CN-116709175-B - Multi-array direct positioning method based on two-dimensional discrete Fourier transform

Abstract

The invention discloses a multi-array direct positioning method based on two-dimensional discrete Fourier transform, which comprises the steps of firstly calculating cross covariance of signals received by each observation station, obtaining azimuth information which is automatically well matched by each observation station through a two-dimensional discrete Fourier transform (two-dimensional Discrete Fourier Transform, 2D-DFT) technology, then constructing a phase rotation matrix to compensate the azimuth information of each observation station to obtain more accurate azimuth information, and finally combining the accurate information of all the observation stations to directly solve a target position according to a least square idea. The multi-array direct positioning method based on the two-dimensional discrete Fourier transform can effectively position the target. In addition, the method does not need two-dimensional spectrum peak searching, and the calculation complexity is remarkably reduced. Under the condition of low signal to noise ratio, the positioning performance of the method is close to that of a minimum variance undistorted response (Minimum Variance Distortionless Response, MVDR) direct positioning algorithm, and is superior to a traditional Angle of Arrival-K-Means (AOA-K-Means) clustering two-step positioning method.

Inventors

• SHI XINLEI
• ZHANG XIAOFEI
• ZENG HAOWEI
• QIAN YANG
• SUN YUXIN

Assignees

• 南京航空航天大学

Dates

Publication Date

20260505

Application Date

20230518

Claims (1)

1. 1. The multi-array direct positioning method based on the two-dimensional discrete Fourier transform is characterized by comprising the following steps of: Step 1), constructing a multi-array combined positioning model to obtain received signal information ; Step 1.1), constructing an array flow pattern for each observation station ; M is the number of large-scale uniform linear array elements equipped for each observation station, and K is the number of radiation sources; for the steering vector, d represents the array element spacing, Representing the signal wavelength; Representing the position vector of the first observation station, 、 Respectively the horizontal and vertical coordinates, the position vector of the kth radiation source is , 、 Respectively the horizontal and vertical coordinates thereof; total position vector , Representing the angle of arrival of the kth radiation source received by the ith observation station, Representation vector taking Is selected from the group consisting of a first element, Representation vector taking The first element of (a); Representing a 2-norm; step 1.2), obtaining a received signal of the first observation station at the sampling time t by adopting a multi-array combined positioning model , Is that A dimensional transmit signal vector, the covariance matrix of which is a diagonal matrix; Representation of A wigowski white noise vector; step 2), calculating a cross covariance matrix of the signals received by each observation station, and performing two-dimensional discrete Fourier transform on the cross covariance matrix; Step 2.1), calculating the cross covariance of the 1 st base station received signal and the 1 st+1 th base station received signal according to the following formula : Wherein T represents the number of shots, L represents the number of observation stations; step 2.2), constructing a normalized DFT matrix : 。 In the formula, The (m 1 ,n 1 ) th element of the matrix is ; Matrix after 2D-DFT processing of cross covariance of 1 st base station and 1 st+1st base station with respect to steering vector of kth source ,l=1,2,...,L-1; Array The (u, v) th element of (a) is: When the physical array element number M approaches infinity, i.e There must be a pair of integers So that At the same time All of the remaining elements of (c) are 0, at which point, An ideal sparsity is achieved, and all power is concentrated in the second frequency-discrete Fourier transform (2D-DFT) spectrum Point, azimuth information automatically matched by each base station is formed by The position of the non-zero point is obtained, , ; Step 2.3) according to Performing 2D-DFT on received signal cross covariance and calculating matrix Index value corresponding to the largest K elements of (a) , ; Step 2.4) according to , , The initial estimation of the azimuth angle is carried out, Representing the initial estimate of the arrival angle of the 1 st observation station at k radiation sources, Representing the initial estimated value of the angle of arrival of the k radiation sources by the (1+1) th observation station; step 3), constructing a phase rotation matrix and compensating the direction information; Step 3.1), defining a phase rotation matrix 、 ; In which the phase is shifted , ; The cross covariance after phase rotation and 2D-DFT conversion is recorded as follows: Matrix array The (u 1 ,v 1 ) th element is: there must be an offset phase , So that , At this time matrix There will be one and only one non-zero element, i.e. "power leakage" is stopped; step 3.2), searching according to the following formula And Is a function of the estimated value of (a): Wherein, the Representation matrix Is the first of (2) The number of rows of the device is, Representation matrix Is the first of (2) The number of columns in a row, Representing a 2-norm; step 3.3) according to And The azimuth angle is accurately estimated, For an accurate estimate of the angle of arrival of the k radiation sources for the 1 st observation station, For an accurate estimate of the angle of arrival of the k radiation sources for the l +1 observation station, ; Step 4), according to the formula Direct solution of target position vector estimation In which, in the process, ; ; 。

Description

Multi-array direct positioning method based on two-dimensional discrete Fourier transform Technical Field The invention relates to the technical field of wireless positioning, in particular to a multi-array direct positioning method based on two-dimensional discrete Fourier transform. Background The conventional multi-array passive positioning technology is mostly a two-step positioning technology, wherein intermediate parameters are estimated from an original signal and data association is performed, and then the position of a radiation source is estimated through methods of exhaustive search, least square, gradient descent and the like, but the conventional two-step positioning method has a difficult problem in data association. From the point of view of information theory, the fewer processing steps on the signal, the better the performance of the algorithm in theory. The direct positioning technology is a technology without parameter association, can directly estimate the position of a radiation source from an original signal, and compared with the traditional two-step positioning technology, the direct positioning avoids the transmission of parameter association errors, so that the position estimation performance is improved to some extent, and therefore, the research on a multi-array direct positioning algorithm has important practical application significance. The existing multi-array direct positioning algorithm is to conduct exhaustive search on the cost function, so that the problem of high-dimensional search is solved, and the computational complexity is greatly increased. In practical applications, real-time positioning of the target is mostly needed, which requires the computational complexity of the algorithm. Disclosure of Invention Aiming at the defects related to the background technology, the invention provides a multi-array direct positioning method based on two-dimensional discrete Fourier transform, which obviously reduces the calculation complexity while guaranteeing the estimation performance and is easy to process in real time. The invention adopts the following technical scheme for solving the technical problems: a multi-array direct positioning method based on two-dimensional discrete Fourier transform comprises the following steps: Step 1), constructing a multi-array joint positioning model to obtain received signal information r l (t); step 1.1), constructing an array flow pattern for each observation station M is the number of large-scale uniform linear array elements equipped for each observation station, and K is the number of radiation sources; is a guiding vector, d represents array element spacing, lambda represents signal wavelength, u l＝[xl,yl]T represents position vector of the first observation station, x l、yl is respectively the horizontal and vertical coordinates, position vector of the kth radiation source is p k＝[xk,yk]T,xk、yk is respectively the horizontal and vertical coordinates, k=1, 2, and K is the total position vector Θ l,k represents the angle of arrival of the kth radiation source received by the first observation station, u l (1) represents the first element in the vector u l, and p k (1) represents the first element in the vector p k; step 1.2), obtaining a received signal of the first observation station at the sampling time t by adopting a multi-array combined positioning model S (t) is a K×1-dimensional transmission signal vector, the covariance matrix of which is a diagonal matrix, n l (t) represents an M×1-dimensional Gaussian white noise vector; step 2), calculating a cross covariance matrix of the signals received by each observation station, and performing two-dimensional discrete Fourier transform on the cross covariance matrix; Step 2.1), calculating a cross covariance R 1,l of the 1 st base station received signal and the 1 st+1 th base station received signal according to the following formula: wherein T represents the number of shots, t=1, 2,..t, L represents the number of observation stations; step 2.2), constructing a normalized DFT matrix Wherein the (m 1,n1) th element of the D matrix is Matrix after 2D-DFT processing of cross covariance of 1 st base station and 1 st+1st base station with respect to steering vector of kth source ArrayThe (u, v) th element of (a) is: When the number M of physical array elements approaches infinity, i.e. M.fwdarw.infinity, there must be a pair of integers (u k,vk) such that At the same timeAll of the remaining elements of (c) are 0, at which point,The ideal sparseness is achieved, all power is concentrated at the (u k,vk) th point of the 2D-DFT spectrum, and the azimuth information of automatic matching of each base station is formed byThe position of the non-zero point is obtained, and theta 1,k＝arcsin(2uk/M),θl+1,k＝arcsin(2vk/M); Step 2.3) according to Performing 2D-DFT on received signal cross covariance and calculating matrixIndex value corresponding to the largest K elements of (a)k=1,2,...,K; Step 2.4