CN109143155B - Correlated signal direction of arrival estimation method and system based on mutual prime array - Google Patents
Correlated signal direction of arrival estimation method and system based on mutual prime array Download PDFInfo
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Abstract
The invention provides a correlation signal direction of arrival estimation method and system based on a relatively prime array, which are used for sampling signals received by the relatively prime array to obtain time domain discrete signals; then, by setting the array element number of the subarray, obtaining fourth-order cumulant of the subarray signal according to the time domain discrete signal, and performing forward and backward smoothing on the fourth-order cumulant of the subarray signal to obtain smoothed fourth-order cumulant; and carrying out eigenvalue decomposition on the smoothed fourth-order cumulant to obtain a projection operator, and finally estimating the direction of arrival of the signal according to all the projection operators by using a Root-MUSIC algorithm. The method and the system carry out signal direction-of-arrival estimation by combining the mutual prime array and the fourth-order cumulant, can effectively ensure the precision of the estimation result under the condition of not increasing the number of array elements, and have better effect when the number of signals is more than the number of the array elements; and the signal correlation can be effectively eliminated, the spatial resolution of the signal is enhanced, and the method can be suitable for various complex environments.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to a correlation signal direction of arrival estimation method and system based on a mutual prime array.
Background
In array signal processing, Direction-of-Arrival (DOA) estimation is an effective method for determining signal Direction and estimating source position, and is applied to the fields of radar, communication, medicine and the like. In the field of DOA estimation, a subspace method represented by a MUltiple Signal Classification (MUSIC) algorithm is widely used. The MUSIC algorithm is widely applied because it obtains orthogonal signal subspace and noise subspace by decomposing the correlation matrix of the signal, and has the characteristic of spatial super-resolution.
However, in the conventional MUSIC algorithm, a large amount of sample data is generally required to ensure the estimation accuracy of the algorithm; meanwhile, in order to obtain a large amount of sampling data, the number of array elements is generally increased. Although the estimation precision of the MUSIC algorithm can be improved by increasing the number of the array elements, the method not only increases the data receiving amount, but also brings huge pressure to data transmission, storage and processing, thereby increasing the implementation difficulty of hardware and being difficult to meet the actual engineering requirements.
In view of the above, it is desirable to provide a method and a system for estimating a signal direction of arrival, which can ensure estimation accuracy, without increasing the number of array elements.
Disclosure of Invention
The invention provides a correlation signal direction-of-arrival estimation method and system based on a mutual prime array, aiming at overcoming the problem that the estimation accuracy is difficult to apply to a complex application environment because the number of array elements is generally increased to ensure the estimation accuracy when the traditional DOA estimation method is used for estimating the signal direction-of-arrival in the prior art.
In one aspect, the present invention provides a correlation signal direction of arrival estimation method based on a mutual prime array, including:
sampling signals received by a preset number of target arrays according to a time domain to obtain time domain discrete signals corresponding to each target array, wherein each two target arrays are mutually prime arrays;
for any target array, setting the array element number of the sub-array of the target array, and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array;
for any two target arrays, obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to sub-array signals corresponding to all sub-arrays of the two target arrays;
performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix;
and estimating the direction of arrival of the signal according to all projection operators by using a Root-MUSIC algorithm.
Preferably, the obtaining of the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-arrays specifically includes:
for any target array, taking the array element number of the sub-array corresponding to the target array as a target number, and combining the adjacent array elements of the target number in all the array elements of the target array to obtain all the sub-arrays of the target array;
and separating the sub-array signal corresponding to each sub-array from the time domain discrete signal corresponding to the target array to obtain the sub-array signals corresponding to all the sub-arrays of the target array.
Preferably, the fourth-order cumulant matrix after smoothing corresponding to the two target arrays is obtained according to the sub-array signals corresponding to all the sub-arrays of the two target arrays, which specifically includes:
for any two target arrays, randomly selecting one sub array from the respective sub arrays of the two target arrays to carry out pairwise combination to obtain a plurality of sub array combinations, and for any one sub array combination, obtaining a fourth-order cumulant matrix corresponding to the sub array combination according to sub array signals corresponding to all the sub arrays in the sub array combination;
and performing forward and backward smoothing treatment on the fourth-order cumulant matrixes corresponding to all the sub-array combinations to obtain the smoothed fourth-order cumulant matrixes corresponding to the two target arrays.
Preferably, a fourth-order cumulant matrix corresponding to the sub-array combination is obtained according to the sub-array signals corresponding to all the sub-arrays in the sub-array combination, and the specific calculation formula is as follows:
wherein x is1a(t) is a sub-array signal corresponding to sub-array a of the target array 1; x is the number of2b(t) is the sub-array signal corresponding to sub-array b of the target array 2; rabAnd combining the corresponding fourth-order cumulant matrix for the sub-arrays formed by the sub-array a and the sub-array b.
Preferably, the fourth-order cumulant matrix corresponding to all the sub-array combinations is subjected to forward and backward smoothing to obtain the smoothed fourth-order cumulant matrices corresponding to the two target arrays, and the specific calculation formula is as follows:
wherein R is12The smoothed fourth-order cumulant corresponding to the target array 1 and the target array 2; a is any sub-array of the target array 1; b is any sub-array of the target array 2; n is a radical of1The array element number of the target array 1; m1The number of array elements of each sub array of the target array 1; n is a radical of2Is the array element number of the target array 2; m2The number of array elements of each sub array of the target array 2; j is a permutation matrix with the inverse of the angular array element being 1.
Preferably, the eigenvalue decomposition is performed on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix, and the method specifically includes:
for any one smoothed fourth-order cumulant matrix, carrying out eigenvalue decomposition on the smoothed fourth-order cumulant matrix to obtain a plurality of eigenvectors;
screening out the characteristic vectors meeting preset conditions from all the characteristic vectors according to the characteristic values of all the characteristic vectors to serve as target characteristic vectors;
and combining all target characteristic vectors into a target matrix, and obtaining a projection operator corresponding to the smoothed fourth-order cumulant matrix according to the target matrix.
Preferably, the Root-MUSIC algorithm is used to estimate the direction of arrival of the signal according to all projection operators, specifically:
for any projection operator, constructing a polynomial function corresponding to the projection operator by using a preset function construction method;
establishing a target equation according to the polynomial functions corresponding to all the projection operators, and solving the target equation to obtain equation roots distributed on a unit circle;
and estimating the direction of arrival of the signal according to the equation root.
In one aspect, the present invention provides a correlation signal direction of arrival estimation system based on a mutual prime array, including:
the signal acquisition module is used for sampling signals received by a preset number of target arrays according to a time domain to obtain a time domain discrete signal corresponding to each target array, wherein each two target arrays are mutually prime arrays;
the signal preprocessing module is used for setting the array element number of the sub-array of the target array for any target array and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array;
the smoothing calculation module is used for obtaining a smoothed fourth-order cumulant matrix corresponding to any two target arrays according to the sub-array signals corresponding to all the sub-arrays of the two target arrays;
the eigenvalue decomposition module is used for performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix;
and the direction-of-arrival estimation module is used for estimating the direction of arrival of the signal according to all the projection operators by utilizing a Root-MUSIC algorithm.
In one aspect, the present invention provides an electronic device comprising:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, the processor being capable of performing any of the methods described above when invoked by the processor.
In one aspect, the invention provides a non-transitory computer readable storage medium storing computer instructions that cause a computer to perform any of the methods described above.
The invention provides a correlation signal direction of arrival estimation method and system based on a relatively prime array, which are used for sampling signals received by the relatively prime array to obtain time domain discrete signals; then, by setting the array element number of the subarray, obtaining fourth-order cumulant of the subarray signal according to the time domain discrete signal, and performing forward and backward smoothing on the fourth-order cumulant of the subarray signal to obtain smoothed fourth-order cumulant; and carrying out eigenvalue decomposition on the smoothed fourth-order cumulant to obtain a projection operator, and finally estimating the direction of arrival of the signal according to all the projection operators by using a Root-MUSIC algorithm. The method and the system carry out signal direction-of-arrival estimation by combining the mutual prime array and the fourth-order cumulant, can effectively ensure the precision of the estimation result under the condition of not increasing the number of array elements, and have better effect when the number of signals is more than the number of the array elements; and the method can effectively remove signal correlation, enhance the spatial resolution of signals, be suitable for various complex environments and effectively meet various actual engineering requirements.
Drawings
FIG. 1 is a schematic overall flowchart of a correlation signal direction of arrival estimation method based on a mutual prime array according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an overall structure of a correlation signal direction of arrival estimation system based on a mutual prime array according to an embodiment of the present invention;
fig. 3 is a schematic structural framework diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Fig. 1 is a schematic overall flow chart of a correlation signal direction of arrival estimation method based on a relatively prime array according to an embodiment of the present invention, and as shown in fig. 1, the present invention provides a correlation signal direction of arrival estimation method based on a relatively prime array, including:
s1, sampling signals received by a preset number of target arrays according to a time domain to obtain time domain discrete signals corresponding to each target array, wherein each two target arrays are mutually prime arrays;
specifically, a preset number of target arrays are first arranged, where the target arrays may be array antennas for receiving signals, and each two target arrays are mutually prime arrays. The reciprocal element array is a sparse array with a special arrangement mode, can construct a virtual uniform array, and has a good effect when the number of signals is more than that of array elements. For example, the number of array elements of a pair of the inter-element arrays is a and B, respectively, and the pair of the inter-element arrays can construct a virtual array with the number of array elements a × B, so that the number of signals that can be processed by the pair of the inter-element arrays is a × B, and a × B is greater than a + B, that is, the number of signals that can be processed is greater than the total number of array elements. Therefore, under the condition of the same array element, the correlated signal arrival direction estimation method based on the mutual prime array in the embodiment can process more signals compared with the traditional DOA estimation method.
In this embodiment, 3 target arrays, namely, a target array 1, a target array 2, and a target array 3 are arranged in total, and the number of array elements of the target array 1, the target array 2, and the target array 3 is N, respectively1、N2And N3. In order to make every two of the target arrays 1, 2 and 3 mutually a mutual prime array, the positions of the target array 1 may be arranged as { An }1d|n1＝0,...,N1-1 }; the position of the target array 2 is arranged as { Bn2d|n2＝0,...,N2-1 }; the position of the target array 3 is arranged to be Cn3d|n3＝0,...,N3-1}. Thus, the target array 1 has an array element pitch of a × d; the array element spacing of the target array 2 is B x d; the target array 3 has array element spacing C x d. Wherein A, B and C are positive integers of two interlinines; d is a fundamental unit of array element spacing, which typically does not exceed a half wavelength. In other embodiments, the preset number of target arrays may be set according to actual requirements, and is not specifically limited herein.
After a preset number of target arrays are arranged, signals are received using the preset number of target arrays. And then sampling signals received by a preset number of target arrays according to the time domain, and after certain pretreatment is carried out on the sampled signals, obtaining time domain discrete signals corresponding to each target array. The number of snapshots of the sample can be set according to actual requirements, and is not specifically limited here.
S2, for any target array, setting the array element number of the sub-array of the target array, and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array;
specifically, on the basis of the above technical solution, for any one target array in a preset number of target arrays, the number of array elements of the sub-array of the target array is set, the number of array elements of each sub-array of the same target array is the same, and the number of array elements of the sub-array should be smaller than the total number of array elements of the target array, which may be specifically set according to actual requirements, and is not specifically limited here. All the sub-arrays in the target array can be determined according to the number of the array elements of the sub-arrays, and finally, the sub-array signals corresponding to all the sub-arrays of the target array (i.e., the signals received by all the array elements in the sub-arrays) are obtained from the time domain discrete signals corresponding to the target array. Similarly, the sub-array signals corresponding to all the sub-arrays of other target arrays can be obtained according to the steps of the method.
S3, for any two target arrays, obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to the sub-array signals corresponding to all the sub-arrays of the two target arrays;
specifically, after obtaining the sub-array signals corresponding to all the sub-arrays of each target array, for any two target arrays, one sub-array is randomly selected from the respective sub-arrays of the two target arrays to be combined pairwise, so that a plurality of sub-array combinations are obtained for the two target arrays, and each sub-array combination includes two sub-arrays. And for any sub-array combination in the sub-array combinations, obtaining sub-array signals respectively corresponding to two sub-arrays in the sub-array combination, and performing fourth-order cumulant calculation on the sub-array signals respectively corresponding to the two sub-arrays to obtain a fourth-order cumulant matrix corresponding to the sub-array combination. On the basis, the fourth-order cumulant matrix corresponding to all the sub-array combinations is subjected to forward and backward smoothing, and the smoothed fourth-order cumulant matrix corresponding to the two target arrays can be obtained. Similarly, according to the steps of the method, the smoothed fourth-order cumulant matrix corresponding to any other two target arrays can be obtained. The smoothed fourth order cumulant matrix effectively decorrelates the signals.
It should be noted that the fourth-order cumulant represents a statistical relationship between signals of four array elements, and contains more information than the second-order statistics, which is beneficial to increase the equivalent aperture of the array and increase the spatial resolution. Moreover, the fourth-order cumulant can also inhibit Gaussian noise, and has a good effect in a Gaussian-distributed color noise environment.
S4, performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix;
specifically, on the basis of the above technical solution, for any two target arrays, a corresponding smoothed fourth-order cumulant matrix can be obtained, and thus, a plurality of smoothed fourth-order cumulant matrices can be obtained. On the basis, for any one smoothed fourth-order cumulant matrix, eigenvalue decomposition is carried out on the smoothed fourth-order cumulant matrix to obtain a plurality of eigenvectors, then all eigenvectors are arranged according to the absolute value of the eigenvalue, and a larger eigenvalue and a smaller eigenvalue are separated, wherein the larger eigenvalue is generally more than 10 times of the smaller eigenvalue. And finally, obtaining a projection operator corresponding to the smoothed fourth-order cumulant matrix according to a matrix formed by the eigenvectors corresponding to the smaller eigenvalues. Similarly, the projection operator corresponding to the other smoothed fourth-order cumulant matrix can be obtained according to the steps of the method.
And S5, estimating the direction of arrival of the signal according to all projection operators by using a Root-MUSIC algorithm.
Specifically, after the projection operator corresponding to each smoothed fourth-order cumulant matrix is obtained, the Root-MUSIC algorithm is used for estimating the direction of arrival of the signal according to all the projection operators. The Root-MUSIC algorithm is specifically as follows: firstly, a polynomial function corresponding to each projection operator is constructed, then an equation is established according to the polynomial functions corresponding to all the projection operators, the equation is solved, equation roots distributed on unit circles are obtained, and finally the direction of arrival of signals can be estimated according to the equation roots.
The invention provides a correlation signal direction of arrival estimation method based on a relatively prime array, which comprises the steps of sampling signals received by the relatively prime array to obtain time domain discrete signals; then, by setting the array element number of the subarray, obtaining fourth-order cumulant of the subarray signal according to the time domain discrete signal, and performing forward and backward smoothing on the fourth-order cumulant of the subarray signal to obtain smoothed fourth-order cumulant; and carrying out eigenvalue decomposition on the smoothed fourth-order cumulant to obtain a projection operator, and finally estimating the direction of arrival of the signal according to all the projection operators by using a Root-MUSIC algorithm. The method estimates the direction of arrival of the signals by combining the mutual prime array and the fourth-order cumulant, can effectively ensure the precision of the estimation result under the condition of not increasing the number of array elements, and has better effect when the number of the signals is more than the number of the array elements; and the method can effectively remove signal correlation, enhance the spatial resolution of signals, be suitable for various complex environments and effectively meet various actual engineering requirements.
Based on any of the embodiments above, a correlation signal direction-of-arrival estimation method based on a mutual prime array is provided, and sub-array signals corresponding to all sub-arrays of the target array are obtained from time-domain discrete signals corresponding to the target array according to the array element number of the sub-arrays, specifically: for any target array, taking the array element number of the sub-array corresponding to the target array as a target number, and combining the adjacent array elements of the target number in all the array elements of the target array to obtain all the sub-arrays of the target array; and separating the sub-array signal corresponding to each sub-array from the time domain discrete signal corresponding to the target array to obtain the sub-array signals corresponding to all the sub-arrays of the target array.
Specifically, in this embodiment, for any one target array, the number of array elements of the sub-array of the target array is set, the number of array elements of the sub-array is used as the target number, and all the sub-arrays of the target array can be obtained by combining the adjacent array elements of the target number in all the array elements of the target array. On the basis, the sub-array signals corresponding to each sub-array are separated from the time domain discrete signals corresponding to the target array, and the sub-array signals corresponding to all the sub-arrays of the target array can be obtained.
For example, for target array 1, target array 2, and target array 3, T is performed on signals received by target array 1, target array 2, and target array 3sSampling of each snapshot to obtain time domain discrete signals x corresponding to the target array 1, the target array 2 and the target array 3 respectively1(t)、x2(t) and x3(t)，x1(t)、x2(t) and x3(t) may be specifically represented as:
x1(t)＝[x1(0，t)，...，x1(N1-1,t)]T,t＝1,...,Ts；
x2(t)＝[x2(0,t),...，x2(N2-1，t)]T，t＝1，...，Ts；
x3(t)＝[x3(0，t)，...,x3(N3-1,t)]T,t＝1,...,Ts；
wherein N is1The number of array elements of the target array 1; n is a radical of2The number of array elements of the target array 2; n is a radical of3The number of array elements of the target array 3.
Further, the number of array elements of the sub-array of the target array 1 is set to M1The number of array elements of the sub-array of the target array 2 is set to M2The number of array elements of the sub-array of the target array 3 is set to M3. On the basis, N can be obtained for the target array 11-M1+1 sub-arrays; n is obtained for the target array 22-M2+1 sub-arrays; n is obtained for the target array 33-M3+1 sub-arrays. Finally, the time domain discrete signals x corresponding to the target array 1, the target array 2 and the target array 31(t)、x2(t) and x39t), sub-array signals x corresponding to each of the sub-arrays of the target array 1, the target array 2, and the target array 3 are separated respectively1a(t)、x2b(t) and x3c(t), which can be expressed in particular as:
x1a(t)＝[x1(a,t),...,x1(a+M1-1,t)]T,a＝0,...,N1-M1；
x2b(t)＝[x2(b,t),...,x2(b+M2-1,t)]T,b＝0，...,N2-M2；
x3c(t)＝[x3(c,t),...,x3(c+M3-1,t)]T,c＝0,...,N3-M3；
wherein, a is any sub-array in the target array 1; b is any sub-array in the target array 2; c is any one of the sub-arrays in the target array 3.
The invention provides a correlation signal direction of arrival estimation method based on a mutual prime array, which is characterized in that for any target array, the number of array elements of a sub-array corresponding to the target array is used as a target number, and in all the array elements of the target array, adjacent array elements of the target number are combined to obtain all the sub-arrays of the target array; and separating the sub-array signal corresponding to each sub-array from the time domain discrete signal corresponding to the target array to obtain the sub-array signals corresponding to all the sub-arrays of the target array, so that the fourth-order cumulant of the sub-array signals can be obtained by combining all the sub-array signals, and the spatial resolution of the signals can be enhanced.
Based on any of the above embodiments, a correlation signal direction-of-arrival estimation method based on a mutual prime array is provided, and a smoothed fourth-order cumulant matrix corresponding to the two target arrays is obtained according to sub-array signals corresponding to all sub-arrays of the two target arrays, specifically: for any two target arrays, randomly selecting one sub array from the respective sub arrays of the two target arrays to carry out pairwise combination to obtain a plurality of sub array combinations, and for any one sub array combination, obtaining a fourth-order cumulant matrix corresponding to the sub array combination according to sub array signals corresponding to all the sub arrays in the sub array combination; and performing forward and backward smoothing treatment on the fourth-order cumulant matrixes corresponding to all the sub-array combinations to obtain the smoothed fourth-order cumulant matrixes corresponding to the two target arrays.
Specifically, in this embodiment, for any two target arrays, one sub-array is randomly selected from the respective sub-arrays of the two target arrays to perform pairwise combination, so that a plurality of sub-array combinations can be obtained for the two target arrays, and each sub-array combination includes two sub-arrays. And for any sub-array combination in the sub-array combinations, obtaining sub-array signals respectively corresponding to two sub-arrays in the sub-array combination, and performing fourth-order cumulant calculation on the sub-array signals respectively corresponding to the two sub-arrays to obtain a fourth-order cumulant matrix corresponding to the sub-array combination. The specific calculation formula is as follows:
wherein x is1a(t) is a sub-array signal corresponding to sub-array a of the target array 1; x is the number of2b(t) is the sub-array signal corresponding to sub-array b of the target array 2; rabCombining a corresponding fourth-order cumulant matrix for the sub-array formed by the sub-array a and the sub-array b; e represents expectation.
It should be noted that, in this embodiment, the preset number of the target arrays is 3, that is, there are 3 target arrays, which are the target array 1, the target array 2, and the target array 3 respectively; a. b and c are respectively any one sub-array of the target array 1, the target array 2 and the target array 3. According to the calculation formula, the fourth-order cumulant R corresponding to the sub-array combination formed by any one sub-array a in the target array 1 and any one sub-array b in the target array 2 can be calculated and obtainedab. Similarly, according to the above calculation formula, the fourth-order cumulant R corresponding to the sub-array combination formed by any one sub-array a in the target array 1 and any one sub-array c in the target array 3 can also be calculatedacAnd a fourth-order cumulative quantity R corresponding to a sub-array combination formed by any one sub-array b in the target array 2 and any one sub-array c in the target array 3bc。
On the basis, the fourth-order cumulant matrix corresponding to all the sub-array combinations is subjected to forward and backward smoothing, and the smoothed fourth-order cumulant matrix corresponding to the two target arrays can be obtained. The specific calculation formula is as follows:
wherein R is12The smoothed fourth-order cumulant corresponding to the target array 1 and the target array 2; a is any sub-array of the target array 1; b is any sub-array of the target array 2; n is a radical of1The array element number of the target array 1; m1The number of array elements of each sub array of the target array 1; n is a radical of2Is the array element number of the target array 2; m2The number of array elements of each sub array of the target array 2; j is a permutation matrix with the inverse of the angular array element being 1.
It should be noted that the number of array elements of the target array 1 is N1And the number of array elements M of each sub-array of the target array 11Then the number of sub-arrays of the target array 1 is N1-M1+ 1; therefore, the value of a in the above calculation formula is (0, N)1-M1). The array element number of the target array 2 is N2And the number of array elements M of each sub-array of the target array 22Then the number of sub-arrays of the target array 2 is N2-M2+ 1; therefore, the value of b in the above calculation formula is (0, N)2-M2)。
Similarly, according to the steps of the method, the smoothed fourth-order cumulant matrix R corresponding to any other two target arrays can be obtained13And R23. The smoothed fourth-order cumulant matrix obtained by the steps of the method can effectively remove the signal correlation.
The invention provides a correlation signal direction of arrival estimation method based on a mutual prime array, for any two target arrays, respectively selecting a sub-array from all sub-arrays of the two target arrays to combine to obtain a plurality of sub-array combinations, for any one sub-array combination, obtaining a fourth-order cumulant matrix corresponding to the sub-array combination according to sub-array signals corresponding to all sub-arrays in the sub-array combination; and performing forward and backward smoothing treatment on the fourth-order cumulant matrixes corresponding to all the sub-array combinations to obtain the smoothed fourth-order cumulant matrixes corresponding to the two target arrays. According to the method, the fourth-order cumulant matrix of the sub-array signals is obtained by carrying out fourth-order cumulant calculation on the sub-array signals, and then the fourth-order cumulant matrix of the sub-array signals is subjected to smoothing processing, so that signal correlation can be effectively eliminated, the spatial resolution of the signals is enhanced, and the accuracy of the signal estimation result is improved.
Based on any one of the embodiments, a correlation signal direction-of-arrival estimation method based on a mutual prime array is provided, and eigenvalue decomposition is performed on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix, specifically: for any one smoothed fourth-order cumulant matrix, carrying out eigenvalue decomposition on the smoothed fourth-order cumulant matrix to obtain a plurality of eigenvectors; screening out the characteristic vectors meeting preset conditions from all the characteristic vectors according to the characteristic values of all the characteristic vectors to serve as target characteristic vectors; and combining all target characteristic vectors into a target matrix, and obtaining a projection operator corresponding to the smoothed fourth-order cumulant matrix according to the target matrix.
Specifically, for any one smoothed fourth-order cumulant matrix, eigenvalue decomposition is performed on the smoothed fourth-order cumulant matrix to obtain a plurality of eigenvectors, and the eigenvectors meeting preset conditions are screened out from all the eigenvectors according to the eigenvalues of all the eigenvectors and used as target eigenvectors. In this embodiment, all the feature vectors are arranged according to the absolute value of the feature values, a larger feature value and a smaller feature value are separated, where the larger feature value is generally more than 10 times of the smaller feature value, and the feature vector corresponding to the smaller feature value is used as the target feature vector. And finally, combining the eigenvectors corresponding to the smaller eigenvalues into a target matrix, and obtaining a projection operator corresponding to the smoothed fourth-order cumulant matrix according to the target matrix. Similarly, the projection operator corresponding to the other smoothed fourth-order cumulant matrix can be obtained according to the steps of the method.
For example, for the aboveFour-order cumulant matrix R after 3 smoothing obtained in method embodiment12、R13And R23With R12For example, for R12After the characteristic decomposition is carried out, the target matrix formed by the obtained smaller characteristic values is V12nThen the corresponding projection operator
In the same way, R can be obtained13And R23Corresponding projection operator T13And T23Where H represents the conjugate transpose of the matrix.
The invention provides a correlation signal direction of arrival estimation method based on a mutual prime array, which comprises the steps of carrying out eigenvalue decomposition on a fourth-order cumulant matrix after smoothing to obtain a plurality of eigenvectors; screening out the characteristic vectors meeting preset conditions from all the characteristic vectors according to the characteristic values of all the characteristic vectors to serve as target characteristic vectors; and combining all target characteristic vectors into a target matrix, and obtaining a projection operator corresponding to the smoothed fourth-order cumulant matrix according to the target matrix. The method obtains the projection operator by carrying out eigenvalue decomposition on the smoothed fourth-order cumulant matrix, and is favorable for estimating the direction of arrival of the signal according to the projection operator.
Based on any of the embodiments above, a correlation signal direction-of-arrival estimation method based on a mutual prime array is provided, which estimates the direction-of-arrival of a signal according to all projection operators by using a Root-MUSIC algorithm, and specifically includes: for any projection operator, constructing a polynomial function corresponding to the projection operator by using a preset function construction method; establishing a target equation according to the polynomial functions corresponding to all the projection operators, and solving the target equation to obtain equation roots distributed on a unit circle; and estimating the direction of arrival of the signal according to the equation root.
Specifically, on the basis of obtaining the plurality of projection operators, for any one projection operator, a polynomial function corresponding to the projection operator is constructed by using a preset function construction method. Projection operator T obtained in the above method embodiment12For example, a polynomial function of its corresponding constructionf12(z) is:
z＝exp(jω)；
wherein j is an imaginary unit, namely a root number-1; omega is an arbitrary number; m1The number of array elements of each sub array of the target array 1; m2The number of array elements of each sub-array of the target array 2. Similarly, a projection operator T can be obtained13And T23Corresponding polynomial function f13(z) and f23(z)。
Further, an objective equation is established according to the polynomial functions corresponding to all the projection operators, and the objective equation is solved to obtain equation roots distributed on the unit circle. Obtaining a polynomial function f12(z)、f13(z) and f23On the basis of (z), establishing a target equation as follows:
f(z)＝f12(z)+f13(z)+f23(z)＝0
solving the above equation to obtain the ith equation root distributed on the unit circle
Finally, estimating the direction of arrival of the signal according to the equation root, and estimating the direction of arrival of the signal according to the equation root
For example, the final estimated direction of arrival of the signal can be expressed as:
the invention provides a correlation signal direction of arrival estimation method based on a mutual prime array, which is characterized in that for any projection operator, a polynomial function corresponding to the projection operator is constructed by utilizing a preset function construction method; establishing a target equation according to the polynomial functions corresponding to all the projection operators, and solving the target equation to obtain equation roots distributed on a unit circle; and estimating the direction of arrival of the signal according to the equation root. The method obtains the projection operator based on the mutual prime matrix and the fourth-order cumulant, and then estimates the direction of arrival of the signal according to the projection operator, so that the accuracy of the estimation result can be effectively ensured under the condition of not increasing the number of array elements.
Fig. 2 is a schematic diagram of an overall structure of a correlation signal direction of arrival estimation system based on a relatively prime array according to an embodiment of the present invention, and as shown in fig. 2, a correlation signal direction of arrival estimation system based on a relatively prime array is provided according to any of the embodiments, including:
the signal acquisition module 1 is configured to sample signals received by a preset number of target arrays according to a time domain to obtain a time domain discrete signal corresponding to each target array, where each two target arrays are mutually prime arrays;
the signal preprocessing module 2 is configured to set, for any one target array, the array element number of the sub-array of the target array, and obtain, according to the array element number of the sub-array, sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array;
the smoothing calculation module 3 is configured to, for any two target arrays, obtain a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to sub-array signals corresponding to all sub-arrays of the two target arrays;
the eigenvalue decomposition module 4 is used for performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix;
and the direction-of-arrival estimation module 5 is used for estimating the direction of arrival of the signal according to all the projection operators by utilizing a Root-MUSIC algorithm.
Specifically, the present invention provides a correlation signal direction-of-arrival estimation system based on a mutual prime array, which includes a signal acquisition module 1, a signal preprocessing module 2, a smoothing calculation module 3, a characteristic value decomposition module 4, and a direction-of-arrival estimation module 5, and the method in any one of the above method embodiments is implemented through cooperation between the modules, and the specific implementation process may refer to the above method embodiments, which is not described herein again.
The related signal direction-of-arrival estimation system based on the relatively prime array provided by the invention samples signals received by the relatively prime array to obtain time domain discrete signals; then, by setting the array element number of the subarray, obtaining fourth-order cumulant of the subarray signal according to the time domain discrete signal, and performing forward and backward smoothing on the fourth-order cumulant of the subarray signal to obtain smoothed fourth-order cumulant; and carrying out eigenvalue decomposition on the smoothed fourth-order cumulant to obtain a projection operator, and finally estimating the direction of arrival of the signal according to all the projection operators by using a Root-MUSIC algorithm. The system estimates the direction of arrival of signals by combining the mutual prime array and the fourth-order cumulant, can effectively ensure the accuracy of an estimation result under the condition of not increasing the number of array elements, and has better effect when the number of the signals is more than the number of the array elements; and the method can effectively remove signal correlation, enhance the spatial resolution of signals, be suitable for various complex environments and effectively meet various actual engineering requirements.
Fig. 3 shows a block diagram of an electronic device according to an embodiment of the present invention. Referring to fig. 3, the electronic device includes: a processor (processor)31, a memory (memory)32, and a bus 33; wherein, the processor 31 and the memory 32 complete the communication with each other through the bus 33; the processor 31 is configured to call program instructions in the memory 32 to perform the methods provided by the above-mentioned method embodiments, for example, including: sampling signals received by a preset number of target arrays according to a time domain to obtain time domain discrete signals corresponding to each target array, wherein each two target arrays are mutually prime arrays; for any target array, setting the array element number of the sub-array of the target array, and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array; for any two target arrays, obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to sub-array signals corresponding to all sub-arrays of the two target arrays; performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix; and estimating the direction of arrival of the signal according to all projection operators by using a Root-MUSIC algorithm.
The present embodiment discloses a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the method provided by the above-mentioned method embodiments, for example, comprising: sampling signals received by a preset number of target arrays according to a time domain to obtain time domain discrete signals corresponding to each target array, wherein each two target arrays are mutually prime arrays; for any target array, setting the array element number of the sub-array of the target array, and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array; for any two target arrays, obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to sub-array signals corresponding to all sub-arrays of the two target arrays; performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix; and estimating the direction of arrival of the signal according to all projection operators by using a Root-MUSIC algorithm.
The present embodiments provide a non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the methods provided by the above method embodiments, for example, including: sampling signals received by a preset number of target arrays according to a time domain to obtain time domain discrete signals corresponding to each target array, wherein each two target arrays are mutually prime arrays; for any target array, setting the array element number of the sub-array of the target array, and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array; for any two target arrays, obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to sub-array signals corresponding to all sub-arrays of the two target arrays; performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix; and estimating the direction of arrival of the signal according to all projection operators by using a Root-MUSIC algorithm.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above-described embodiments of the electronic device and the like are merely illustrative, where the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may also be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, the method of the present application is only a preferred embodiment and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A correlation signal direction of arrival estimation method based on a mutual prime array is characterized by comprising the following steps:
sampling signals received by a preset number of target arrays according to a time domain to obtain time domain discrete signals corresponding to each target array, wherein each two target arrays are mutually prime arrays;
for any target array, setting the array element number of the sub-array of the target array, and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array;
for any two target arrays, obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to sub-array signals corresponding to all sub-arrays of the two target arrays;
performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix;
estimating the direction of arrival of the signal according to all projection operators by utilizing a Root-MUSIC algorithm;
obtaining a smoothed fourth-order cumulant matrix corresponding to the two target arrays according to the sub-array signals corresponding to all the sub-arrays of the two target arrays, specifically:
for any two target arrays, randomly selecting one sub array from the respective sub arrays of the two target arrays to carry out pairwise combination to obtain a plurality of sub array combinations, and for any one sub array combination, obtaining a fourth-order cumulant matrix corresponding to the sub array combination according to sub array signals corresponding to all the sub arrays in the sub array combination;
performing forward and backward smoothing on the fourth-order cumulant matrixes corresponding to all the sub-array combinations to obtain the smoothed fourth-order cumulant matrixes corresponding to the two target arrays;
performing forward and backward smoothing on the fourth-order cumulant matrixes corresponding to all the sub-array combinations to obtain the smoothed fourth-order cumulant matrixes corresponding to the two target arrays, wherein the specific calculation formula is as follows:
wherein R is12The smoothed fourth-order cumulant corresponding to the target array 1 and the target array 2; a is any sub-array of the target array 1; b is any sub-array of the target array 2; n is a radical of1The array element number of the target array 1; m1The number of array elements of each sub array of the target array 1; n is a radical of2Is the array element number of the target array 2; m2The number of array elements of each sub array of the target array 2; j is a permutation matrix with the inverse of the angular array element being 1.
2. The method according to claim 1, wherein the obtaining of the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-arrays specifically comprises:
for any target array, taking the array element number of the sub-array corresponding to the target array as a target number, and combining the adjacent array elements of the target number in all the array elements of the target array to obtain all the sub-arrays of the target array;
and separating the sub-array signal corresponding to each sub-array from the time domain discrete signal corresponding to the target array to obtain the sub-array signals corresponding to all the sub-arrays of the target array.
3. The method according to claim 1, wherein the fourth-order cumulant matrix corresponding to the sub-array combination is obtained according to the sub-array signals corresponding to all the sub-arrays in the sub-array combination, and the specific calculation formula is:
wherein x is1a(t) is a sub-array signal corresponding to sub-array a of the target array 1; x is the number of2b(t) is the sub-array signal corresponding to sub-array b of the target array 2; rabAnd combining the corresponding fourth-order cumulant matrix for the sub-arrays formed by the sub-array a and the sub-array b.
4. The method according to claim 1, wherein the eigenvalue decomposition is performed on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix, specifically:
for any one smoothed fourth-order cumulant matrix, carrying out eigenvalue decomposition on the smoothed fourth-order cumulant matrix to obtain a plurality of eigenvectors;
screening out the characteristic vectors meeting preset conditions from all the characteristic vectors according to the characteristic values of all the characteristic vectors to serve as target characteristic vectors;
and combining all target characteristic vectors into a target matrix, and obtaining a projection operator corresponding to the smoothed fourth-order cumulant matrix according to the target matrix.
5. The method according to claim 1, characterized in that the direction of arrival of the signal is estimated from all projection operators using the Root-MUSIC algorithm, in particular:
for any projection operator, constructing a polynomial function corresponding to the projection operator by using a preset function construction method;
establishing a target equation according to the polynomial functions corresponding to all the projection operators, and solving the target equation to obtain equation roots distributed on a unit circle;
and estimating the direction of arrival of the signal according to the equation root.
6. A correlation signal direction-of-arrival estimation system based on a mutual prime array, comprising:
the signal acquisition module is used for sampling signals received by a preset number of target arrays according to a time domain to obtain a time domain discrete signal corresponding to each target array, wherein each two target arrays are mutually prime arrays;
the signal preprocessing module is used for setting the array element number of the sub-array of the target array for any target array and acquiring the sub-array signals corresponding to all the sub-arrays of the target array from the time domain discrete signals corresponding to the target array according to the array element number of the sub-array;
the smoothing calculation module is used for obtaining a smoothed fourth-order cumulant matrix corresponding to any two target arrays according to the sub-array signals corresponding to all the sub-arrays of the two target arrays;
the eigenvalue decomposition module is used for performing eigenvalue decomposition on each smoothed fourth-order cumulant matrix to obtain a projection operator corresponding to each smoothed fourth-order cumulant matrix;
the direction-of-arrival estimation module is used for estimating the direction of arrival of the signal according to all the projection operators by utilizing a Root-MUSIC algorithm;
the correlation signal direction-of-arrival estimation system based on the mutual prime array is further used for randomly selecting one sub array from the respective sub arrays of any two target arrays to carry out pairwise combination to obtain a plurality of sub array combinations, and for any one sub array combination, obtaining a fourth-order cumulant matrix corresponding to the sub array combination according to the sub array signals corresponding to all the sub arrays in the sub array combination; performing forward and backward smoothing on the fourth-order cumulant matrixes corresponding to all the sub-array combinations to obtain the smoothed fourth-order cumulant matrixes corresponding to the two target arrays;
the correlation signal direction-of-arrival estimation system based on the relatively prime array is further configured to perform forward and backward smoothing on the fourth-order cumulant matrices corresponding to all sub-array combinations to obtain smoothed fourth-order cumulant matrices corresponding to the two target arrays, and the specific calculation formula is as follows:
wherein R is12The smoothed fourth-order cumulant corresponding to the target array 1 and the target array 2; a is any sub-array of the target array 1; b is any sub-array of the target array 2; n is a radical of1The array element number of the target array 1; m1The number of array elements of each sub array of the target array 1; n is a radical of2Is the array element number of the target array 2; m2The number of array elements of each sub array of the target array 2; j is a permutation matrix with the inverse of the angular array element being 1.
7. An electronic device, comprising:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of any of claims 1 to 5.
8. A non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the method of any one of claims 1 to 5.
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