A method for estimating the subspace dimension of random signals
By improving the Bayesian information quantity criterion and combining the probability density of received data and feature structures, the robustness problem of traditional methods under low signal-to-noise ratio and low array received data quantity is solved, and better estimation effect is achieved.
Patent Information
- Application Number
- CN202111669812.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-12-30
- Publication Date
- 2025-08-12
- Estimated Expiration
- 2041-12-30
AI Technical Summary
The traditional subspace dimension estimation method based on Bayesian information quantity criterion is poorly robust under low signal-to-noise ratio and low array reception data quantity.
By constructing the improved Bayesian information quantity criterion expression, considering the probability density of the received data and the probability density of the characteristic structure, the new Bayesian information quantity criterion expression is constructed in combination with the two to estimate the subspace dimensions.
Under the conditions of low signal-to-noise ratio and low array reception data volume, the robustness of subspace dimension estimation is improved.
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Figure CN114330447B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of array signal processing, and in particular relates to a method for estimating the dimension of a random signal subspace based on an improved Bayesian information criterion. Background Art
[0002] Subspace estimation is an important research topic in array signal processing, and subspace dimension estimation algorithms are an important component of subspace estimation algorithms. Currently, the most commonly used subspace dimension estimation algorithm is the one based on the information criterion. Among these algorithms, the most widely used is the one based on the Bayesian information criterion. This algorithm uses the probability density of the received data as a likelihood function to estimate the subspace dimension.
[0003] However, when deriving the likelihood function, the traditional subspace dimension estimation method based on the Bayesian information criterion only considers the probability density of the received data and ignores the probability density of the feature structure corresponding to the received data, which makes the traditional subspace dimension estimation method based on the Bayesian information criterion less robust. Summary of the Invention
[0004] The purpose of the present invention is to solve the problem of poor robustness of the traditional subspace dimension estimation method based on the Bayesian information criterion, and to propose a method for random signal subspace dimension estimation.
[0005] The technical solution adopted by the present invention to solve the above technical problems is:
[0006] A method for estimating the subspace dimension of a random signal, the method specifically comprising the following steps:
[0007] Step S1: Receive data using a sensor array consisting of N array elements, and calculate the covariance matrix of the received data;
[0008] Step S2: performing eigenvalue decomposition on the covariance matrix to obtain the eigenvalues of the covariance matrix;
[0009] Step S3: Calculate the probability density of the received data and the probability density of the eigenvalue according to the eigenvalue solved in step S2;
[0010] Step S4: constructing an improved Bayesian information criterion expression based on the probability density of the received data and the probability density of the eigenvalues;
[0011] The expression of the improved Bayesian information criterion is:
[0012] BIC=-2lgf1+f2)+Mlg(L)
[0013] Where: BIC represents the Bayesian information value, M represents the degrees of freedom of the subspace, L represents the number of sampling points of the data received by the array element, f1 is the probability density of the received data, and f2 is the probability density of the eigenvalue;
[0014] The probability density f1 of the received data is:
[0015]
[0016] Among them, r represents the signal subspace dimension, λ i represents the i-th eigenvalue of the covariance matrix, and lg represents the logarithm with base 10;
[0017] The degree of freedom M of the subspace is:
[0018]
[0019] Step S5: Based on the improved Bayesian information criterion expression, the subspace dimension corresponding to the maximum Bayesian information value is solved.
[0020] Furthermore, the sensor array composed of N array elements is used to receive data, and the received data includes a target signal and a Gaussian white noise signal.
[0021] Furthermore, in step S2, the covariance matrix is subjected to eigenvalue decomposition to obtain the eigenvalues of the covariance matrix; the specific process is as follows:
[0022] R=UWU H
[0023] Where R is the covariance matrix calculated in step S1, U represents the eigenvector matrix, W represents the eigenvalue matrix, and U H represents the transpose conjugate operation of U;
[0024] The number of columns of the eigenvector matrix U is equal to the number of array elements in the sensor array, and each column of the eigenvector matrix represents an eigenvector;
[0025] The eigenvalue matrix is a diagonal matrix, and the eigenvalues are arranged on the diagonal in descending order.
[0026] Furthermore, the probability density f2 of the eigenvalue is:
[0027]
[0028] in, represents the true value of the i-th eigenvalue of the covariance matrix of the array receiving data, λ j represents the j-th eigenvalue of the covariance matrix, σ 2 represents the variance of Gaussian white noise;
[0029] Γ(·) represents a mathematical operation. For any positive integer n, Γ(n) is expressed as:
[0030] Γ(n)=(n-1)·(n-2)·2·1
[0031] The beneficial effects of the present invention are:
[0032] The method of the present invention not only considers the probability density of the received data, but also considers the probability density of the characteristic structure corresponding to the received data. An improved Bayesian information criterion expression is constructed by combining the probability density of the received data and the probability density of the characteristic structure corresponding to the received data. The subspace dimension is then estimated based on the constructed improved Bayesian information criterion expression. This allows the method of the present invention to still have good estimation robustness under conditions of low signal-to-noise ratio and low array received data volume. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 is a flow chart of the method of the present invention;
[0034] Figure 2(a) shows the curve of the estimation success rate versus SNR when L = 300;
[0035] Figure 2(b) shows the curve of the estimation success rate versus SNR when L = 1000;
[0036] Figure 3(a) shows the curve of the estimation success rate versus the number of sampling points when SNR = -4dB;
[0037] FIG3( b ) is a curve showing the variation of the estimation success rate with the number of sampling points when SNR=-10 dB. DETAILED DESCRIPTION
[0038] Specific implementation method 1. Combination Figure 1 This embodiment describes a method for estimating the dimension of a random signal subspace, which specifically includes the following steps:
[0039] Step S1: Receive data using a sensor array consisting of N array elements, and calculate the covariance matrix of the received data;
[0040] Step S2: performing eigenvalue decomposition on the covariance matrix to obtain the eigenvalues of the covariance matrix;
[0041] Step S3: Calculate the probability density of the received data and the probability density of the eigenvalue according to the eigenvalue solved in step S2;
[0042] Step S4: constructing an improved Bayesian information criterion expression based on the probability density of the received data and the probability density of the eigenvalues;
[0043] The expression of the improved Bayesian information criterion is:
[0044] BIC=-2lg(f1+f2)+Mlg(L)
[0045] Where: BIC represents the Bayesian information value, M represents the degrees of freedom of the subspace, L represents the number of sampling points of the data received by the array element, f1 is the probability density of the received data, and f2 is the probability density of the eigenvalue;
[0046] The probability density f1 of the received data is:
[0047]
[0048] Among them, r represents the signal subspace dimension, λ i represents the i-th eigenvalue of the covariance matrix (i.e., the i-th eigenvalue in the descending order), and lg represents the logarithm with base 10;
[0049] The degree of freedom M of the subspace is:
[0050]
[0051] Step S5: Based on the improved Bayesian information criterion expression, the subspace dimension corresponding to the maximum Bayesian information value is solved.
[0052] The probability density of the array receiving data, the probability density of the eigenvalues and the degrees of freedom of the subspace are all related to the subspace dimension. The information values corresponding to all possible subspace dimension values are calculated according to the improved Bayesian information criterion expression in step S4. The subspace dimension value corresponding to the maximum information value is equal to the signal system space dimension.
[0053] The method of the present invention is applicable to the case of random signals, which means that it is applicable to the case where the noise in the received data is not a deterministic signal, that is, the noise in the received data is a random signal, which obeys a certain probability distribution and cannot be described by a clear mathematical relationship. For example, when using a sensor array to receive underwater target signals (such as submarine or AUV signals), the received data contains noise signals of the loading platform (the noise signal of the ship's engine or propeller).
[0054] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that a sensor array consisting of N array elements is used to receive data, and the received data includes a target signal and a Gaussian white noise signal.
[0055] Other steps and parameters are the same as those in the first embodiment.
[0056] Specific embodiment three: This embodiment differs from specific embodiment one or two in that, in step S2, the covariance matrix is subjected to eigenvalue decomposition to obtain the eigenvalues of the covariance matrix; the specific process is as follows:
[0057] R=UWU H
[0058] Where R is the covariance matrix calculated in step S1, U represents the eigenvector matrix, W represents the eigenvalue matrix, and U H represents the transpose conjugate operation of U;
[0059] The number of columns of the eigenvector matrix U is equal to the number of array elements in the sensor array, and each column of the eigenvector matrix represents an eigenvector;
[0060] The eigenvalue matrix is a diagonal matrix. Only the values on the diagonal of the matrix are not zero, and the eigenvalues are arranged on the diagonal in descending order.
[0061] Other steps and parameters are the same as those in the first or second embodiment.
[0062] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the probability density f2 of the eigenvalue is:
[0063]
[0064] in, represents the true value of the i-th eigenvalue of the covariance matrix of the array receiving data, λ j represents the j-th eigenvalue of the covariance matrix, σ 2 represents the variance of Gaussian white noise;
[0065] Γ(·) represents a mathematical operation. For any positive integer n, Γ(n) is expressed as:
[0066] Γ(n)=(n-1)·(n-2)·2·1
[0067] The other steps and parameters are the same as those in the first to third embodiments.
[0068] Experimental part
[0069] The simulations were used to verify the estimation success rate of the proposed method for different signal-to-noise ratios and different numbers of sampling points, and to evaluate the performance of the algorithm. Figures 2(a) and 2(b) show the curves of the estimation success rate changing with SNR when L=300 and L=1000, respectively. Figures 3(a) and 3(b) show the curves of the estimation success rate changing with the number of sampling points when there are fewer sampling points and more sampling points, respectively. The vertical axis "P c" represents the detection success rate, "AIC", "BIC" and "BIC2" represent the subspace dimension estimation algorithms based on Akaike's information criterion, conventional Bayesian information criterion and second-type Bayesian information criterion, respectively, and "GBIC" represents the improved Bayesian information criterion described in the present invention. By comparison, it can be found that the convergence speed and detection success rate of the method of the present invention are better than those of other methods, and it has the best robustness to the signal-to-noise ratio and the number of sampling points.
[0070] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.
Claims
1. A method for estimating the subspace dimension of a random signal, characterized in that: The method specifically comprises the following steps: Step S1: Receive data using a sensor array consisting of N array elements, and calculate the covariance matrix of the received data; Step S2: performing eigenvalue decomposition on the covariance matrix to obtain the eigenvalues of the covariance matrix; Step S3: Calculate the probability density of the received data and the probability density of the eigenvalue according to the eigenvalue solved in step S2; Step S4: constructing an improved Bayesian information criterion expression based on the probability density of the received data and the probability density of the eigenvalues; The expression of the improved Bayesian information criterion is: BIC=-2lg(f1+f2)+Mlg(L) Where: BIC represents the Bayesian information value, M represents the degrees of freedom of the subspace, L represents the number of sampling points of the data received by the array element, f1 is the probability density of the received data, and f2 is the probability density of the eigenvalue; The probability density f1 of the received data is: Among them, r represents the signal subspace dimension, λ i represents the i-th eigenvalue of the covariance matrix, and lg represents the logarithm with base 10; The degree of freedom M of the subspace is: The probability density f2 of the eigenvalue is: in, represents the true value of the i-th eigenvalue of the covariance matrix of the array receiving data, λ j represents the j-th eigenvalue of the covariance matrix, σ 2 represents the variance of Gaussian white noise; Γ(·) represents a mathematical operation. For any positive integer n, Γ(n) is expressed as: Γ(n)=(n-1)·(n-2)·2·1 Step S5: Based on the improved Bayesian information criterion expression, the subspace dimension corresponding to the maximum Bayesian information value is solved.
2. The method for estimating the dimension of a random signal subspace according to claim 1, wherein: The sensor array composed of N array elements is used to receive data, and the received data includes a target signal and a Gaussian white noise signal.
3. The method for estimating the dimension of a random signal subspace according to claim 2, wherein: In step S2, the covariance matrix is subjected to eigenvalue decomposition to obtain the eigenvalues of the covariance matrix; The specific process is: R=WUU H Where R is the covariance matrix calculated in step S1, U represents the eigenvector matrix, W represents the eigenvalue matrix, and U H represents the transpose conjugate operation of U; The number of columns of the eigenvector matrix U is equal to the number of array elements in the sensor array, and each column of the eigenvector matrix represents an eigenvector; The eigenvalue matrix is a diagonal matrix. Only the values on the diagonal of the matrix are not zero, and the eigenvalues are arranged on the diagonal in descending order.