Information source number estimation method in array direction finding based on improved smooth order sequence method

Abstract

An information source number estimation method in array direction finding based on an improved smooth order sequence method is executed under the condition that the ratio M / T0 of the number M of array elements to the number T0 of signal sampling points is not larger than 1.6, and comprises the following steps that a covariance matrix of observation signals of T0 sampling points received by an antenna array of M array elements is calculated; smoothing the covariance matrix through a forward spatial smoothing method to obtain a group of smoothed covariance matrixes; performing signal source number estimation on the covariance matrixes in the smoothed group by applying a minimum description length criterion to obtain a smoothed order sequence; performing reverse processing on the smooth order sequence to obtain a reverse sequence; and judging the monotonicity of the reverse sequence, and determining the number of finally output information sources according to the monotonicity and the magnitude and occurrence frequency of the numerical values in the reverse sequence. According to the estimation method, high-accuracy signal source number estimation can be carried out under the conditions that coherent signals exist in array direction finding and the number of antenna array elements and the number of signal sampling points are in the same order of magnitude.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, specifically to a method for estimating the number of sources in direction finding based on an improved smoothed order array. Background Technology

[0002] Accurate estimation of the number of sources is a necessary condition for the correct DOA estimation of an array direction-finding system. Currently, there are several main methods for source number estimation:

[0003] (1) Information theory criterion methods. These include the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Minimum Description Length (MDL), and Kullback Information Criterion (KIC). These methods are suitable for Gaussian white noise environments. To make source number estimation applicable to colored noise conditions, a method combining eigenvalue diagonal loading with information theory criteria is usually adopted. However, there is no theoretically definite method for determining the diagonal loading amount, which is a key factor affecting the application effect of information theory criterion methods based on diagonal loading under colored noise conditions.

[0004] (2) Methods for processing eigenvalues / singular values ​​of the covariance matrix of the observed signal. These mainly include methods for determining the number of signal sources based on the ratio of eigenvalues ​​to singular values. These methods are suitable for Gaussian white noise conditions.

[0005] (3) Geil Circle Transform. This method does not use the eigenvalues ​​of the array covariance matrix, but rather the radius of the Geil circle of the array covariance matrix to estimate the number of signal sources. It is suitable for white noise and colored noise conditions. However, because this method involves a key parameter setting that lacks theoretical guidance and relies on empirical values, the source number estimation results vary significantly under different parameter values, making this method inconvenient for practical use.

[0006] (4) Hypothesis testing methods. Hypothesis testing methods include the test of sphericity and eigenvalue detection, which mainly utilize the statistical distribution of sample eigenvalues ​​to construct observation statistics for hypothesis testing and set decision thresholds. From the perspective of aliasing noise in the observed signal, these methods are suitable for Gaussian white noise environments.

[0007] However, the methods described above are difficult to apply when coherent signals exist and the number of array elements and signal sampling points are on the same order of magnitude. Currently, the signal environment faced by array direction finding systems is becoming increasingly complex. The coherence of the incident signal in the array received signal, and the fact that the number of signal sampling points is not much greater than the number of antenna elements, make source number estimation in array direction finding a technical challenge. The smoothed order sequence method can be used to estimate the number of sources in antenna array direction finding when coherent signals exist, but it is not suitable for source number estimation when the ratio of the number of array elements to the number of signal sampling points is greater than 0.4.

[0008] To address the problem of estimating the number of sources in array direction finding when there are coherent signals and the number of antenna array elements is on the same order of magnitude as the number of signal sampling points, this invention presents an improved smooth order sequence method. Summary of the Invention

[0009] The purpose of this invention is to propose a source number estimation method based on the improved smooth order array method for array direction finding, which can perform high-accuracy source number estimation when there are coherent signals in the array direction finding and when the number of antenna array elements and the number of signal sampling points are on the same order of magnitude.

[0010] The technical solution adopted in this invention is: a source number estimation method based on an improved smoothed order array direction finding method, wherein the method is performed under the condition that the ratio M / T0 of the number of array elements M to the number of signal sampling points T0 is not greater than 1.6, and includes the following steps:

[0011] Calculate the covariance matrix of the observed signals received by the antenna array with M elements at T0 sampling points;

[0012] The covariance matrix is ​​smoothed by the forward space smoothing method to obtain a set of smoothed covariance matrices;

[0013] The source number is estimated by applying the minimum description length criterion (MDL) to the covariance matrix of the smoothed group, resulting in a smoothed order column.

[0014] The smoothed ordered sequence is reversed to obtain a reversed sequence;

[0015] Determine the monotonicity of the reverse sequence, and determine the final number of source data based on the monotonicity, the magnitude of the values ​​in the reverse sequence, and the frequency of occurrence.

[0016] As the preferred solution, the smoothed covariance matrix is:

[0017]

[0018] in, P is the smoothed covariance matrix; M is the number of matrix elements; P M-k,jLet P be a (Mk)×M dimensional permutation matrix. M-k,j =[I (M-k)×(M-k) 0 (M-k)×k ]; k is a positive integer, k = 1, 2, ..., M-1; j represents I (M-k)×(M-k) In P M-k,j The position shifted backward in the middle, j = 0, 1, ..., k; R0 is the covariance matrix obtained from the received signal of the M-dimensional antenna array; x(t) is the observed signal, x(t) = [x1(t), x2(t), ..., x M (t)] T The superscript T indicates transpose, and the superscript H indicates conjugate transpose.

[0019] As a preferred option, the smooth order is listed as follows:

[0020]

[0021] Where, n * The source number estimation results obtained by applying the Minimum Description Length (MDL) criterion; This represents minimizing the objective function MDL(n); T0 is the number of signal sampling points; M is the number of array elements; n * The result represents the source number estimation, where n is the number of candidate sources, L(n) is the likelihood ratio, and P... i For the smoothed n * .

[0022] As a preferred approach, the minimum description length criterion (MDL) is applied to the covariance matrix within the smoothed group to estimate the number of sources, resulting in M ​​types of source number estimation results. The M types of source number estimation results include M-1 types of source number estimation results obtained by traversing k from 1 to M-1 according to the MDL criterion, and one type of source number estimation result obtained by directly estimating the number of sources on the covariance matrix R0 using the minimum description length criterion (MDL).

[0023] As a preferred approach, the steps for determining the final number of source data in the output based on monotonicity and the magnitude and frequency of values ​​in the reverse sequence are as follows:

[0024] If the reverse sequence is not monotonically increasing, the first maximum value of the reverse sequence is selected as the final number of source values. If the reverse sequence is monotonically increasing and the sequence values ​​include 1, the number of times each value appears in the reverse sequence is counted, and the value with the most occurrences in the sequence is selected as the final number of source values. If the reverse sequence is monotonically increasing but the sequence values ​​do not include 1, the value with the largest value in the sequence is selected as the final number of source values.

[0025] As a preferred embodiment, when the incident signal does not contain a coherent signal, the number of array elements M and the number of incident signals K satisfy M≥K+1; when the incident signal contains a coherent signal, the number of array elements M and the number of incident signals K satisfy M≥2K.

[0026] As a preferred embodiment, the step of determining the monotonicity of the reverse sequence is achieved by calculating the difference of the reverse sequence and determining whether all difference values ​​are greater than or equal to zero.

[0027] Compared with the prior art, the beneficial effects of the present invention are:

[0028] This invention combines forward smoothing and the minimum description length criterion in the source number estimation process, and analyzes the sequence morphology through logic. It can be used for source number estimation in array direction finding when there are coherent incident signals or when all incident signals are incoherent, and the ratio of the number of array elements to the number of incident signal sampling points can reach 1.6. When there are coherent incident signals, it can be used for source number estimation when the ratio of the number of array elements to the number of signal sampling points is greater than 0.4. When all incident signals are incoherent, it can be applied to source number estimation when the ratio of the number of array elements to the number of signal sampling points is greater than 0.5. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 The results show the source number estimation for different signal coherence group numbers.

[0031] Figure 2 The results of source number estimation under different array element numbers and coherent incident signal numbers;

[0032] Figure 3 The source number estimation results are given for different array element numbers when the number of incoherent incident signals is 6.

[0033] Figure 4 The source number estimation results are given for different numbers of array elements and sampling points when the incident signal is coherent.

[0034] Figure 5 For incoherent incident signals, the source number estimation results are given under different array element numbers and sampling point numbers;

[0035] Figure 6 This is a schematic diagram of the processing flow of the present invention. Detailed Implementation

[0036] The present invention will now be described in detail through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0037] It should be noted that, unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "a," "an," or "the," etc., used in the specification and claims of this patent application do not express a limitation on quantity, but rather indicate the presence of at least one; the terms "first," "second," and "third," as used herein, should not be considered as a limitation on the order of components, but are merely for distinguishing different components; the terms "comprising," "including," etc., indicate that the elements or objects preceding "comprising" or "including" encompass the elements or objects listed following "comprising" or "including" and their equivalents, but do not exclude other elements or objects having the same function.

[0038] To more clearly describe this source number estimation method based on the improved smoothed order array direction finding method, combined with the appendix... Figure 1-6 This embodiment is described as follows:

[0039] like Figure 6 As shown, a method for estimating the number of sources in direction finding based on an improved smoothed order array method includes the following steps:

[0040] S1: Suppose a one-dimensional uniform linear antenna array has M elements, and the measured M-dimensional observation signal is x(t), x(t) = [x1(t), x2(t), ..., x... M (t)] T (The superscript T indicates transpose), the sampling point numbers t = 1, 2, ..., T0, where T0 is the number of signal sampling points. Calculate the covariance matrix of the observed signal. (The superscript H indicates the conjugate transpose); R0 is the covariance matrix calculated from the received signal X from the M-dimensional array.

[0041] R0 is an M×M dimensional matrix. Let k be a positive integer, k = 1, 2, ..., M-1, and define an (Mk)×M dimensional matrix P. M-k,j j = 0, 1, ..., k:

[0042] P M-k,j =[I (M-k)×(M-k) 0 (M-k)×k (1)

[0043] P M-k,j It is a permutation matrix consisting of an (Mk)×(Mk) dimensional identity matrix L.(M-k)×(M-k) and (Mk)×k dimensional 0 element matrix 0 (M-k)×k composition.

[0044] Once the value of k is determined, P M-k,j It varies as j takes different values, j represents I (M-k)×(M-k) In P M-k,j The position shifted backwards. For example, when M=4, k=1, j=0,

[0045]

[0046] Among them, P 4-1,0 The first 3 columns form I (4-1)×(4-1) The 4th column forms 0 (4-1)×1 .

[0047] When M=4, k=1, j=1

[0048]

[0049] Among them, P 4-1,0 The last 3 columns form I (4-1)×(4-1) The first column consists of 0. (4-1)×1 .

[0050] When M=4, k=2, j=0

[0051]

[0052] Among them, P 4-1,0 The first two columns form I (4-2)×(4-2) The third and fourth columns form 0. (4-2)×2 .

[0053] When M=4, k=2, j=1

[0054]

[0055] Among them, P 4-1,1 The second and third columns form I (4-2)×(4-2) Columns 1 and 4 together form 0 (4-2)×2 .

[0056] Using P M-k,j Divide R0 into cross-overlapping matrices And by finding its average matrix, we can obtain

[0057]

[0058] The cross-overlap matrix sequence in the above formula is actually a forward space smoothing matrix.

[0059] Assume the signal source consists of a group of L correlated sources, denoted as g.i (i = 1, 2, ..., L), where i = 1 indicates that the group is a single independent signal; i = 3 indicates that the group has 3 coherent sources, and L is the maximum correlation coefficient. If g2 = 3, it indicates that there are 3 correlation groups, each with two coherent sources, and the number of correlation groups is...

[0060]

[0061] The total number of signal sources is

[0062]

[0063] In the formula, f q This represents the number of signal sources in the q-th related group.

[0064] If the data covariance matrix is ​​obtained from a finite number of snapshots, then:

[0065]

[0066] Where the dimension of I is (Mk)×(Mk). σ 2 The power of the Gaussian white noise incident on the array.

[0067] and The dimension of the signal subspace is The rank of the smooth order is given by:

[0068]

[0069] At the same time, according to the MDL criterion, we can obtain:

[0070]

[0071] According to equation (7), the number of signal sources incident on the antenna array can be obtained for each value of k. When k traverses from 1 to M-1, M-1 source number estimation results can be obtained. By applying the MDL criterion to directly estimate the source number of R0, one source number estimation result can be obtained, and thus M source number estimation results can be obtained.

[0072] The improved smooth order column method is based on the above algorithm, taking the smooth order column in reverse order. Without loss of generality, let:

[0073]

[0074] P i If i = 1, 2, ..., M are arranged in reverse order, the following reverse sequence is obtained:

[0075] P′ j ,j=1,2,…,M (9)

[0076] Obviously P′1 = P M ,P′2=P M-1 ,…,P′ M =P1.

[0077] For the sequence shown in equation (9), we can determine whether it is a monotonically increasing sequence by calculating the difference. If P′ j If the sequence j = 1, 2, ..., M is not monotonically increasing, then P′ j The first maximum value of j = 1, 2, ..., M is taken as the number of sources in the final output; if P′ j If the sequence j = 1, 2, ..., M is monotonically increasing and contains the value 1, then calculate the statistical value of P′. j The number of occurrences of each value in the sequence j = 1, 2, ..., M is used as the number of information sources in the final output; if P′ j If the sequence j = 1, 2, ..., M is monotonically increasing, but does not contain the value 1, then the largest value in the sequence is taken as the final output source number.

[0078] The estimation method described above uses the Minimum Description Length (MDL) criterion, which is an information theory-based method for estimating the number of sources. This is equivalent to applying information theory criteria to determine the rank of the covariance matrix R0 of the antenna array received signal. First, a set of probabilistic models, i.e., probability density functions, must be available. Assume the observed signal vector is x(t) = [x1(t), x2(t), ..., x...]. M (t)] T If the observed vectors are complex Gaussian random vectors with zero mean and independent and identically distributed, then the joint probability density function of the observed vectors can be obtained. Under the above Gaussian assumption, the following covariance matrix can be obtained:

[0079]

[0080] here Let σ represent a positive semi-definite matrix of rank k. 2 It is an unknown scalar. Here, k∈{0,1,…,m-1} represents the number of all possible sources, and M is the dimension of the observed signal. According to the spectral decomposition theory in matrix theory, matrix R... (k) It can be represented as:

[0081]

[0082] Here λ1,…,λ k and V1,…,V k They are R (k) The eigenvalues ​​and eigenvectors of θ. (k) Let the parameter vector of the probabilistic model be:

[0083]

[0084] Since the observation vector x(t) = [x1(t), x2(t), ..., x M (t)] T They are independent and identically distributed complex Gaussian random variables with zero mean, and their joint probability density function is:

[0085]

[0086] Take the logarithm of the above expression and compare it with the parameter vector Θ. (k) Ignoring irrelevant terms, we obtain the following log-likelihood function:

[0087]

[0088] tr represents the trace of the matrix, and T0 represents the number of signal sampling points. It is the sampling covariance matrix.

[0089] Parameter Θ (k) The maximum likelihood estimate is the parameter value that maximizes equation (14). In the literature, the maximum likelihood estimate of these parameters is given by the following equation:

[0090]

[0091] Where l1>l2>…>l M It is the sampling covariance matrix Eigenvalues, C1, C2, ..., C M yes The eigenvectors. Substituting the maximum likelihood function estimate of the parameters shown in equation (15) into the log-likelihood function shown in equation (14), and through some calculations, we can obtain the following equation:

[0092]

[0093] The logarithmic part in equation (16) is the ratio of the geometric mean to the arithmetic mean of the Mk small eigenvalues.

[0094] Parameter vector Θ (k) The free parameters can be determined by Θ (k) The degrees of freedom of the space are calculated using the parameters Θ. (k) The eigenvalues ​​in the vector are real parameters, and the eigenvectors are complex vectors; therefore, the parameter vector Θ is... (k) There are a total of k+1+2Mk real parameters. However, due to the parameter vector Θ (k) The eigenvectors in the vector are pairwise orthogonal unit vectors, so Θ (k) The k+1+2Mk parameters are not all independent, which makes Θ (k) The number of parameters that can be freely varied is reduced.

[0095] First, due to the unit norm constraint of the eigenvectors, Θ (k) The degrees of freedom are reduced by 2k, and due to the orthogonality constraint of the eigenvectors, Θ (k) The degrees of freedom are reduced by 2.5k(k-1). Thus, the parameter vector Θ (k) The degree of freedom is k(2M-k)+1.

[0096] Based on the above derivation, the Minimum Description Length (MDL) criterion can be obtained. The source number estimation method based on the MDL criterion achieves the desired source number n by minimizing the objective function MDL. * The adaptive determination and MDL calculation principle are as follows:

[0097]

[0098] In the formula, n * The result represents the source number estimation, where n is the number of candidate sources, L(n) is the likelihood ratio, and P... i For the smoothed n * .

[0099] The invention will be further described below with reference to experimental test diagrams.

[0100] 1. Experimental conditions setup:

[0101] The experimental verification of this invention was carried out under computer simulation conditions, and the simulation software used was MATLAB R2014a. In order to verify the effectiveness of this invention, four sets of experimental tests were carried out. By estimating the accuracy of the number of sources, the estimation results of the number of sources were examined under different numbers of coherent signal groups in the incident signal, the estimation results of the number of sources under different numbers of sources and incident signals, the influence of the number of array elements and the number of sampling points on the estimation of the number of sources under the presence of coherent signals, and the influence of the number of array elements and the number of sampling points on the estimation of the number of sources under the presence of no coherent signals in the incident signal. The source number estimation methods used for comparison with the technical solution of this invention are: AIC algorithm[2], MDL algorithm[3], KIC algorithm[4], Chafen algorithm[5], and classical smoothed order sequence method (SS)[1]. This method is called the improved smoothed order sequence algorithm (MSS).

[0102] Example 1: Source number estimation results under different signal coherence group numbers

[0103] Five radar radiation source signals are provided, all of which are single-frequency continuous wave (CW) modulation schemes with a pulse width of 30 μs and carrier frequencies of f1 and f2 respectively. c1 f c2 f c3 f c4 and f c5The second signal amplitude is 0.7 + 0.6i, the fourth signal amplitude is 0.3 + 0.7i, and the amplitudes of other signals are all 1. The pulse repetition frequency is 10 kHz. A coherent signal environment is constructed by changing the incident signal carrier frequency. The signal incident angles are -45°, -30°, 20°, 35°, and 50°. The signal sampling frequency is 60 MHz, and the number of signal sampling points is 101. The number of array elements is 10, the maximum signal frequency that the array can receive is 240 MHz, and the element spacing is half the minimum wavelength of the incident signal. The signal-to-noise ratio range is -20 dB to 30 dB, the signal-to-noise ratio step size is 2 dB, and the number of Monte Carlo simulations is 500. The source number estimation results for different numbers of coherent signal groups are as follows. Figure 1 As shown.

[0104] from Figure 1 It can be seen that for the problem of estimating the number of sources in an incident signal containing coherent signals, even if the number of signal sampling points is much larger than the number of array elements, the AIC, MDL, KIC, and Chafen algorithms are no longer applicable, while the Smooth Order Array (SS) method and its improved version (MSS) method are applicable. The more coherent the incident signal, the higher the signal-to-noise ratio (SNR) required for accurate source number estimation. If there are no incoherent signals in the incident signal, the MSS algorithm requires a SNR several dB higher than that required by the MDL, KIC, Chafen, and SS algorithms.

[0105] Example 2: Source number estimation results for different array element numbers and incident signal numbers

[0106] The number of array elements and the number of incident radar radiation source signals were varied. The intra-pulse modulation method was CW, the pulse width was 30μs, the carrier frequency was 10MHz, and the signal amplitude varied. The pulse repetition frequency was 10kHz. The minimum interval of the signal incident angle was 6°. The signal sampling frequency was 60MHz, and the number of signal sampling points was 101. The number of array elements was 10, the maximum frequency of the signal that the array could receive was 240MHz, and the element spacing was half the minimum wavelength of the incident signal. The signal-to-noise ratio range was -20dB to 30dB, the signal-to-noise ratio step size was 2dB, and the number of Monte Carlo simulations was 500. The source number estimation results for different numbers of array elements and incident signals are as follows: Figure 2 , Figure 3 As shown.

[0107] from Figure 2 It can be seen that for estimating the number of sources under coherent signal incidence, the number of array elements must be at least twice the number of signals, and the beamwidth ( M (where M is the number of array elements) must be no less than the angular interval between adjacent incident signals in order to achieve 100% accurate source number estimation using the SS and MSS algorithms under a signal-to-noise ratio of approximately 10 dB or higher. The AIC, MDL, KIC, and Chafen methods failed to estimate the source number.

[0108] from Figure 3 It can be seen that, in the case of no coherent signal incident, when the number of array elements is one more than the number of incident signals, and the signal-to-noise ratio (SNR) is approximately -2 dB or higher, the AIC, MDL, KIC, SS, and MSS algorithms can all accurately estimate the number of incident sources with 100% probability. Comparing the MSS and SS algorithms, the former typically requires a higher SNR (several dB higher than the latter) for accurate source estimation. Figure 2 and Figure 3 The comparison shows that when coherent signals are incident, the antenna array aperture becomes smaller, resulting in a larger beamwidth, a smaller spatial resolution, and the source number estimation cannot break through the Rayleigh limit. However, the source number estimation for incoherent signals can break through the Rayleigh limit.

[0109] Example 3: The impact of the number of array elements and sampling points on the estimation of the number of signal sources in the presence of coherent signals.

[0110] There are five coherent radar radiation source signals, all of which are CW modulated within a pulse, with carrier frequencies of fc1, fc2, fc3, fc4, fc5, fc6, fc7, fc8, fc9, ... c3 f c4 and f c5 The carrier frequency is 10MHz. The amplitude of the second signal is 0.7+0.6i, the amplitude of the fourth signal is 0.3+0.7i, and the amplitude of other signals is 1. The pulse repetition frequency is 10kHz. The signal incident angles are -45°, -34°, -23°, -4°, and 20°. The duration and pulse width of the incident signal are changed, i.e., the number of signal sampling points is changed. The signal sampling frequency is 60MHz. The maximum frequency of the signal that the array can receive is 240MHz, and the element spacing is half the minimum wavelength of the incident signal. The signal-to-noise ratio range is -20dB to 30dB, the signal-to-noise ratio step size is 2dB, and the number of Monte Carlo simulations is 500. The source number estimation results for different numbers of array elements and sampling points are as follows. Figure 4 As shown.

[0111] from Figure 4It can be seen that, for coherent signal incidence, when the ratio of the number of array elements to the number of signal sampling points is less than approximately 0.4, and the beamwidth calculated from the number of array elements is not greater than the difference in angle between adjacent incident signals, the SS method can accurately estimate the number of incident sources with 100% probability under approximately 0 dB conditions. When the ratio of the number of array elements to the number of incident signals is greater than approximately 0.4, the AIC, MDL, KIC, Chafen, and SS methods cannot correctly obtain the source number estimation results, while the MSS algorithm is still applicable and can accurately estimate the source number with 100% probability under a signal-to-noise ratio of over 0 dB conditions.

[0112] Example 4: The impact of the number of array elements and sampling points on the estimation of the number of information sources when the incident signal does not contain coherent signals.

[0113] There are five incoherent radar radiation source signals, all with CW intra-pulse modulation and carrier frequencies of fi and fj respectively. c1 =10MHz, f c2 =9MHz, f c3 =8MHz, f c4 =7MHz and f c5 =6MHz. The amplitude of the second signal is 0.7+0.6i, the amplitude of the fourth signal is 0.3+0.7i, and the amplitude of other signals is 1. The pulse repetition frequency is 10kHz. The signal incident angles are -45°, -34°, -23°, -4°, and 20°. The duration and pulse width of the incident signal are changed, i.e., the number of signal sampling points is changed. The signal sampling frequency is 60MHz. The maximum frequency of the signal that the array can receive is 240MHz, and the element spacing is half the minimum wavelength of the incident signal. The signal-to-noise ratio range is -20dB to 30dB, the signal-to-noise ratio step size is 2dB, and the number of Monte Carlo simulations is 500. The source quantity estimation results for different numbers of array elements and sampling points are as follows. Figure 5 As shown.

[0114] Analysis of the experimental results shows that, in the absence of coherent signals in the incident signal, when the ratio of the number of array elements to the number of signal sampling points is greater than approximately 0.5, the AIC, MDL, KIC, Chafen, and SS methods all struggle to accurately estimate the number of sources, while the MSS algorithm can correctly estimate the number of sources. Through a series of experiments, it can be concluded that when the ratio of the number of array elements M to the number of signal sampling points T0 is not greater than 1.6, the MSS algorithm can be used for source number estimation.

[0115] Based on the above experimental results, when coherent signals exist in array direction finding and the number of antenna array elements and signal sampling points are on the same order of magnitude, the present invention can accurately estimate the number of signal sources with a high probability.

[0116] The parts not described in detail in the above embodiments are existing technologies.

[0117] It should be noted that although the present invention has been described through the above embodiments, the present invention may have many other embodiments. Without departing from the spirit and scope of the present invention, those skilled in the art can obviously make various corresponding changes and modifications to the present invention, but all such changes and modifications should fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A source number estimation method based on an improved smoothed order array direction finding method, characterized in that: The method is performed under the condition that the ratio M / T0 of the number of array elements M to the number of signal sampling points T0 is not greater than 1.6, and includes the following steps: Calculate the covariance matrix of the observed signals received by the antenna array with M elements at T0 sampling points; The covariance matrix is ​​smoothed by the forward space smoothing method to obtain a set of smoothed covariance matrices; The source number is estimated by applying the minimum description length criterion (MDL) to the covariance matrix of the smoothed group, resulting in a smoothed order column. The smoothed ordered sequence is reversed to obtain a reversed sequence; Determine the monotonicity of the reverse sequence, and determine the final number of source data based on the monotonicity, the magnitude of the values ​​in the reverse sequence, and the frequency of occurrence.

2. The source number estimation method based on the improved smoothed order array direction finding method according to claim 1, characterized in that: The smoothed covariance matrix is: in, P is the smoothed covariance matrix; M is the number of matrix elements; P M-k,j Let P be a (Mk)×M dimensional permutation matrix. M-k,j =[I (M-k)×(M-k) 0 (M-k)×k ]; k is a positive integer, k = 1, 2, ..., M-1; j represents I (M-k)×(M-k) In P M-k,j The position shifted backward in the middle, j = 0, 1, ..., k; R0 is the covariance matrix obtained from the received signal of the M-dimensional antenna array; x(t) is the observed signal, x(t) = [x1(t), x2(t), ..., x M (t)] T The superscript T indicates transpose, and the superscript H indicates conjugate transpose.

3. The source number estimation method based on the improved smoothed order array direction finding method according to claim 1, characterized in that: The smooth order is listed as: Where, n * The source number estimation results obtained by applying the Minimum Description Length (MDL) criterion; Let M(n) represent minimizing the objective function MDL(n); T0 is the number of signal sampling points; M is the number of array elements; n is the number of candidate sources; and L(n) is the likelihood ratio.

4. The source number estimation method based on the improved smoothed order array direction finding method according to claim 1, characterized in that: The minimum description length criterion (MDL) is applied to the covariance matrix within the smoothed group to estimate the number of sources, resulting in M ​​types of source number estimation results. The M types of source number estimation results include M-1 types of source number estimation results obtained by traversing k from 1 to M-1 according to the MDL criterion, and one type of source number estimation result obtained by directly estimating the source number of the covariance matrix R0 using the minimum description length criterion (MDL).

5. The source number estimation method based on the improved smoothed order array direction finding method according to claim 1, characterized in that, The steps to determine the final number of source data in the output based on monotonicity and the magnitude and frequency of values ​​in the reverse sequence are as follows: If the reverse sequence is not monotonically increasing, the first maximum value of the reverse sequence is selected as the final number of source values. If the reverse sequence is monotonically increasing and the sequence values ​​include 1, the number of times each value appears in the reverse sequence is counted, and the value with the most occurrences in the sequence is selected as the final number of source values. If the reverse sequence is monotonically increasing but the sequence values ​​do not include 1, the value with the largest value in the sequence is selected as the final number of source values.

6. The source number estimation method based on the improved smoothed order array direction finding method according to claim 1, characterized in that: When the incident signal does not contain a coherent signal, the number of array elements M and the number of incident signals K must satisfy M≥K+1; when the incident signal contains a coherent signal, the number of array elements M and the number of incident signals K must satisfy M≥2K.

7. The source number estimation method based on the improved smoothed order array direction finding method according to claim 1, characterized in that: The step of determining the monotonicity of the reverse sequence is achieved by calculating the difference of the reverse sequence and determining whether all difference values ​​are greater than or equal to zero.

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