A robust detection method for source number based on translation invariance

Abstract

The present invention discloses a robust detection method for source numbers based on translation invariance. Firstly, a data matrix is ​​constructed, and then a potential signal subspace is extracted from an impulse noise environment in a robust manner, and the rank of the subspace is estimated. The method has the characteristics of being resistant to impulse spikes and having a small amount of calculation.

Description

Technical Field

[0001] The invention relates to the technical field of signal processing, and in particular to a robust detection method for signal source numbers based on translation invariance. Background Art

[0002] The development of underwater acoustic communication technology is a need for the national marine strategy and modern naval construction. Due to the severe attenuation of electromagnetic waves in water, high-frequency radio communications cannot be applied to underwater communication scenarios. The communication between underwater vehicles and mother ships / bases can adopt an ultra-low frequency band of 3-300Hz. Practice has proved that the suitable carrier frequency for underwater acoustic communication is about 4kHz, which shows that its BW0.707 bandwidth is extremely low, which is essentially different from the high-frequency radio communication that people are familiar with. In addition, the marine environment is complex and the noise interference is large. Therefore, underwater acoustic communication technology is quite difficult. Although conventional wireless communication technology cannot be directly applied to underwater acoustic communication, it is the same in principle. In general, we deal with baseband signals. Therefore, the key to signal processing for underwater acoustic communication lies in the correction of traditional models. This patent proposes a robust detection method for the number of signal sources based on translation invariance, which is used to detect the number of underwater target objects.

[0003] In an impulse noise environment, the number of detection sources K, the signal model diagram is as shown in the attached Figure 5 :

[0004] There is a uniform linear array (ULA) composed of N sensors, which is used to receive the fluctuation signals s1(t),s2(t),…,s from K targets. K (t). At time t, the signal received by the ULA can be modeled as:

[0005] y(t)=As(t)+n(t),t=1,2,…,T,

[0006] in,

[0007] y(t)=[y1(t) … y N (t)] T ,

[0008] s(t)=[s1(t) … s K (t)] T ,

[0009] A=[a(θ1) … a(θ K )],

[0010]

[0011] λ is the signal wavelength, d is the array element spacing, θ kis the direction angle of the kth target, and n(t)=[n1(t) … n N (t)] T is the noise on each array element at time t.

[0012] Here, the noise vector n(t) is modeled as impulsive noise.

[0013] For the above model, the existing source detection scheme is:

[0014] 1) Information theory criteria, including MDL criterion, AIC criterion, GIC criterion, etc.: not applicable to impulse noise and attenuated signals;

[0015] 2) Rank estimation methods, including SAMOS, ESTER, MUSIC, etc.: not applicable to impulse noise;

[0016] 3) Robust information theory criteria, including robust MDL criterion, robust AIC criterion, robust BIC criterion, etc.: They are not applicable to attenuated signals and consistency cannot be guaranteed;

[0017] 4) MCD estimator, MM estimator: consistency cannot be guaranteed. Summary of the invention

[0018] In view of the defects existing in reality, the present invention provides a robust detection method for source number based on translation invariance.

[0019] In order to solve the above technical problems, the technical solution of the present invention is:

[0020] A robust detection method for source number based on translation invariance comprises the following steps:

[0021] First, construct the data matrix:

[0022] Y=X+N,

[0023] Among them, Y = [y(1) … y(T)], X = A[s(1) … s(T)] and N = [n(1) … n(T)] are the clean signal and noise signal parts respectively.

[0024] On the one hand, by singular value decomposition, we can get:

[0025]

[0026] in, and They are respectively composed of the left singular vector and the right singular vector corresponding to the largest K singular values ​​of X, and is a diagonal matrix whose diagonal elements are the largest K singular values ​​of X.

[0027] On the other hand, since the rank of X is K, X can be decomposed into:

[0028]

[0029] in, and is a column full rank matrix. K =[a1 … a K ].

[0030] Comparing (1) and (2), we can get that the signal subspace of X is:

[0031]

[0032] Here we propose that by estimating A K Obtain signal subspace information by minimizing the fitting error l p -norm (1≤p<2), estimate A K :

[0033]

[0034] Regarding the method of solving (3):

[0035] Using a loop iteration method, in the tth iteration, the following two sub-problems are solved in sequence:

[0036]

[0037] For all possible values ​​of the number of sources l = 1, 2, ..., L:

[0038] When l = K, estimate A in turn K The columns are:

[0039]

[0040]

[0041] Among them, a k , b k are the kth columns of A and B (k = 1, 2, ..., K). Formula (6) shows that when estimating the kth column (a k ,b k ), the previous columns are fixed to the estimated values, that is: The low-rank decomposition performed according to formula (6) is called serial robust low-rank decomposition.

[0042] It can be seen that when l = K, the serial robust low-rank decomposition method is equivalent to the greedy algorithm. Definition By AK is composed of the left singular vectors corresponding to its largest K singular values. Since the signal subspace Therefore satisfies translational invariance:

[0043]

[0044] where and respectively represent the matrices composed of the bottom N - 1 and top N - 1 rows of , and is an orthogonal matrix.

[0045] Therefore, the rank of the matrix is K.

[0046] · When l < K, the low - rank decomposition procedure in Equation (6) stops after estimating ;

[0047] · When l > K, the low - rank decomposition procedure in Equation (6) continues until all estimations are completed.

[0048] Therefore, when l ≠ K, A l = [a1 … a l does not satisfy translational invariance, and the rank of the matrix is greater than l, where is composed of the left singular vectors corresponding to the largest l singular values of A l .

[0049] In practice, we cannot obtain the clean signal X. Therefore, estimating from the observed data matrix Y is denoted as

[0050] Based on the above, we can estimate the rank of the signal subspace , that is, the number of signal sources K, by comparing the magnitudes of the smallest l singular values of the matrix .

[0051] Specifically, the detection criterion for the number of signal sources K is:

[0052]

[0053] where L < min{(N - 1) / 2, T}, and

[0054]

[0055] Here, is The smallest l singular values ​​of .

[0056] By adopting the above technical solution, the present invention has the following beneficial effects:

[0057] First, compared with the l2-norm, l p -norm has good resistance to pulse spikes;

[0058] Secondly, according to the traditional rank estimation idea, it is necessary to estimate the potential signal subspace for all possible values ​​of the number of signal sources l = 1, 2, ..., L. After that, the corresponding cost function value is calculated, and the rank estimation of the signal subspace is obtained by comparison - this method is very computationally intensive. The serial robust low-rank decomposition method described in the present invention can effectively reduce the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 The performance comparison of various detection schemes of the algorithm of the present invention in the GMM noise environment is shown in FIG.

[0060] Figure 2 The performance comparison of the algorithm of the present invention among various detection schemes in a GGD noise environment is shown in Figure 1. The horizontal axis is the signal-to-noise ratio, and the vertical axis is the correct detection probability.

[0061] Figure 3 Figure 2 is a graph of the threshold signal-to-noise ratio (dB) of various detection schemes in a GMM noise environment.

[0062] Figure 4 This is a graph of the threshold signal-to-noise ratio (dB) of various detection schemes in a GGD noise environment.

[0063] Figure 5 It is a schematic diagram of a signal model in the background technology. DETAILED DESCRIPTION

[0064] The specific embodiments of the present invention are further described below in conjunction with the accompanying drawings. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0065] Embodiment 1:

[0066] A robust detection method for source number based on translation invariance comprises the following steps:

[0067] First, construct the data matrix:

[0068] Y=X+N,

[0069] Among them, Y = [y(1) … y(T)], X = A[s(1) … s(T)] and N = [n(1) … n(T)] are the clean signal and noise signal parts respectively.

[0070] On the one hand, by singular value decomposition, we can get:

[0071]

[0072] in, and They are respectively composed of the left singular vector and the right singular vector corresponding to the largest K singular values ​​of X, and is a diagonal matrix whose diagonal elements are the largest K singular values ​​of X.

[0073] On the other hand, since the rank of X is K, X can be decomposed into:

[0074]

[0075] in, and is a column full rank matrix. K =[a1 … a K ].

[0076] Comparing (1) and (2), we can get that the signal subspace of X is:

[0077]

[0078] By estimating A K Obtain signal subspace information, and by minimizing the fitting error l p -norm (1≤p<2), estimate A K :

[0079]

[0080] Regarding solution (3):

[0081] Using a loop iteration method, in the tth iteration, the following two sub-problems are solved in sequence:

[0082]

[0083] For all possible values ​​of the number of sources l = 1, 2, ..., L:

[0084] When l = K, estimate A in turn K The columns are:

[0085]

[0086] Among them, ak , b k are the k-th columns of A and B respectively (k = 1, 2, …, K). Equation (6) means that when estimating the k-th column (a k , b k ), the previous columns are fixed as the estimated values, that is: The low-rank decomposition performed according to Equation (6) is called serial robust low-rank decomposition. Thus, when l = K, the serial robust low-rank decomposition method is equivalent to the greedy algorithm.

[0087] Definition is composed of the left singular vectors of A K corresponding to its largest K singular values. Since the signal subspace Therefore satisfies translational invariance:

[0088]

[0089] where and represent the matrices composed of the bottom N - 1 and top N - 1 rows of respectively, and is an orthogonal matrix.

[0090] Therefore, the rank of matrix is K.

[0091] · When l < K, the low-rank decomposition procedure in Equation (6) stops after estimating ;

[0092] · When l > K, the low-rank decomposition procedure in Equation (6) continues until all estimations are completed.

[0093] Therefore, when l ≠ K, A l = [a1 … a l does not satisfy translational invariance, and the rank of matrix is greater than l, where is composed of the left singular vectors of A l corresponding to its largest l singular values.

[0094] In practice, we cannot obtain the clean signal X. Therefore, estimating from the observed data matrix Y is denoted as

[0095] Based on the above, we can estimate the signal subspace by comparing the magnitudes of the smallest l singular values of matrix The rank, i.e., the number of signal sources K. Specifically, the detection criterion for the number of signal sources K is as follows:

[0096]

[0097] where L < min{(N - 1) / 2, T}, and

[0098]

[0099] Here, is the l smallest singular values of

[0100] Example 2:

[0101] Simulation test results: Figure 1 .

[0102] Noise model: Gaussian mixture model (GMM) —— c1 = 0.1, c2 = 0.9,

[0103] In addition, set the parameters K = 2, N = 12, T = 20.

[0104] Target signal:

[0105] θ1 is uniformly distributed between -30 0 and -20 0 while θ2 is uniformly distributed between 0 0 and 10 0 .

[0106] s1(t) and s2(t) follow independent complex-valued Gaussian distributions.

[0107] Evaluation index:

[0108] Probability of correct detection (PCD): PCD = S0 / S1 * 100%, where S0 and S1 are the number of correct detections and the total number of detections, respectively.

[0109] Referring to Appendix Figure 1 and Appendix Figure 3 , the line corresponding to the icon R - SAMOS in the attached drawings is the correct detection probability curve of the source number robust detection method based on translational invariance described in the present invention. In a GMM noise environment, compared with traditional source algorithms, a higher accuracy rate can be obtained at a lower signal-to-noise ratio; at the same time, an accuracy rate of 100% can be obtained when the signal-to-noise ratio is 3 dB, which is far better than existing source algorithms.

[0110] Simulation test results: Figure 2 .

[0111] Noise model: Generalized Gaussian distribution (GGD) β=0.5.

[0112] In addition, set parameters K=2, N=12, T=20.

[0113] Target signal:

[0114] θ1 at -30 0 ~-20 0 Uniformly distributed between 0 ~10 0 Evenly distributed between.

[0115] s1(t) and s2(t) obey independent complex-valued Gaussian distributions.

[0116] Evaluation indicators:

[0117] Probability of correct detection (PCD): PCD = S0 / S1*100%, where S0 and S1 are the number of correct detections and the total number of detections, respectively.

[0118] Refer to the attached Figure 2 and attached Figure 4 , the line corresponding to the icon R-SAMOS in the attached figure is the correct detection probability curve of the robust detection method for source numbers based on translation invariance of the present invention. In the GGD noise environment, the robust detection method for source numbers based on translation invariance of the present invention can obtain a higher accuracy rate when the signal-to-noise ratio is low compared with the traditional source algorithm; at the same time, it can obtain 100% accuracy when the signal-to-noise ratio is 4dB, which is much better than the existing source algorithm.

[0119] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A robust detection method for source number based on translation invariance, characterized by: It includes the following steps: First, construct a data matrix: Y = X + N, where Y = [y(1) … y(T)], X = A[s(1) … s(T)] and N = [n(1) … n(T)] are the clean signal and noise signal parts respectively; By singular value decomposition, we can obtain: in, and They are respectively composed of the left singular vector and the right singular vector corresponding to the largest K singular values ​​of X, and is a diagonal matrix, and the diagonal elements are the largest K singular values ​​of X; Since the rank of X is K, X can be decomposed by low-rank decomposition as: in, as well as A is a full-rank matrix. K =[a1 … a K ]; according to It can be obtained that the signal subspace of X is: By estimating A K Obtain signal subspace information by minimizing the fitting error l p -norm (1≤p<2), estimate A K : Regarding the solution of (3): Adopt a cyclic iterative method. In the t-th iteration, solve the following two sub-problems in sequence: For all possible values of the number of sources l = 1, 2, …, L: When l = K, estimate A in turn K The columns are: Among them, a k , b k are the kth columns of A and B (k = 1, 2, ..., K) respectively; Formula (6) indicates that when estimating the kth column (a k ,b k ), the previous columns are fixed to the estimated values, that is: The low-rank decomposition performed according to formula (6) is called serial robust low-rank decomposition; When l = K, the serial robust low-rank decomposition method is equivalent to the greedy algorithm; define By A K The left singular vectors corresponding to the largest K singular values ​​are composed of; since the signal subspace therefore Satisfies translation invariance: in, and Respectively indicated by The matrix consisting of the bottom N-1 and top N-1 rows, D = is an orthogonal matrix; Therefore, the matrix The rank of is K; in addition, · When l < K, the low-rank decomposition procedure in Equation (6) stops after estimating and then halts. When l>K, the low-rank decomposition procedure in (6) continues until All estimates completed; When l≠K, A l =[a1 … a l ] does not satisfy translation invariance, so the matrix The rank of is greater than l, where By A l The left singular vectors corresponding to its largest l singular values ​​are composed of; Estimate from the observed data matrix Y Recorded as By comparing different l values, the matrix The smallest l singular value sizes, estimating the signal subspace The rank of is the number of information sources K; The detection criterion for the number of sources K is: where L < min{(N - 1) / 2, T}, and for The smallest l singular values ​​of .

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