Radiation source number estimation method suitable for unmanned aerial vehicle array direction finding system

Abstract

A radiation source number estimation method suitable for an unmanned aerial vehicle array direction-finding system comprises the following steps: receiving observation signals through an antenna array, and calculating a covariance matrix of the observation signals; presetting the number of information sources, constructing a smoothing matrix containing a permutation matrix, and smoothing the covariance matrix based on the smoothing matrix to obtain a smoothed covariance matrix; performing information source number estimation on the smoothed covariance matrix based on an eigenvalue entropy calculation method to obtain an information source number estimation result; and arranging the information source number estimation results in an inverted order, and judging the monotonicity of the inverted sequence after the inverted order arrangement. According to the method, a new signal source number estimation scheme in array DOA estimation is provided, and due to the fact that the number of needed signal sampling points is very small, the method is suitable for signal source number estimation of an unmanned aerial vehicle array direction finding system under the conditions that received signals are small samples, aliasing color noise exists in observation signals and coherence exists in incident signals.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a method for estimating the number of radiation sources suitable for an array direction-finding system carried by an unmanned aerial vehicle. Background Art

[0002] Correct estimation of the number of signal sources is a necessary condition for the array direction finding system to correctly estimate DOA. Currently, there are mainly the following methods for estimating the number of signal sources:

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

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

[0005] (3) Gale circle transform method. This method does not use the eigenvalues ​​of the array covariance matrix, but instead uses the radius of the Gale circle of the array covariance matrix to estimate the number of signal sources. It is applicable to both white noise and colored noise conditions. Since this method involves a key parameter setting that lacks theoretical guidance and relies on empirical values, the signal source number estimation results of this method vary greatly under different parameter values. Therefore, this method is not convenient for practical use.

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

[0007] In a complex electromagnetic environment where the received signal is a small sample, the observed signal is mixed with colored noise, and the incident signal has coherence, no effective method for estimating the number of signal sources has been reported in the literature. Summary of the Invention

[0008] The purpose of the present invention is to propose a radiation source number estimation method suitable for unmanned aerial vehicle array direction finding systems, and to provide a new source number estimation scheme in array DOA estimation. Since a small number of signal sampling points are required, the present invention is suitable for unmanned aerial vehicle array direction finding systems when the received signal is a small sample, the observed signal is aliased with colored noise, and the incident signal has coherence.

[0009] The technical solution adopted by the present invention is: a method for estimating the number of radiation sources applicable to an array direction finding system onboard an unmanned aerial vehicle, comprising the following steps:

[0010] receiving an observation signal through an antenna array, and calculating a covariance matrix of the observation signal;

[0011] Presetting the number of information sources and constructing a smoothing matrix including a permutation matrix, and smoothing the covariance matrix based on the smoothing matrix to obtain a smoothed covariance matrix;

[0012] Estimating the number of information sources on the smoothed covariance matrix based on an eigenvalue entropy calculation method to obtain an estimation result of the number of information sources;

[0013] Arrange the estimated results of the number of signal sources in reverse order, and determine the monotonicity of the reverse sequence after the reverse order arrangement:

[0014] If the reverse sequence is not monotonically increasing, the first maximum value of the reverse sequence is the number of incident signal sources; if the reverse sequence is monotonically increasing and the sequence value contains 1, the number of times each value in the reverse sequence appears is counted, and the value with the largest number of occurrences is the number of incident signal sources; if the reverse sequence is monotonically increasing but the sequence value does not contain 1, the largest value in the reverse sequence is the number of incident signal sources.

[0015] As a preferred solution, the smoothing process includes forward smoothing and backward smoothing. The smoothed covariance matrix for:

[0016]

[0017] in, is the forward spatial smoothing matrix obtained by forward smoothing, is the backward spatial smoothing matrix obtained by backward smoothing.

[0018] As a preferred solution, the forward spatial smoothing matrix for:

[0019]

[0020] Where, k is the number of preset signal sources; M is the number of elements in the antenna array; P M-k,j=[I (M-k)×(M-k) 0 (M-k)×k ], P M-k,j is a (Mk)×M dimensional permutation matrix, which is composed of the (Mk)×(Mk) dimensional identity matrix I (M-k)×(M-k) and (Mk)×k-dimensional 0-element matrix 0 (M-k)×k Composition, j represents I (M-k)×(M-k) In P M-k,j The position of the backward movement in the middle; R0 is the covariance matrix; P M-k,j The transpose of .

[0021] As a preferred solution, the backward spatial smoothing matrix for:

[0022]

[0023] Where J is a permutation matrix of (Mk)×(Mk) dimensions; (·) H represents the conjugate transpose.

[0024] As a preferred solution, the formula for estimating the number of signal sources based on the eigenvalue entropy calculation method is:

[0025]

[0026] Where, P k is the estimated result of the number of signal sources obtained by the eigenvalue entropy calculation method; for The singular values ​​obtained by singular value decomposition, c and b are the serial numbers of the singular values, Representation matrix The number of ranks, that is, the matrix Dimension of K G (x) is the Gaussian kernel function.

[0027] As a preferred solution, the monotonicity determination is achieved by calculating the difference of the reverse sequence.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The present invention combines rank smoothing of the covariance matrix of antenna array received signals with entropy calculation of the covariance matrix eigenvalues ​​to provide a new scheme for estimating the number of signal sources in array DOA estimation. Since a small number of signal sampling points are required, the scheme is suitable for estimating the number of signal sources in unmanned aerial vehicle array direction finding systems when the received signal is a small sample, the observed signal is mixed with colored noise, and the incident signal has coherence. The scheme can also be used for estimating the number of signal sources in unmanned aerial vehicle array direction finding systems when coherent incident signals exist or when all incident signals are incoherent. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0031] Figure 1 The estimated results of the number of signal sources are as follows: the number of array elements is 10, the number of sampling points is 101, the observed signal is mixed with colored noise, and the number of signal coherence groups is different;

[0032] Figure 2 The estimated results of the number of signal sources when the number of sampling points is 101, the number of array elements is different, and the observed signal contains aliased colored noise;

[0033] Figure 3 is the estimated result of the number of signal sources when five signals are incident and the observed signal contains aliased colored noise;

[0034] Figure 4 is the estimated result of the number of signal sources when the number of incident independent signals K = 3;

[0035] Figure 5 is the estimated result of the number of signal sources when the number of incident independent signals K = 4;

[0036] Figure 6 is the estimated result of the number of signal sources when the number of incident independent signals K = 5;

[0037] Figure 7 is the estimated result of the number of signal sources when the number of incident independent signals K = 6;

[0038] Figure 8 Comparison of the number of incident signals that can be resolved under different numbers of array elements;

[0039] Figure 9 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0040] The present invention is described in detail below by way of exemplary embodiments. However, it should be understood that elements, structures, and features in one embodiment may also be beneficially combined in other embodiments without further description.

[0041] It should be noted that: unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning understood by persons having ordinary skills in the field to which the invention belongs. The words "one", "an" or "the" and the like used in the patent application specification and claims of the present invention do not express a quantity limitation, but indicate the existence of at least one; the words "first", "second" and "third" used herein shall not be regarded as a limitation on the order of components, but are only used to distinguish different components; the words "include" or "comprise" and the like indicate that the elements or objects appearing before "include" or "comprise" include the elements or objects listed after "include" or "comprise" and their equivalents, but do not exclude other elements or objects with the same function.

[0042] In order to more clearly describe the radiation source number estimation method applicable to the UAV array direction finding system, combined with the attached Figure 1-9 Describing the embodiment:

[0043] like Figure 9 As shown, a method for estimating the number of radiation sources for an array direction finding system onboard an unmanned aerial vehicle comprises the following steps:

[0044] S1: Assume that the UAV-mounted one-dimensional uniform linear antenna array has M array elements, and the M-dimensional observation signal obtained by measurement is x(t), x(t) = [x1(t), x2(t),…, x M (t)] T (superscript T indicates transpose), sampling point t = 1, 2, ..., T0, T0 is the number of signal sampling points, calculate the covariance matrix of the observed signal (superscript H indicates conjugate transpose);

[0045] S2: Let the number of preset signal sources be k, where k is a positive integer, k = 1, 2, ..., M-1, and define a (Mk) × M-dimensional matrix P M-k,j , j=0,1,…,k:

[0046] P M-k,j =[I (M-k)×(M-k) 0 (M-k)×k ](1)

[0047] P M-k,j is a permutation matrix, which consists of the (Mk)×(Mk)-dimensional identity matrix I (M-k)×(M-k) and (Mk)×k-dimensional 0-element matrix 0 (M-k)×k composition.

[0048] When the value of k is determined, P M-k,j As j takes different values, j represents I (M-k)×(M-k) In P M-k,jFor example, when M=4, k=1, j=0,

[0049]

[0050] Among them, P 4-1,0 The first three columns of I (4-1)×(4-1) , the 4th column consists of 0 (4-1)×1 .

[0051] When M=4, k=1, j=1,

[0052]

[0053] Among them, P 4-1,0 The last three columns form I (4-1)×(4-1) , the first column consists of 0 (4-1)×1 .

[0054] When M=4, k=2, j=0,

[0055]

[0056] Among them, P 4-1,0 The first two columns of I (4-2)×(4-2) , the 3rd and 4th columns form 0 (4-2)×2 .

[0057] When M=4, k=2, j=1,

[0058]

[0059] Among them, P 4-1,1 The 2nd and 3rd columns form I (4-2)×(4-2) , the 1st and 4th columns form 0 (4-2)×2 .

[0060] Using P M-k,j Split R0 into a cross-overlap matrix And find the average matrix, we can get

[0061]

[0062] The cross-overlap matrix sequence in the above formula is essentially a forward spatial smoothing matrix.

[0063] S3: Perform backward smoothing on R0. Let J be a permutation matrix of (Mk) × (Mk) dimensions. The backward smoothing matrix of R0 is expressed as:

[0064]

[0065] Where, It means to find the conjugate of R0.

[0066] according to and Get the smoothed covariance matrix

[0067]

[0068] The idea behind spatial decorrelation is used here. The idea behind spatial decorrelation is to divide the entire array into overlapping subarrays and then average the covariance matrices of the subarray received signals to obtain a spatially smoothed covariance matrix, thereby decorrelation or reducing the correlation of the incident signal. Forward smoothing essentially means averaging the submatrices of the sample covariance matrix along its main diagonal, while backward smoothing essentially means averaging the conjugate submatrices of the sample covariance matrix along its main diagonal.

[0069] Although the idea of ​​spatial smoothing decorrelation is borrowed, the algorithm in this section smoothes the received signal covariance matrix differently from the spatial smoothing algorithm. The technology of the present invention smoothes the received signal covariance matrix by decimating the original covariance matrix and then averaging it, as shown in Equations (2) and (3). The number of decimations is M, that is, the number of decimations is equal to the number of array elements. Spatial smoothing algorithms, whether forward spatial smoothing (FOSS), backward spatial smoothing (BOSS), or forward and backward spatial smoothing (FBSS), require setting the number of sub-array elements (to be greater than the number of incident signals) and the number of smoothing times (equal to the number of sub-arrays). Since the number of incident signals in practice is unknown, the number of signal sources cannot be estimated based on the spatial smoothing algorithm. Instead, the number of signal sources is required as an input condition, and then the DOA estimation work is performed based on the spatial smoothing algorithm. When the technology of the present invention smoothes the received signal covariance matrix, it does not need to set the number of incident signals, so it has the adaptive ability to automatically set according to the number of antenna array elements.

[0070] Assume that the signal source consists of L groups of related sources, denoted as g i (i=1,2,…,L), if i=1, it means that the group is a single independent signal; i=3, it means that the group has 3 coherent sources, and L is the maximum correlation coefficient. If g2=3, it means that there are 3 coherent groups, each with two coherent sources, then the number of coherent groups is

[0071]

[0072] The total number of signal sources is

[0073]

[0074] Where, f q Indicates the number of signal sources in the qth correlation group.

[0075] If the data covariance matrix is ​​obtained from a finite number of snapshots, then

[0076]

[0077] Where, the dimension of I is (Mk)×(Mk). σ 2 is the power of the Gaussian white noise incident on the array.

[0078] and The dimension of the signal subspace is The rank of , so the smoothed order is

[0079]

[0080] At the same time, combined with the eigenvalue entropy calculation method (EEE), we can get

[0081]

[0082] According to formula (9), 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 types of signal source number estimation results can be obtained. Directly apply EEE to estimate the number of signal sources on R0 and obtain one signal source number estimation result, thereby obtaining M types of signal source number estimation results P k ,k=1,2,…,M。

[0083] The improved rank smoothing method is based on the classic rank smoothing algorithm, which takes the reverse order of the rank smoothing sequence and sets P k , k=1,2,…,M are arranged in reverse order to obtain the reverse sequence:

[0084] P′ z ,z=1,2,…,M (10)

[0085] Obviously P′1=P M ,P′2=P M-1 ,…,P′ M =P1.

[0086] For the reverse sequence shown in formula (10), we can determine whether it is a monotonically increasing sequence by taking the difference. z ,z=1,2,…,M sequence is not monotonically increasing, then P′ z ,z=1,2,…,the first maximum value of M is the number of incident signals; if P′ z ,z=1,2,…,M sequence is monotonically increasing, and the sequence value contains 1, then the statistic P′ z ,z=1,2,…,the number of times each value in M ​​appears, the value with the largest number of occurrences is the number of incident signals; if P′ z,z=1,2,…,M sequence is monotonically increasing, but the sequence value does not contain 1, then the largest value in the sequence is the number of incident signals.

[0087] Among them, the calculation formula of the eigenvalue entropy calculation method (EEE) is as follows:

[0088]

[0089] Where, P k is the estimated result of the number of signal sources obtained by the eigenvalue entropy calculation method; for The singular values ​​obtained by singular value decomposition, c and b are the serial numbers of the singular values, Representation matrix The number of ranks, that is, the matrix Dimension of K G (x) is the Gaussian kernel function.

[0090] The EEE algorithm, proposed by Hamid Asadi et al., aims to estimate the number of signal sources in an array when the observed signal is aliased with colored noise. Its basic concept is that the entropy values ​​of the signal and noise eigenvalues ​​differ significantly, while the entropy values ​​corresponding to each signal eigenvalue and each noise eigenvalue do not differ significantly.

[0091] The present invention is further described below in conjunction with the experimental test diagram:

[0092] 1. Experimental conditions setting:

[0093] The experimental verification of the present invention is carried out under computer simulation conditions, and the simulation software adopts MATLAB R2014a. In order to verify the effectiveness of the present invention, simulation experimental tests are carried out. Through the estimation accuracy of the number of radiation sources, the estimation results of the number of signal sources under the conditions of different signal coherence groups in the incident signal, and the estimation results of the number of signal sources under the conditions of high-dimensional small samples, aliased color noise and incident signal coherence are respectively examined. The signal source number estimation methods used for comparison with the technical solution of the present invention are: Gale circle transform algorithm (GDE), classical smooth rank sequence method (SS), eigenvalue entropy calculation method (EEE), based on smooth rank method [1] The combination with EEE is called SSE method, and the technical solution of the present invention (called DSSE).

[0094] Example 1: Experiment on Estimating the Number of Signal Sources under Different Signal Coherence Numbers

[0095] There are five radar radiation source signals, the signal pulse modulation mode is single frequency continuous wave (CW), the pulse width is 30μs, and the carrier frequency is f c1 、f c2、f c3 、f c4 and f c5 . The amplitude of the second signal is 0.7+0.6i, the amplitude of the fourth signal is 0.3+0.7i, and the amplitudes of other signals are all 1. The pulse repetition frequency is 10kHz. By changing the carrier frequency of the incident signal, a coherent signal environment is constructed. The signal incident angles are -45°, -34°, -23, -4°, and 14° respectively. The signal sampling frequency is 60MHz, and the number of signal sampling points is 101. The number of array elements of the unmanned aerial vehicle array direction finding system is 10. The maximum frequency of the signal that the array can receive is 240MHz, and the array element spacing is half of the minimum wavelength of the incident signal.

[0096] The simulation of colored noise adopts the method of mutual coupling of antenna elements. The spatial colored noise covariance matrix R based on the idea of ​​mutual coupling of antenna elements is N The model can be expressed as:

[0097]

[0098] Where p,q=1,2,…,M. represents the color noise amplitude, and ρ represents the correlation coefficient between adjacent array elements. Given the signal-to-noise ratio SNR, assuming that the signal and noise power are P S and P N , then according to the signal-to-noise ratio formula Assume that the power of the received signal of each array element is normalized to 1, that is, P S =1, then we can calculate P N =10 -SNR / 10 ,Right now Therefore, R can be set according to the signal-to-noise ratio. N Key parameters in

[0099] In the simulation experiment, the method of superposition of colored noise is to first normalize the power of the received signal of each array element, and then calculate the covariance matrix according to the signal received by the antenna array. According to the set signal-to-noise ratio SNR, the calculation formula is Set ρ, and R N The covariance matrix of the received signal under a certain signal-to-noise ratio is obtained by adding the expression to the covariance matrix.

[0100] The signal-to-noise ratio range is -20dB to 30dB, the signal-to-noise ratio step is 2dB, and the number of Monte Carlo simulations is 500. The estimated results of the number of signal sources under different coherent signal numbers are as follows: Figure 1 shown.

[0101] Example 2: Estimation of the number of radiating sources in the case of high-dimensional small samples, aliased colored noise, and coherent incident signals

[0102] Assume that the incident signal and array parameters are the same as those in Example 1. c1 =f c2 =f c3 =f c4 =f c5 =10MHz, that is, the five-way signal is coherent. Under different array element numbers and sampling point numbers, the signal source number estimation results are as follows Figure 2-3 As shown, Figure 2 (d) The average time of 200 Monte Carlo simulations of different algorithms at each SNR range of -20 to 30 dB with a step size of 2 dB is calculated, that is, the total time divided by (26×200).

[0103] Example 3: Experiment on the relationship between the number of signal sources and the number of array elements applicable to the algorithm

[0104] Assume that the number of incident independent signals is 3, 4, 5, and 6 respectively, and change the number of array elements respectively to observe the relationship between the number of signal sources and the number of array elements to which the algorithm is applicable. The number of signal sampling points is 101, the signal-to-noise ratio range is -20dB to 30dB, the signal-to-noise ratio step is 2dB, and the number of Monte Carlo simulations is 500. The signal incident angles are -45°, -34°, -23, -4°, 14°, and 20° respectively, and the incident signals correspond to the above angles from left to right. The experimental results are shown in Figure 2. Figure 4-7 shown.

[0105] Compared with the forward smoothing (FOSS) and forward and backward smoothing (FBSS) algorithms, the DSSE technology of the present invention can distinguish the relationship between the number of signal sources and the number of array elements. Figure 8 shown.

[0106] The above experimental results show that the present invention can be used to estimate the number of radiation sources in the case where the received signal of the unmanned aerial vehicle array direction finding system is a small sample, the observed signal is aliased with colored noise, and the incident signal has coherence. In contrast, the GDE algorithm, EEE algorithm, and SS algorithm are not suitable for estimating the number of signal sources under the above circumstances. Compared with the SSE algorithm, the signal-to-noise ratio required for accurately estimating the number of signal sources by the present invention (DSSE) technology is lower. In terms of the number of incident independent signals that the antenna array can resolve, the number of antenna elements M and the number of incident signals K must satisfy the relationship M≥K+2, which is a necessary condition for the applicability of the present invention (DSSE) technology.

[0107] Parts not described in detail in the above embodiments are prior art.

[0108] It should be noted that although the present invention has been described with reference to the above embodiments, the present invention may also have other various embodiments. Without departing from the spirit and scope of the present invention, it is obvious that those skilled in the art may make various corresponding changes and modifications to the present invention, and such changes and modifications shall fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A method for estimating the number of radiation sources for an array direction finding system mounted on an unmanned aerial vehicle, characterized in that: The following steps are involved: receiving an observation signal through an antenna array, and calculating a covariance matrix of the observation signal; Presetting the number of information sources and constructing a smoothing matrix including a permutation matrix, and smoothing the covariance matrix based on the smoothing matrix to obtain a smoothed covariance matrix; Estimating the number of information sources on the smoothed covariance matrix based on an eigenvalue entropy calculation method to obtain an estimation result of the number of information sources; Arrange the estimated results of the number of signal sources in reverse order, and determine the monotonicity of the reverse sequence after the reverse order arrangement: If the reverse sequence is not monotonically increasing, the first maximum value of the reverse sequence is the number of incident signal sources; if the reverse sequence is monotonically increasing and the sequence value contains 1, the number of times each value in the reverse sequence appears is counted, and the value with the largest number of occurrences is the number of incident signal sources; if the reverse sequence is monotonically increasing but the sequence value does not contain 1, the largest value in the reverse sequence is the number of incident signal sources.

2. The method for estimating the number of radiation sources applicable to an array direction finding system onboard an unmanned aerial vehicle according to claim 1, characterized in that: The smoothing process includes forward smoothing and backward smoothing. The covariance matrix after smoothing is for: in, is the forward spatial smoothing matrix obtained by forward smoothing, is the backward spatial smoothing matrix obtained by backward smoothing.

3. The method for estimating the number of radiation sources applicable to an array direction finding system onboard an unmanned aerial vehicle according to claim 2, characterized in that: The forward spatial smoothing matrix for: Where, k is the number of preset signal sources; M is the number of elements in the antenna array; P M-k,j =[I (M-k)×(M-k) 0 (M-k)×k ], P M-k,j is a (Mk)×M dimensional permutation matrix, which is composed of the (Mk)×(Mk) dimensional identity matrix I (M-k)×(M-k) and (Mk)×k-dimensional 0-element matrix 0 (M-k)×k Composition, j represents I (M-k)×(M-k) In P M-k,j The position of the backward movement in the middle; R0 is the covariance matrix; P M-k,j The transpose of .

4. The method for estimating the number of radiation sources applicable to an array direction finding system onboard an unmanned aerial vehicle according to claim 3, characterized in that: The backward spatial smoothing matrix for: Where J is a permutation matrix of (Mk)×(Mk) dimensions; (·) H represents the conjugate transpose.

5. The method for estimating the number of radiation sources applicable to an array direction finding system onboard an unmanned aerial vehicle according to claim 1, characterized in that: The formula for estimating the number of information sources based on the eigenvalue entropy calculation method is: Where, P k is the estimated result of the number of signal sources obtained by the eigenvalue entropy calculation method; for The singular values ​​obtained by singular value decomposition, c and b are the serial numbers of the singular values, Representation matrix The number of ranks, that is, the matrix Dimension of K G (x) is the Gaussian kernel function.

6. The method for estimating the number of radiation sources applicable to an array direction finding system onboard an unmanned aerial vehicle according to claim 1, characterized in that: Monotonicity is determined by calculating the difference of the reverse sequence.

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