probability P fa

[0075] Under the H0 hypothesis:

[0076] (1) When β is given, It obeys the central complex F distribution with 1 degree of freedom and K-N+1, denoted as

[0077] (2) β is a random variable that follows a centralized complex Beta distribution with degrees of freedom K-N+2, N-1, denoted by

[0078] For the AMF-EnRAO two-stage detector, the false alarm probability P fa It can be written as:

[0079]

[0080] Among them, F0(·) represents the random variable given β under the H0 hypothesis. The cumulative probability distribution function (CDF) of Probability density function of the distribution model.

[0081] From formula (11), we can see that the false alarm probability of the AMF-EnRAO detector is the threshold value (η A , η E ). It can be seen that P fa It is independent of the data covariance matrix M. Therefore, the detector has a constant false alarm characteristic.

[0082] Figure 2 Draw P fa 10 respectively -4 , 10 -3 , 10 -2 The corresponding false alarm probability curve. In the figure, the horizontal axis η ENRAO That is η E , the vertical coordinate η AMF That is η A The vertical coordinate sets the threshold along the equal probability curve (η A , η E ), the AMF-EnRAO detector can choose the balance between detection performance and interference suppression performance according to system requirements. E =0 and η A = 0, the new detector will degenerate into a single-order AMF and EnRAO detector respectively. Therefore, by adjusting the value of the threshold pair, the new detector can obtain the characteristics of the single-order AMF and EnRAO detectors while maintaining the performance of CFAR.

[0083] 2.2 Detection Probability P d

[0084] Assume that the target's true guidance vector is v m The mismatch angle between the nominal steering vector v and the nominal steering vector v is denoted by θ. When θ≠0, it is called steering vector mismatch, which will cause loss of detector performance.

[0085] Under the H1 assumption, when the received data contains the target signal:

[0086] (1) When β is given, It follows a non-centralized complex F distribution with 1 degree of freedom, K-N+1, and has a non-centrality parameter of

[0087] δ θ =βSNR cos 2 θ

[0088] Remember to do in, Defined as the signal-to-noise ratio.

[0089] definition

[0090]

[0091] (2)β is a random variable that follows a non-centralized complex Beta distribution with degrees of freedom K-N+2, N-1, and its parameters are

[0092] δ β =SNRsin 2 θ (10)

[0093] Remember to do,

[0094] When the steering vector mismatch occurs, θ≠0, the detection probability of the detector is P d Defined as a function of θ, it can be expressed as:

[0095] P d (θ)=P[t AMF >η A , t EnRAO >η E ; H1]

[0096]

[0097] Among them, F1(·) means that under the H1 assumption, when β is given, the random variable The cumulative probability distribution function (CDF) of Probability density function of the distribution model.

[0098] 3 Performance Analysis

[0099] The performance of the AMF-EnRAO detector is analyzed by simulation method, and the measured data is used to verify the performance of the new detector and the AMF and AMF-EnRAO methods. In the simulation, the complex exponential correlation Gaussian distribution vector is selected as the noise model, and its heterogeneous correlation coefficient ρ = 0.9, that is, the (i, j)th element of the data covariance matrix M is ρ|i-j| , the signal-to-noise ratio is defined as

[0100] In order to compare the suppression performance of the detectors for mismatched signals, a comparison criterion needs to be selected. Here, a set of threshold pairs (η A , η E ), so that the selected specific AMF-EnRAO detector has similar detection performance to the AMF detector in the matching case, and then compares the performance of the two in the mismatched case.

[0101] Figure 3 shows the detection probability P of a selected AMF-EnRAO detector and the AMF detector. d The curves of the signal-to-noise ratio (SNR) and the equal detection probability curves, N = 64, K = 96. As can be seen from Figure 3(a), when cos 2 When θ=1, that is, when the steering vectors match, the two detectors have an intersection in the detection probability curves. This means that at low signal-to-noise ratios, the AMF-EnRAO detector has better detection performance than the AMF detector. In the case of high signal-to-noise ratios, the AMF-EnRAO detector has performance loss compared to the single AMF detector. In the case of mismatched steering vectors (taking cos 2 θ=0.6), compared with the AMF detector AMF-EnRAO can provide good interference suppression capability.

[0102] Figure 3(b) shows the signal-to-noise ratio (SNR) and the mismatch angle (cos) for equal detector probability. 2 θ variation curve. We selected an AMF-EnRAO detector that has the same detection performance as the AMF detector when the detection probability is 0.8 in the matching situation. It can be seen that in the case of mismatch, when the signal-to-noise ratio is 30dB, this detector can provide better interference suppression capability than the AMF detector.

[0103] Similar to the above situation, a group of AMF-EnRAO and AMF-RAO detectors are selected here, which have similar detection performance under signal matching conditions. The performance comparison of this group of detectors is given in Figure 4. fa =10 -4 , N = 64, K = 96. As can be seen from Figure 4(a), when the steering vector matches, i.e., cos 2 When θ = 1, the detection probability curves of the two detectors are similar, especially in the case of high signal-to-noise ratio, they almost overlap. 2When θ = 0.6, the AMF-EnRAO detector has better interference suppression performance than the AMF-RAO detector. Similar to the situation in Figure 3(b), it can be seen from Figure 4(b) that the AMF-EnRAO detector provides better interference suppression capability than the AMF-RAO detector.

[0104] In summary, the two-order tunable space-time adaptive detection method proposed in the present invention comprises the following steps:

[0105] 1) Obtain data collected by uniform sonar line array

[0106] Among them, the number of sonar array elements is N, and each array element receives K collected data Get the observation data matrix Z = [z1, z2, ..., z k ],k=1,…,K

[0107] 2) The test statistic t is obtained by formula (2) and formula (3): AMF and t EnRAO ;

[0108] 3) According to the system's requirements for robustness and interference suppression and the false alarm probability P fa Determine threshold pairs;

[0109] 4) Compare the detection statistic of the two-stage detector with the threshold pair using formula (7);

[0110] 5) When the detection statistics of the two-stage detectors are both greater than the threshold, the target is judged to exist, otherwise it is judged that the target does not exist.

[0111] The method of the present invention is based on the design requirements of the system. By adjusting the threshold pair, the detector can adjust between the robustness of the AMF detector and the interference suppression performance of the EnRAO detector. In the case of target mismatch, the interference suppression capability of the AMF-EnRAO detector is better than that of the AMF and AMF-RAO detectors.

[0112] 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 two-order tunable space-time adaptive detection method, the method comprising: Step 1) receiving the data to be detected collected by the uniform sonar line array to obtain an observation data matrix; Step 2) designing a two-order tunable space-time adaptive detector and calculating corresponding detection statistics respectively, wherein the two-order tunable space-time adaptive detector includes a first-order AMF detector and a second-order EnRAO detector; Step 3) determining a threshold pair that meets the robustness and interference suppression requirements of the two-order tunable space-time adaptive detector according to the false alarm probability; Step 4) comparing the threshold pair with the detection statistic, if the requirement is met, it is determined that the target to be detected exists, otherwise the target to be detected does not exist; The step 2) specifically includes: The detection statistic t of the first-order AMF detector is calculated according to the following formula: AMF : The detection statistic t of the second-order EnRAO detector is calculated according to the following formula: EnRAO : Among them, β is a random variable that satisfies the following formula: is a random variable that satisfies the following formula: The step 3) specifically includes: The false alarm probability P of the two-order tunable space-time adaptive detector is obtained according to the following formula: fa Regarding the threshold pair (η A ,η E ) function, with constant false alarm characteristics: P fa (or A ,or E )=P[t AMF >the A ,t EnRAO >the E ;H0] Among them, F0(·) represents the random variable given β under the H0 hypothesis. The cumulative probability distribution function of p0(·) is The probability density function of the distribution model, u represents a random variable belonging to [0,∞], which is used for integration operations; According to the above formula, the false alarm probability P fa The contour plot under the condition of fa The threshold that meets the requirements is (η A ,η E ).

2. The two-order tunable space-time adaptive detection method according to claim 1, characterized in that: The step 1) specifically includes: A uniform sonar line array is composed of N array elements, using an N×1 dimensional vector Indicates the main data to be detected received by the array. k=1,…,K,z k represents the kth auxiliary data located near the main data, K represents a total of K auxiliary data, represents a complex domain; Based on the binary hypothesis test, H0 and H1 are used to represent the hypothesis of no target signal and the hypothesis of target signal, respectively, satisfying the following formula: in, k=1,…,K,n,n k Respectively represent the background noise data in the data to be detected and the auxiliary data, both of which obey independent and identically distributed Gaussian random distributions with zero mean and the same covariance matrix; represents the unit-normalized main lobe target steering vector, and v0 represents the nominal steering vector; a represents the unknown complex amplitude scalar parameter of the received signal, which represents the reflection characteristics of the target and the channel fading properties; Z = [z1, z2, …, z k ,…,z K ], k=1,…,K, Z represents a set of auxiliary data used to estimate the covariance matrix M, then Among them, E[·] represents the expectation, Represents the conjugate transpose operation.

3. The two-order tunable space-time adaptive detection method according to claim 2, characterized in that: The step 4) specifically includes: The detection statistic and the threshold are matched (η A ,η E ) is compared with, if the detection statistic t of the first-order AMF detector AMF >η A And the detection statistic t of the second-order EnRAO detector EnRAO >η E , then the target to be detected exists, if t AMF <η A or EnRAO <η E , the target to be detected does not exist.

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