A frequency hopping radiation source time difference positioning method based on maximum discrete spectrum value

Abstract

This invention discloses a time-difference localization method for frequency-hopping radiation sources based on the maximum discrete spectral value, relating to the field of frequency-hopping radiation source localization technology. The method includes the following steps: constructing a model of the frequency-hopping signal received by the observation station based on the geometric positions of the observation station and the target radiation source; establishing an approximate expression for the frequency-hopping signal based on the discrete spectral characteristics of the signal; generating an objective function related only to the radiation source position using the target radiation source position information contained in the received signal; and achieving direct localization of the frequency-hopping radiation source through an exhaustive search algorithm. This method is advantageous for direct localization, provides accurate localization, and possesses strong versatility and scalability.

Description

Technical Field

[0001] This invention relates to the field of frequency hopping radiation source localization technology, and in particular to a time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value. Background Technology

[0002] Frequency-hopping signal localization is a passive localization method that uses one or more observation stations to detect electromagnetic wave signals emitted by a frequency-hopping radiation source, estimate localization parameters, and solve localization equations to obtain the target's motion state and position information. Because the observation stations themselves do not radiate signals, it is also called non-cooperative localization or passive localization. Therefore, passive localization has advantages such as high concealment and wide adaptability.

[0003] Traditional TDOA positioning methods are two-step methods: first, time difference parameters are estimated, and then the positioning equation is solved using the estimated time difference to obtain the target's estimated position. This method has been proven to be suboptimal; the two-step approach cannot guarantee observation consistency, and errors in parameter estimation are iterated into the position estimation. Summary of the Invention

[0004] The technical problem to be solved by the present invention is how to provide a frequency hopping radiation source time difference positioning method that is conducive to direct positioning, accurate positioning, and has strong versatility and expandability.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value, comprising the following steps:

[0006] Based on the geometric positions of the observation station and the target radiation source, a model for the observation station receiving frequency-hopping signals is constructed.

[0007] Based on the discrete spectrum characteristics of frequency-hopping signals, an approximate expression for frequency-hopping signals is established;

[0008] By utilizing the target radiation source location information contained in the received signal, a target function that is only related to the radiation source location is generated;

[0009] The frequency-hopping radiation source can be directly located by exhaustive search algorithm.

[0010] The beneficial effects of adopting the above technical solution are as follows: The method described in this application fully considers the distribution characteristics of the discrete spectrum of frequency-hopping signals, retains frequency components with larger discrete spectral values, and expresses the frequency-hopping signal spectrum in a simpler and more intuitive way, facilitating subsequent engineering applications for direct localization of frequency-hopping radiation sources. Furthermore, since the observation time of frequency-hopping signals is short, there is a gap between the theoretical representation of the frequency-hopping signal and the actual spectral distribution. This invention retains the dynamic range of discrete spectral values, which is more conducive to direct localization calculations. Finally, in three-dimensional scenarios, the two-dimensional scenario provided in this invention can be used as a reference for extension, demonstrating strong versatility and expandability. Attached Figure Description

[0011] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0012] Figure 1 This is the main flowchart of the method described in the embodiments of the present invention;

[0013] Figure 2 This is a detailed flowchart of the method described in the embodiments of the present invention;

[0014] Figure 3 This is a schematic diagram showing the locations of the four observation stations and the frequency-hopping radiation source in the method described in this embodiment of the invention;

[0015] Figure 4 This is a spectrum diagram of the frequency hopping signal under noise-free conditions in the method described in the embodiments of the present invention;

[0016] Figure 5 This is a schematic block diagram of the computer device described in the embodiments of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0019] Example 1:

[0020] Overall, such as Figure 1As shown in the figure, this invention discloses a time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value. The method includes the following steps:

[0021] Based on the geometric positions of the observation station and the target radiation source, a model for the observation station receiving frequency-hopping signals is constructed.

[0022] Based on the characteristic that only a few values ​​in the discrete spectrum of a frequency-hopping signal are non-zero within the hopping band range, an approximate expression for the frequency-hopping signal is established.

[0023] By utilizing the target radiation source location information contained in the received signal, an objective function (cost function) that is only related to the radiation source location is generated.

[0024] Direct location is achieved through an exhaustive search algorithm.

[0025] The above steps will be explained in detail below with reference to specific content. Figure 2 Here is a detailed flowchart of the method described in this application:

[0026] I. Constructing the signal receiving model of the observation station:

[0027] (1) Establish a rectangular coordinate system:

[0028] The coordinates of the target radiation source location are denoted as (x... T ,y T There are L observation stations in total, and the coordinates of the i-th observation station are denoted as (x...). i ,y i ), i=1,2,…,L, such as Figure 3 As shown.

[0029] Calculate the time difference of signal arrival at each station relative to the reference station, let τ1=0 and ignore the processing delay of the received signal at each station, then τ i Let be the time difference between the arrival of the signal at observation station i and observation station 1, i.e.:

[0030]

[0031] In this context, the coordinates of the observation station are known quantities, and c is the speed of light. , These are the x and y coordinates of the observation station.

[0032] (2) Constructing a frequency hopping signal model:

[0033] Let s(t) represent the frequency-hopping signal emitted by the radiation source, s h (t) and T d Let H be the h-th hop signal and the dwell time, respectively, for a total of H hop signals. The signal model of the frequency-hopping signal emitted by the target radiation source can be described as:

[0034] ;

[0035] Assuming the number of signal sampling points is N, the frequency hopping signal s[n] can be represented by its inverse discrete Fourier transform as follows:

[0036] ;

[0037] (3) Constructing the received signal model:

[0038] Let A i τ is the attenuation coefficient of the signal received by the observation station. i n represents the time it takes for the signal to arrive at each observation station. i (t) represents the noise signal received by the i-th observation station, then the signal r received by the i-th observation station i Represented as:

[0039] ;

[0040] Let the sampling interval of the signal be T. s If T is the data acquisition time, then the number of sampling points N = T / T s It should be ensured that there is That is, the acquisition time should be long enough to ensure that most of the signals acquired by the nearest and farthest observation stations are correlated. The signals acquired by each station can be discretized as follows:

[0041]

[0042] Time sampling of a signal produces a quantization effect on target position estimation. This is because when a signal is sampled, the estimated value is an integer multiple of the sampling interval, and therefore quantized. Typically, the signal needs to be sampled at a rate much higher than the Nyquist rate.

[0043] II. Establishing an approximate expression for frequency-hopping signals:

[0044] Based on the characteristics of frequency-hopping signals, their multiple sub-bands only occupy a portion of the bandwidth within the hopping band W, resulting in a very limited frequency domain distribution. That is, only a few values ​​of S[n] are non-zero within the hopping band. Assume the number of non-zero values ​​of S[n] is M, and their positions in the discrete spectrum correspond to k1, k2, ... k. M Then there is

[0045] ;

[0046] Because the observation time of frequency-hopping signals is short, there is a discrepancy between the theoretical representation and the actual spectral distribution. Even in the absence of noise, the signal still exhibits a spectrum at other frequency points, deviating from the theoretical result. Figure 4 As shown.

[0047] In practice, S[n] > kS is chosen.max Points of [n] are considered, and other points are ignored, where kS max [n] represents the threshold value, and k is a constant. Based on engineering practice, we can derive:

[0048] ;

[0049] Let f be the number of spectral lines greater than the threshold. M Therefore, the frequency domain vector of the frequency-hopping signal received by the observation station can be approximately written as:

[0050] ;

[0051] III. Constructing the objective function:

[0052] Based on the signals collected by each station and the approximate expression of the frequency hopping signal, let the diagonal matrix be:

[0053] ;

[0054] Then we have:

[0055] ;

[0056] The frequency domain expressions of the signal received by the i-th observation station and the Gaussian white noise are respectively expressed in vector form:

[0057] ;

[0058] Taking the Fourier transform of both sides of the received signal yields:

[0059] ;

[0060] The least squares estimate of the target position P can be expressed as:

[0061] ;

[0062] in:

[0063] ;

[0064] Taking the partial derivative of the above equation with respect to S and minimizing it, we can obtain:

[0065] ;

[0066] Substituting the above equation into the least squares estimation formula and simplifying, we get:

[0067] ;

[0068] Therefore:

[0069] ;

[0070] in:

[0071] ;

[0072] make:

[0073] ;

[0074] Define matrix:

[0075] ;

[0076] X(P) is a function of the time difference τ and is an M×L matrix.

[0077] Then we have:

[0078] ;

[0079] The least squares estimate is:

[0080] ;

[0081] make:

[0082] D(P) = X H (P)X(P)

[0083] The least squares estimation expression is then the objective function (cost function), which depends only on the location of the radiation source and can be rewritten as follows:

[0084]

[0085] Therefore, the multi-station time difference direct positioning least squares estimation of the target location can be expressed as:

[0086]

[0087] IV. Direct localization through exhaustive search algorithms:

[0088] The observation station's mission area is divided into K rows and J columns of grid.

[0089] (1) Calculate the Fourier coefficients S1 of the signal received by observation station No. 1, and retain the condition that S[n] > 1 / 3S max Let the position of a point [n] be denoted as k. m =(k1,k2,…k M ),but:

[0090] ;

[0091] (2) Let the grid number k = 1, j = 1;

[0092] (3) Let the point where the grid is located be the estimated location of the assumed target radiation source;

[0093] (4) Let i = 2;

[0094] (5) Calculate the time difference τ between the estimated location reaching the i-th observation point and reaching the 1st observation station. i ;

[0095] (6) Assuming that the i-th observation station and the 1-th observation station receive the same radiation source signal, calculate the Fourier coefficients S of the signal received by the i-th observation station. i The signals received by the observation station are strongly correlated and should have a strongly correlated frequency domain distribution. Let:

[0096] ;

[0097] (7) Let i = i + 1, repeat step (5) until i = L, and obtain a total of L vectors. Combine the vectors to obtain the composite matrix:

[0098] ;

[0099] (8) Calculate D(P) = X H The largest eigenvalue λ of (P)X(P) kj .

[0100] (9) Let j = j+1, and repeat step (3) until j = J.

[0101] (10) Let k = k+1, and repeat step (3) until k = K.

[0102] The maximum eigenvalue λ is calculated by comparing the estimated locations of the assumed target radiation sources. kj The estimated location of the assumed target radiation source corresponding to the largest eigenvalue is selected as the final estimated target location (x). T ,y T ).

[0103] This invention fully considers the distribution characteristics of the discrete spectrum of frequency-hopping signals, retaining frequency components with larger discrete spectral values, and expressing the frequency-hopping signal spectrum in a simpler and more intuitive way, facilitating subsequent engineering applications for direct localization of frequency-hopping radiation sources. Furthermore, this invention provides a dynamic range for retaining discrete spectral values, which is more beneficial for practical applications of direct localization.

[0104] Example 2

[0105] In one exemplary embodiment, the present invention also provides a computer device, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 5As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements the frequency-hopping radiation source time difference localization method based on the maximum discrete spectral value described in Embodiment 1.

[0106] Those skilled in the art will understand that Figure 5 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0107] In one exemplary embodiment, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0108] In one exemplary embodiment, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0109] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0110] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0111] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units, etc., and are not limited to these.

[0112] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A time-difference localization method for frequency-hopping radiation sources based on the maximum discrete spectral value, characterized in that... Includes the following steps: Based on the geometric positions of the observation station and the target radiation source, a model for the observation station receiving frequency-hopping signals is constructed. Based on the discrete spectrum characteristics of frequency-hopping signals, an approximate expression for frequency-hopping signals is established; By utilizing the target radiation source location information contained in the received signal, a target function that is only related to the radiation source location is generated; The frequency-hopping radiation source can be directly located by exhaustive search algorithm.

2. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 1, characterized in that, The method for constructing a model of frequency-hopping signal reception at an observation station includes the following steps: Establish a rectangular coordinate system and mark the location of the target radiation source and the location of the observation station in the rectangular coordinate system; Constructing a frequency-hopping signal model: A model for the observation station to receive frequency-hopping signals is constructed based on the frequency-hopping signal model.

3. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 2, characterized in that, The method for establishing a rectangular coordinate system includes the following steps: The coordinates of the target radiation source location are denoted as (x... T ,y T There are L observation stations in total, and the coordinates of the i-th observation station are denoted as (x...). i ,y i ), i=1,2,…,L; Calculate the time difference of signal arrival at each station relative to the reference station. Assume τ1=0 and ignore the processing delay of the received signal at each station. Then τ i The time difference between the arrival of the signal at observation station i and observation station 1: ； In this context, the coordinates of the observation station are known quantities, and c is the speed of light.

4. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 3, characterized in that, The method for constructing a frequency-hopping signal model includes the following steps. Let s(t) represent the frequency-hopping signal emitted by the radiation source, and sh(t) and Td be the h-th hop signal and the dwell time, respectively. There are a total of H hop signals. The signal model of the frequency-hopping signal emitted by the target radiation source is described as follows: ； Let the number of signal sampling points be N. The frequency hopping signal s[n] is expressed by its discrete Fourier inverse transform as follows: 。 5. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 4, characterized in that, The method for constructing a model of a frequency-hopping signal received by an observation station includes the following steps: Let A i Let n be the attenuation coefficient of the signal received by the observation station. i (t) represents the noise signal received by the i-th observation station, then the signal r received by the i-th observation station i Represented as: ； Let the sampling interval of the signal be T. s If T is the data acquisition time, then the number of sampling points N = T / T s The signals collected by each station can be discretely described as follows: ； Time sampling of a signal produces a quantization effect on target location estimation.

6. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 1, characterized in that, The method for establishing an approximate expression for a frequency-hopping signal includes the following steps: Based on the characteristics of frequency-hopping signals, let M be the number of non-zero values ​​in the discrete inverse Fourier transform S[n] of the frequency-hopping signal, and let their positions in the discrete spectrum correspond to k1, k2, ... k. M Then we have: ； Choose S[n]>kS max Points of [n] are considered, and other points are ignored, where kS max [n] is the threshold, and k is a constant. Based on engineering practice, we know that: ； Let f be the number of spectral lines greater than the threshold. M The frequency domain vector of the frequency-hopping signal received by the observation station is approximately denoted as: 。 7. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 1, characterized in that, The method for constructing the objective function includes the following steps: Based on the signals collected by each station and the approximate expression of the frequency hopping signal, let the diagonal matrix be: ； Then we have: ； The frequency domain expressions of the signal received by the i-th observation station and the Gaussian white noise are respectively expressed in vector form: ; Taking the Fourier transform of both sides of the received signal yields: ； The least squares estimate of the target position P can be expressed as: ； in: ； Taking the partial derivative of the above equation with respect to S and minimizing it, we can obtain: ； Substituting the above equation into the least squares estimation formula and simplifying, we get: ； have: ； in: ； make: ； Define matrix: ； X(P) is a function of the time difference τ and is an M×L matrix; Then we have: ； The least squares estimate is: ； make: D(P)=X H (P)X(P); The least squares estimation expression is then the objective function, which depends only on the location of the radiation source, and can be rewritten as: ； The multi-station time difference direct positioning least squares estimate of the target location is expressed as: 。 8. The time difference localization method for frequency hopping radiation sources based on the maximum discrete spectral value as described in claim 1, characterized in that, The method for achieving direct localization using an exhaustive search algorithm includes the following steps: Divide the observation station's mission area into a grid of K rows and J columns; (1) Calculate the Fourier coefficients S1 of the signal received by observation station No. 1, and retain the condition that S[n] > 1 / 3S max Let the position of a point [n] be denoted as k. m =(k1,k2,…k M ),but: ； (2) Let the grid number k = 1, j = 1; (3) The points where the grid is located are the estimated locations of the assumed target radiation sources; (4) Let i = 2; (5) Calculate the time difference τ between the estimated location reaching the i-th observation point and reaching the 1st observation station. i ; (6) Assume that the i-th observation station and the 1-th observation station receive the same radiation source signal. Calculate the Fourier coefficients S of the signal received by the i-th observation station. i The signals received by the observation station are strongly correlated and have a strongly correlated frequency domain distribution. Let: ； (7) Let i = i + 1, repeat step (5) until i = L, and obtain a total of L vectors. Combine the vectors to obtain the composite matrix: ； (8) Calculate D(P) = X H The largest eigenvalue λ of (P)X(P) kj ; (9) Let j = j + 1, and repeat step (3) until j = J; (10) Let k = k+1, and repeat step (3) until k = K; The maximum eigenvalue λ is calculated by comparing the estimated locations of the assumed target radiation sources. kj Select the largest feature; The corresponding assumed target radiation source estimated location is the final target estimated location (x). T ,y T ).

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