A method for rapidly determining the location spectrum of a direct positioning grid based on time difference

Abstract

This invention discloses a method for rapidly determining the position spectrum of a time-difference-based direct positioning (TDOL) grid. The method utilizes the recursive computational property of the position spectrum function on a specially designed position grid, employing an FFT algorithm to quickly calculate the position spectrum function values ​​at all grid points, significantly improving the real-time performance of TDOL-based direct positioning. Furthermore, while the time complexity of a naive, equally spaced rectangular grid search-based TDOL direct positioning method is the square of the signal sequence length, the time complexity of this invention is the linear logarithmic of the signal sequence length. Its efficiency in reducing computational complexity increases with the length of the processed signal sequence, enabling more efficient position spectrum calculation and thus better meeting the real-time requirements for signal source location estimation.

Description

Technical Field

[0001] This invention belongs to the field of signal and information processing technology, and in particular relates to a positioning method that constructs a position spectrum function based on signal measurement and calculates the grid position spectrum (position spectrum function value on the grid of the region where the signal source is located) in real time. Background Technology

[0002] In the field of signal and information processing technology, obtaining signal source location information is a basic application requirement, and the positioning technology involved has also received widespread attention.

[0003] Signal source localization technology can be broadly classified into two categories based on the localization process: two-step localization method and direct localization method.

[0004] Traditional two-step localization methods first estimate intermediate localization parameters (e.g., signal arrival time, signal arrival angle, etc.) and then calculate the signal source position. This method is characterized by low computational complexity but poor noise resistance. Direct localization methods, on the other hand, construct a position spectrum function based on the original signal measurements and estimate the signal source position by calculating a grid-based position spectrum, exhibiting stronger noise resistance. Compared to the two-step method, which only searches for one-dimensional intermediate localization parameters, the direct method requires a two-dimensional position grid search, resulting in higher computational complexity.

[0005] However, the equidistant rectangular grids commonly used in direct positioning methods are a naive gridding scheme. This scheme does not establish the correlation between the calculation process of the position spectrum function at different grid points, resulting in low efficiency in calculating the grid position spectrum. Therefore, rapidly determining the grid position spectrum based on time difference can further improve the real-time performance of direct positioning methods. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of existing technologies by disclosing a method for rapidly determining the grid position spectrum of direct positioning based on time difference. This method significantly improves the computational efficiency of the grid position spectrum by establishing the recursive computational properties of the position spectrum function among grid points, thereby enhancing the real-time performance of the direct positioning method based on time difference.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A method for rapidly determining the location spectrum of a direct positioning grid based on time difference, the method comprising the following steps:

[0009] S1: In offline mode, select two receiving stations P in sequence. i and P j As the focal point, the distance difference corresponds to a time difference that is an integer multiple of the reciprocal of the signal bandwidth. Construct a family of hyperbolas, where k is an integer, c is the speed of light, and B is the signal bandwidth;

[0010] The common intersection point g of the hyperbola family constitutes the designed location grid point set G, where N is the number of receiving stations and C represents the number of combinations;

[0011] The coordinates of each grid point, the distance difference parameter of the hyperbola to which it belongs, and the distribution of the half-branch of the hyperbola [g,k] are used to determine the location of each grid point. ij Stored in memory;

[0012] S2: In online mode, select the received signals from two receiving stations sequentially, and take the conjugate of one of the received signals. With another received signal y j Doing the Hadamard product yields Data vectors r ij The resulting data vector is then subjected to an L-point Fast Fourier Transform followed by cyclic shifting. The FFT transformation result d is obtained. ij ;

[0013] S3: Based on the distance difference between the grid point g and the hyperbola to which it belongs and the half-branch assignment [g,k] stored in memory. ij ], select the corresponding FFT transformation results to construct the data matrix Ψ(g);

[0014] S4: Calculate the largest eigenvalue λ of the data matrix. max (Ψ(g)) represents the position spectrum function value at the corresponding grid point.

[0015] According to a preferred embodiment, the hyperbola family constructed in step S1 is:

[0016] k∈Z, and

[0017] Where Z is an integer and M is a point on the hyperbola.

[0018] According to a preferred embodiment, the position coordinates g in step S1 are obtained by solving the following family of hyperbolic equations.

[0019] k∈Z, and Z is an integer.

[0020] According to a preferred embodiment, in step S2,

[0021]

[0022] Among them, symbols The symbol FFT(·) represents the Hadamard product, and the symbol circshift[x,l] represents the cyclic shift of vector x by l bits.

[0023] According to a preferred embodiment, in step S3...

[0024]

[0025] According to a preferred embodiment, the position spectral function value J(g) in step S4 is: J(g) = λ max (Ψ(g)), where λ max (X) represents finding the largest eigenvalue of matrix X.

[0026] The aforementioned main solution of the present invention and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed by the present invention. Those skilled in the art, after understanding the solution of the present invention, will realize that there are many combinations based on existing technology and common knowledge, all of which are technical solutions to be protected by the present invention, and will not be exhaustively listed here.

[0027] The beneficial effects of this invention are:

[0028] In the time-difference-based direct positioning method, the present invention makes full use of the recursive computational property of the position spectrum function on a specially designed position grid, and uses the FFT algorithm to quickly calculate the position spectrum function values ​​at all grid points, which significantly improves the real-time positioning performance of the time-difference-based direct positioning method.

[0029] The present invention employs a naive, equally spaced rectangular grid search-based direct positioning method with a time complexity of the square of the signal sequence length. The present invention has a time complexity of the linear logarithmic of the signal sequence length. Its efficiency in reducing computational complexity increases with the length of the processed signal sequence, enabling more efficient calculation of the position spectrum and thus better meeting the real-time requirements for signal source position estimation. Detailed Implementation

[0030] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0031] Example 1:

[0032] Taking a signal source located at (15,15) with a known waveform, and signals with bandwidth B = 200MHz received by base stations located at (0,0), (30,0), and (0,30) respectively, the received signals are first preprocessed, and the frequency domain response y of the multipath channel is estimated using the known transmitted signal waveform.i ∈C L×1 Let i = 1, 2, 3, L = 200. Then, based on the estimation of the channel frequency domain response, a position spectrum function is constructed, and the signal source location is searched. The purpose of implementing this invention is to quickly calculate the position spectrum function value on a specially designed position grid, and efficiently complete the signal source location search.

[0033] The process in this example is as follows:

[0034] Step 1: In offline mode, select the coordinates of two receiving stations sequentially to make P. i and P j With the focal point as the time difference corresponding to an integer multiple of the reciprocal of the signal bandwidth. Construct a system of equations for a family of hyperbolas with respect to the position coordinate g. The solutions to this system form the position grid G. The table below shows the position grid stored in memory, the distance differences between the corresponding hyperbolas, and the affiliation of the hyperbolas' half branches:

[0035]

[0036] Step 2: In the online state, select the estimated channel frequency domain response of two receiving stations in sequence, and take the conjugate of one of the channel frequency domain responses. With the frequency domain response y of another channel j Performing the Hadamard product (element-wise multiplication) yields Data vectors r ij The data vectors are arranged into a matrix by columns as shown in the table below:

[0037]

[0038]

[0039] The data matrix is ​​obtained by performing an FFT column-wise and then cyclically shifting the data.

[0040]

[0041] Step 3: Based on the grid point coordinates stored in memory, the distance difference between the corresponding hyperbolas, and the half-branch affiliation [g,k], ij The corresponding FFT transformation results are selected to construct the data matrix Ψ(g). The data matrices corresponding to the 1st and 200th grid points are given below.

[0042]

[0043]

[0044]

[0045] Step 4: Calculate the largest eigenvalue of the data matrix as the position spectral function value at the corresponding grid point. The vector of objective function values ​​at all grid points is as follows:

[0046] 1.0e-17*

[0047] Columns 1 to 10 are: 0.0852 0.1532 0.1576 0.0767 0.1250 0.0857 0.2097 0.0433 0.1378 0.0952

[0049] …………

[0050] Columns 191 to 200 are 0.0093 0.0137 0.0215 0.0275 0.0015 0.0210 0.0006 0.0104 0.0256 0.0071

[0052] In this embodiment, the traditional time-difference-based direct positioning method requires 67.8942 seconds to calculate the position spectrum function values ​​at all 2247 grid points, while the proposed method for rapidly determining the position spectrum of the time-difference-based direct positioning grid in this invention only takes 0.352396 seconds. The beneficial effect of this invention is a reduction in computation time of 192.6 times.

[0053] In the time-difference-based direct positioning method, the present invention makes full use of the recursive computational property of the position spectrum function on a specially designed position grid, and uses the FFT algorithm to quickly calculate the position spectrum function values ​​at all grid points, which significantly improves the real-time positioning performance of the time-difference-based direct positioning method.

[0054] The present invention employs a naive, equally spaced rectangular grid search-based direct positioning method with a time complexity of the square of the signal sequence length. The present invention has a time complexity of the linear logarithmic of the signal sequence length. Its efficiency in reducing computational complexity increases with the length of the processed signal sequence, enabling more efficient calculation of the position spectrum and thus better meeting the real-time requirements for signal source position estimation.

[0055] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for rapidly determining the position spectrum of a direct positioning grid based on time difference, characterized in that, The method for directly locating the grid position spectrum includes the following steps: S1: In offline mode, select two receiving stations P in sequence. i and P j As the focal point, the distance difference corresponds to a time difference that is an integer multiple of the reciprocal of the signal bandwidth. Construct a family of hyperbolas, where k is an integer, c is the speed of light, and B is the signal bandwidth; The common intersection point g of the hyperbola family constitutes the designed location grid point set G, where N is the number of receiving stations and C represents the number of combinations; The coordinates of each grid point, the distance difference parameter of the hyperbola to which it belongs, and the distribution of the half-branch of the hyperbola [g,k] are used to determine the location of each grid point. ij Stored in memory, k ij For hyperbolic parameters; S2: In online mode, select the received signals from two receiving stations sequentially, and take the conjugate of one of the received signals. With another received signal y j Doing the Hadamard product yields Data vectors r ij The resulting data vector is then subjected to an L-point Fast Fourier Transform followed by cyclic shifting. The FFT transformation result d is obtained. ij ; S3: Based on the distance difference between the grid point g and the hyperbola to which it belongs and the half-branch assignment [g,k] stored in memory. ij ], select the corresponding FFT transformation results to construct the data matrix Ψ(g); S4: Calculate the largest eigenvalue λ of the data matrix. max (Ψ(g)) represents the position spectrum function value at the corresponding grid point.

2. The method for directly locating the grid position spectrum as described in claim 1, characterized in that, The hyperbola family constructed in step S1 is: and Where M is a point on the hyperbola.

3. The method for directly locating the grid position spectrum as described in claim 2, characterized in that, The position coordinates g in step S1 are obtained by solving the following family of hyperbolic equations. and 4. The method for directly locating the grid position spectrum as described in claim 3, characterized in that, In step S2, Among them, symbols The symbol FFT(·) represents the Hadamard product, and the symbol circshift[x,l] represents the cyclic shift of vector x by l bits.

5. The method for directly locating the grid position spectrum as described in claim 4, characterized in that, In step S3, 6. The method for directly locating the grid position spectrum as described in claim 5, characterized in that, Position spectral function values ​​in step S4: J(g)=λ max (Ψ(g)) Where, λ max (X) represents finding the largest eigenvalue of matrix X.

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