Distributed radar track association method based on signal similarity

Abstract

The invention provides a distributed radar track association method based on signal similarity. The method comprises the following steps: initializing parameters and preprocessing echo signals; constructing a phase compensation function of the reference radar frequency domain echo signal; calculating the similarity between the reference radar and other local radar echo signals and the probability density of the frequency domain echo signal reflected by the same target as the reference radar frequency domain echo signal; and obtaining a distributed radar track association result. According to the method, the probability density of the local radar frequency domain echo signal possibly reflected by the same target as the reference radar is determined through the similarity function of the reference radar frequency domain echo signal and the local radar frequency domain echo signal; and the relevance of track points corresponding to targets observed by the reference radar and the partial local radar is judged through the coincidence degree of the similarity function and the probability density, the influence of the target shape and the scattering characteristic on the consistency of the similarity and the probability density is fully considered, and the relevance precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar detection, and relates to a distributed radar track association method based on signal similarity, which can be used for more accurate identification and tracking of targets. Background Art

[0002] Distributed radars are multiple radar nodes that are dispersed in spatial positions and cooperate with each other. With the performance bottleneck of a single radar and the dilemmas in dealing with new threats, the radar detection system is changing from single-radar detection to distributed multi-radar cooperative detection. Compared with a single radar, distributed multi-radars can collect target scattering information and motion information from multiple dimensions such as space and frequency. Through information fusion, more accurate identification and tracking of targets can be achieved. In the process of cooperation, distributed radars will inevitably face the problem of whether the targets observed by different radars are the same target, and it is necessary to carry out research on distributed radar track association. After each local radar receives its respective measurement information, local processing is first performed to obtain local tracks, and then the local tracks are sent to the fusion center for processing. An important task of the fusion center is to perform track-track association to determine whether the local tracks from different radars correspond to the same target. In fact, it is to solve the problem of duplicate tracking in the radar space coverage area. Therefore, track association is also called de-duplication.

[0003] In order to improve the accuracy of track association, for example, a patent application with the application publication number CN113835082A and the name "Method and Device for Distributed Radar Track Association" discloses a distributed radar track association method. This method obtains the tracks of the first radar node and the second radar node within a set time period and initializes the parameters of the association method; screens out the corresponding track points with a distance less than the track point distance threshold in the tracks of the first radar node and the second radar node, sets them as association point pairs, and saves the association point pairs to a point set; establishes a unified coordinate system for the track points of the first radar node and the second radar node under the point cloud registration algorithm according to the point set; performs track mapping calculation on any track points of the first radar node and the second radar node in the unified coordinate system; according to the track mapping calculation results, determines whether the tracks of the first radar node and the second radar node are saved as independent tracks or associated tracks, realizing de-duplication in the distributed radar space area. This invention screens association points through the threshold calculated from the random errors contained in each measurement information, reducing the influence of random errors on the track association accuracy. However, when judging whether track points are associated, it only considers the relationship between the distance between the track points observed by different radars and the threshold, without considering characteristics such as the shape and scattering characteristics of the target, which affects the further improvement of the association accuracy. Summary of the Invention

[0004] The object of the present invention is to overcome the defects existing in the above-mentioned prior art, and a distributed radar track association method based on signal similarity is proposed to solve the technical problem of low track association accuracy existing in the prior art.

[0005] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Initialize parameters and preprocess the echo signals:

[0007] Initialize 1 reference radar, K local radars and I moving targets in a two-dimensional space. Each radar includes N array elements, and the track of each moving target includes T m track points; sample the echo signals of each target received by each array element of each radar at T time points, and then preprocess the echo signal s(t,n) of the nth array element at the tth time point to obtain the corresponding frequency-domain echo signal S(f,n) of s(t,n), where K≥2, N≥8, T≥2, T m ≥2, I≥1, k∈[1,K];

[0008] (2) Construct the phase compensation function of the reference radar frequency-domain echo signal:

[0009] Construct the phase compensation function H of the reference radar frequency-domain echo signal, including the distance-dimensional phase compensation function with the difference between the distances from each target to the reference radar and the kth local radar as a variable and the angle-dimensional phase compensation function with the difference between the sine values of the angles between the lines connecting each target to the reference radar and the kth local radar and the x-axis as a variable

[0010] (3) Calculate the similarity between the reference radar and the echo signals of other local radars:

[0011] Perform phase compensation on the frequency-domain echo signal S0(f,n) of the reference radar through the phase compensation function H, and calculate the similarity function between the phase-compensated frequency-domain echo signal S0'(f,n) and the frequency-domain echo signal S k (f,n) of the kth local radar

[0012] (4) Calculate the probability density of the frequency-domain echo signal that is the reflection of the same target as the reference radar frequency-domain echo signal:

[0013] Judge whether it satisfies If so, the frequency-domain echo signals of the kth local radar and the reference radar may be reflections of the same target, and through Calculate the probability density of the frequency-domain echo signal that is the reflection of the same target as the reference radar's frequency-domain echo signal

[0014] (5) Obtain the distributed radar track association result:

[0015] Calculate the similarity function Normalized result of and Coincidence degree F, and when F≥η' for the coincidence degree of F with the threshold η', some of the K local radars are associated with the track points of the target observed by the reference radar, that is, some local radars are associated with the track of the target observed by the reference radar, and the remaining radars are not associated with the track of the target observed by the reference radar.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] The present invention determines the probability density of the frequency-domain echo signal of the local radar that may be the reflection of the same target as the reference radar through the similarity function between the frequency-domain echo signal after phase compensation of the reference radar and the frequency-domain echo signal of each local radar, and further determines the association between the reference radar and the track points of the target corresponding to some local radars through the coincidence degree of the normalized result of the similarity function and the probability density. Since the similarity function contains phase information and distance information reflecting the target shape and scattering characteristics, it is beneficial to obtain associated tracks with more consistent target shapes and scattering characteristics between the reference radar and the local radars. Description of the Drawings

[0018] Figure 1 Is the implementation flowchart of the present invention. Detailed Embodiment

[0019] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

[0020] Referring to Figure 1 , the present invention includes the following steps:

[0021] Step 1) Initialize parameters and preprocess the echo signal:

[0022] Initialize 1 reference radar, K local radars, and I moving targets in a two-dimensional space. Each radar includes N array elements, and the track of each moving target includes T m Track points; sample the echo signal of each target received by each array element of each radar at T time points, and then preprocess the echo signal s(t,n) of the nth array element at the tth time point to obtain the frequency-domain echo signal S(f,n) corresponding to s(t,n), where K≥2, N≥8, T≥2, T m≥2, I≥1, k∈[1, K]; In this embodiment, K = 2, N = 8, T = 1024, T m = 50, I = 1.

[0023] The implementation steps for preprocessing the echo signal s(t, n) of the nth array element at the tth time point are as follows:

[0024] Perform Fourier transform on the echo signal s(t, n) of the nth array element at the tth time point, and perform pulse compression on the signal after Fourier transform to implement the preprocessing of s(t, n), obtaining the frequency-domain echo signal S(f, n) corresponding to s(t, n):

[0025]

[0026] where σ, f c , f, B are respectively the amplitude, carrier frequency, frequency variable after Fourier transform, and bandwidth of S(f, n), exp[·] represents the exponential function, j is the imaginary number, c is the speed of light, R represents the distance from the target corresponding to s(t, n) to the radar where the nth array element is located, θ represents the angle between the line connecting the target corresponding to s(t, n) and the nth array element and the x-axis, λ is the wavelength of s(t, n), d is the array element spacing of the radar, and noise is the noise. In this embodiment, σ = 0.1, f c = 3×10 9 Hz, B = 400 MHz, d = 0.05 m. It can be seen from the formula that the phase of the frequency-domain echo signal of the target clearly reflects the distance and angle information of the target, facilitating subsequent operations such as phase compensation. Therefore, the signal is transformed to the frequency domain and then pulse compression processing is performed to ensure that the distance and angle information of the target in the frequency-domain echo signal is significant.

[0027] Step 2) Construct the phase compensation function of the reference radar frequency-domain echo signal:

[0028] Construct the phase compensation function of the reference radar frequency-domain echo signal including the distance-dimensional phase compensation function with the difference in the distances from each target to the reference radar and the kth local radar as the variable and the angle-dimensional phase compensation function with the difference in the sine values of the angles between the lines connecting each target to the reference radar and the kth local radar and the x-axis as the variable

[0029]

[0030] From the form of the frequency-domain echo signal, it can be seen that the distance and angle information of the target are reflected in the phase of the frequency-domain echo signal. There are differences in the distance and angle between the reference radar and the local radar relative to the target. When the values of the variables in the phase compensation function are exactly the distance difference and angle difference between the reference radar and the local radar relative to the target, the difference between the two signals is the smallest. That is, at the values of the variables of this phase compensation function, the similarity between the two signals is the highest.

[0031] Step 3) Calculate the similarity between the echo signals of the reference radar and other local radars:

[0032] Through the phase compensation function Perform phase compensation on the frequency-domain echo signal S0(f,n) of the reference radar, and calculate the similarity function between the phase-compensated frequency-domain echo signal S0'(f,n) and the frequency-domain echo signal S k (f,n) of the kth local radar The phase-compensated frequency-domain echo signal S0'(f,n), and its expression is:

[0033]

[0034] The similarity function with the frequency-domain echo signal S k (f,n) of the kth local radar The calculation formula is:

[0035]

[0036] Among them, S0' represents the matrix composed of S0'(f,n), and S k ' represents the matrix composed of S k '(f,n), tr(·) represents the trace operation, S0' T 、S k T respectively represent the transposed results of S0' and S k '. From the form of the frequency-domain echo signal and the phase compensation function, it can be seen that multiplying the frequency-domain echo signal by the phase compensation function can complete the phase compensation of the frequency-domain echo signal.

[0037] Step 4) Calculate the probability density of the frequency-domain echo signal reflected by the same target as the frequency-domain echo signal of the reference radar:

[0038] Judge Whether it satisfies with the preset threshold η If so, the frequency-domain echo signals of the kth local radar and the reference radar may be reflected by the same target, and by Calculate the probability density of the frequency-domain echo signal reflected by the same target as the frequency-domain echo signal of the reference radar The frequency-domain echo signal of the reference radar is the probability density of the frequency-domain echo signal reflected by the same target The calculation formula is as follows:

[0039]

[0040] Wherein, σ ΔR respectively represent the mean value and the root mean square error, respectively represent the mean value and the root mean square error. According to and the distribution of, the value range of the variable can be determined. The determination of the mean value and the root mean square error is obtained by calculating the geometric positions of the reference radar, the local radar and the target. The distance and angle from the reference radar to the local radar are (R, θ), and the distance and angle from the reference radar to the target are (R0, θ0). The distance and angle from the kth local radar to the target are (R k , θ k ). Under the assumption that the frequency-domain echo signals of the reference radar and the kth local radar are the frequency-domain echo signals reflected by the same target, there is a geometric relationship:

[0041]

[0042] The equation can be transformed into:

[0043]

[0044] The difference between the measured distance value and the sine value of the angle of the reference radar and the local radar for the observed target can be expressed as:

[0045]

[0046] After introducing Gaussian random errors to (R, θ), (R0, θ0), (R k , θ k ), the distance difference with error approximately follows a Gaussian distribution with as the mean value and σ ΔR as the root mean square error. The difference between the sine values of the angles with error approximately follows a Gaussian distribution with as the mean value and as the root mean square error. Adding random errors to (R, θ), (R0, θ0), (R k , θ k ) and performing a Monte Carlo experiment can obtain the specific mean value and root mean square error of the distance difference with error and .

[0047] Step 5) Obtain the distributed radar track association result:

[0048] Calculate the normalization result of the similarity function and the coincidence degree F with When F≥η', some of the K local radars are associated with the track points of the target observed by the reference radar, that is, some of the local radars are associated with the track of the target observed by the reference radar, and the remaining radars are not associated with the track of the target observed by the reference radar. Normalize the similarity function , and the formula is:

[0049]

[0050] where ∫· represents the integral operation, represents the differential operation. The coincidence degree F between the normalized similarity and is calculated by the formula:

[0051]

[0052] where represents a function whose value is or under different conditions. After normalizing the similarity function, the function value of the similarity function to some extent characterizes the probability that the track points of the target observed by the reference radar and the local radar are associated when the phase compensation parameter is and . The coincidence degree F reflects the consistency between the probability density function under the assumed conditions and the actual probability density function. When the actual situation is highly consistent with the assumption, it can be judged that the track points of the target observed by the reference radar and the local radar are associated. The threshold η' usually takes a value of 95%, and can be adjusted according to specific experimental results to ensure the accuracy of the track point association judgment. The judgment of the association between the reference radar and the track of the target observed by the local radar is carried out on the basis of the judgment of each pair of track points. When most of the track points in the tracks obtained by the reference radar and the local radar are associated with each other, the entire track is judged to be associated.

Claims

1. A distributed radar track association method based on signal similarity, characterized in that It includes the following steps: (1) Initialize parameters and preprocess the echo signal: Initialize 1 reference radar, K local radars, and I moving targets in a two-dimensional space. Each radar consists of N array elements, and the track of each moving target includes T m track points; sample the echo signals of each target received by each array element of each radar at T time points, and then preprocess the echo signal s(t, n) of the nth array element at the tth time point to obtain the corresponding frequency-domain echo signal S(f, n) of s(t, n), where K≥2, N≥8, T≥2, T m ≥2, I≥1, k∈[1, K]; (2) Construct the phase compensation function of the reference radar frequency-domain echo signal: Construct the phase compensation function H of the reference radar frequency domain echo signal, including the distance dimension phase compensation function with the difference in the distance from each target to the reference radar and the k-th local radar as the variable and the difference in the sine value of the angle between the line connecting each target to the reference radar and the k-th local radar and the x-axis as the variable angle dimension phase compensation function (3) Calculate the similarity between the reference radar and the echo signals of other local radars: Perform phase compensation on the frequency-domain echo signal S0(f,n) of the reference radar through the phase compensation function H, and calculate the similarity function between the frequency-domain echo signal S0'(f,n) after phase compensation and the k-th local radar frequency-domain echo signal S k (f,n) (4) Calculate the probability density of the frequency-domain echo signal that is the reflection of the same target as the reference radar frequency-domain echo signal: Judge Whether it meets the pre-set threshold η If so, the frequency-domain echo signals of the k-th local radar and the reference radar may be reflections from the same target, and through Calculate the probability density of the frequency-domain echo signal that is the reflection from the same target as the frequency-domain echo signal of the reference radar (5) Obtain the distributed radar track association result: Calculation of similarity function Normalized result and coincidence degree F, and when F satisfies F≥η' with the threshold η', some of the K local radars are associated with the track points of the target observed by the reference radar, that is, some local radars are associated with the track of the target observed by the reference radar, and the remaining radars are not associated with the track of the target observed by the reference radar.

2. The method according to claim 1, wherein The preprocessing of the echo signal s(t,n) of the nth array element at the tth time point described in step (1) is realized as follows: Perform Fourier transform on the echo signal s(t,n) of the nth array element at the tth time point, and perform pulse compression on the signal after Fourier transform to obtain the frequency-domain echo signal S(f,n) corresponding to s(t,n): Among them, σ, f c , f, and B are the amplitude, carrier frequency, frequency variable after Fourier transform, and bandwidth of S(f,n) respectively. exp[·] represents the exponential function, j is the imaginary unit, c is the speed of light, R represents the distance from the target corresponding to s(t,n) to the radar where the nth array element is located, θ represents the angle between the line connecting the target corresponding to s(t,n) and the nth array element and the x-axis, λ is the wavelength of s(t,n), d is the array element spacing of the radar, and noise is the noise.

3. The method according to claim 2, wherein The distance dimension phase compensation function described in step (2) and the angle dimension phase compensation function Their expressions are respectively as follows:

4. The method according to claim 3, characterized in that, The phase-compensated frequency-domain echo signal S0'(f,n) described in step (3) has the following expression:

5. The method according to claim 3, characterized in that The similarity function between the phase-compensated frequency-domain echo signal \(S_0'(f,n)\) described in step (3) and the \(k\)th local radar frequency-domain echo signal \(S\) k (f,n) is calculated as follows: Among them, S0' represents the matrix composed of S0'(f,n), S k ' represents the matrix composed of S k '(f,n), tr(·) represents the trace operation, S0' T 、S k T respectively represent the transposed results of S0' and S k '.

6. The method according to claim 3, characterized in that, The probability density of the frequency-domain echo signal that is the reflection of the same target as the reference radar frequency-domain echo signal described in step (4) The calculation formula is as follows: Among them, σ ΔR respectively represent the mean value and root mean square error of respectively represent the mean value and root mean square error of 7. The method according to claim 6, characterized in that, The normalization of the similarity function described in step (5) is carried out according to the formula: wherein, ∫· represents an integration operation, represents a differentiation operation.

8. The method according to claim 7, wherein The normalized similarity described in step (5) and The coincidence degree F is calculated by the formula: Among them, represents a function whose value is or under different conditions.

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