A Doppler through-wall radar target tracking and positioning method

Abstract

The present invention discloses a Doppler through-the-wall radar target tracking and positioning method, comprising the following steps: acquiring a radar echo signal and demodulating it to obtain a demodulated radar echo signal; processing the radar echo signal, judging the echo data state, obtaining Doppler frequency unambiguous state data, and then constructing an input vector; constructing an STFT initial prediction model and an NGRC initial error prediction model; using the Doppler unambiguous state data to train the STFT initial prediction model to obtain an STFT prediction model; using the STFT prediction model, calculating error vector data; using the error vector data to train the NGRC initial error prediction model to obtain an NGRC error prediction model; using the STFT prediction model and the NGRC error prediction model, predicting the target Doppler frequency ambiguous state data, and completing through-the-wall radar target tracking and positioning. The method of the present invention can effectively suppress accumulated errors and improve the target tracking performance of the Doppler through-the-wall radar.

Description

Technical Field

[0001] The invention belongs to the technical field of radar target tracking, and in particular relates to a Doppler through-wall radar target tracking and positioning method. Background Art

[0002] As an efficient detection method, Doppler through-wall radar plays a vital role in tracking humans in law enforcement, urban warfare, and other areas due to its low cost and compact size. However, the complex wall-penetrating environment and the uncertainty of target motion complicate real-time processing. High-precision target tracking relies not only on high-quality signal processing algorithms but also on effectively addressing multipath effects and noise interference. In Doppler through-wall radar systems, signals experience severe attenuation and reflections as they penetrate walls, resulting in blurred and complex echo signals. Multipath causes the received radar signal to contain mixed information from multiple reflection paths, further complicating signal processing.

[0003] Traditional target tracking methods, such as those based on Kalman filters and particle filters, rely heavily on assumptions about the target's motion model and estimate the target's state by filtering the observed data. However, these methods are susceptible to multipath effects and wall attenuation in complex through-wall environments, resulting in reduced tracking accuracy.

[0004] The short-time Fourier transform (STFT) is a commonly used signal processing method that converts time-domain signals into the time-frequency domain to analyze the signal's frequency characteristics. The STFT performs well in processing non-stationary signals and can effectively extract the Doppler shift characteristics of a target. However, using the STFT alone for target tracking still presents challenges with multipath effects and noise interference. Summary of the Invention

[0005] The present invention aims to provide a Doppler through-wall radar target tracking and positioning method. The method is based on the STFT-NGRC joint algorithm, applies the STFT to identify the Doppler frequency ambiguity region of the radar echo, and proposes an NGRC error prediction model to estimate the target Doppler frequency in the ambiguity region. The method effectively eliminates the accumulated Doppler frequency prediction error through adaptive error compensation processing, thereby improving the target tracking performance of the through-wall radar.

[0006] The present invention provides a Doppler through-wall radar target tracking and positioning method, comprising the following steps:

[0007] S1. Acquire and demodulate the radar echo signal to obtain a demodulated radar echo signal;

[0008] S2. Process the radar echo signal obtained in step S1 to determine the echo data status, obtain the Doppler frequency unambiguous state data, and then construct the input vector;

[0009] S3. Construct the STFT initial prediction model and the NGRC initial error prediction model;

[0010] S4. Using the Doppler frequency unambiguous state data obtained in step S2 to train the STFT initial prediction model obtained in step S3, a STFT prediction model is obtained;

[0011] S5. Using the STFT prediction model obtained in step S4, the error vector data is calculated;

[0012] S6. Using the error vector data obtained in step S5 to train the NGRC initial error prediction model obtained in step S3, a NGRC error prediction model is obtained;

[0013] S7. Use the STFT prediction model obtained in step S4 and the NGRC error prediction model obtained in step S6 to predict the target Doppler frequency ambiguity state data and complete the through-wall radar target tracking and positioning.

[0014] Step S1 is specifically as follows: using a Doppler wall-penetrating radar to transmit signals with carrier frequencies f1 and f2, and obtaining radar echo signals through a radar receiver Rxj, j∈{1,2,3};

[0015] The demodulated radar echo signal is expressed using the following formula:

[0016]

[0017] Where h is the attenuation factor of the target echo component; v(t) is the instantaneous radial velocity between the target and the radar; φ i is the phase constant of the echo component; f di is the carrier frequency f i The Doppler frequency of the corresponding target; C is the speed of light; p is the number of carrier frequency points; a i is the target surface scattering coefficient; j is the imaginary unit.

[0018] Step S2 is specifically as follows: first, the radar echo signal obtained in step S1 is subjected to short-time Fourier transform processing, which is expressed by the following formula:

[0019]

[0020] Among them, R ij (t+τ) is the corresponding carrier frequency f at the radar receiver Rxj i Echo signal at time (t+τ); STFT_R ij(t,f) is the time-frequency distribution of the corresponding echo signal; h(τ) is the window function; τ is the time delay; the frequency corresponding to the energy peak at each moment in the time-frequency distribution is extracted as a rough estimate of the target instantaneous frequency, expressed using the following formula:

[0021]

[0022] Among them, STFT_f ij (t,f) is the corresponding carrier frequency f at the radar receiver Rxj i The target instantaneous frequency;

[0023] The number of targets to be identified at each time step t is counted, and the maximum number of targets within the detection cycle is used as the estimated value, which is expressed using the following formula:

[0024] l(n)=l(n·Δt)=max[l1(n·Δt), l2(n·Δt)]

[0025]

[0026] Among them, l j (n·Δt), j = 1, 2 is the number of time-frequency distribution peaks at each time step n·Δt at the radar receiver Rxj; Δt is the sampling interval; L is the estimated number of targets; if the number of time-frequency distribution peaks l j (n·Δt), j = 1, 2 are both equal to the target number estimate L, then the echo data of the step size is in the Doppler frequency unambiguous state, otherwise the echo data is in the Doppler frequency ambiguous state;

[0027] The three-dimensional input vector is expressed using the following formula:

[0028]

[0029] Among them, x, y, z are three-dimensional input vectors; is the Doppler frequency estimate of the target at the radar receiver Rx1 corresponding to the frequency f1; is the Doppler frequency estimate of the target at the radar receiver Rx1 corresponding to the frequency f2; is the Doppler frequency estimation value of the target corresponding to the frequency f1 at the radar receiver Rx2; STFT is the STFT frequency estimation method.

[0030] In step S3, the STFT initial prediction model includes a feature vector extraction module and a Doppler frequency prediction module;

[0031] The feature vector extraction module processes the input three-dimensional input vector X to obtain the total feature vector, specifically:

[0032] Linear eigenvectorlin,n It consists of 3k sample observations input at the current time step and the previous k-1 time steps, and is calculated using the following formula:

[0033]

[0034] Where X(n) is the value of the input vector X at the current time step n; It is a vector stacking operation;

[0035] Nonlinear eigenvector nonlin is a linear eigenvector○ lin,n The quadratic nonlinear function is calculated by the following formula:

[0036]

[0037] Among them, the operator Calculate ○ first lin,n The outer product p of all elements out , and then for p out The unique monomials in the vector composed of p are collected, out Use the following calculation:

[0038]

[0039] in, To calculate the outer product of all elements; p out For (3k) 2 A symmetric matrix of elements; nonlin is a symmetric matrix p out (3k)(3k+1) / 2 upper triangular elements;

[0040] Total eigenvector total,n is a constant, linear eigenvector○ lin,n and nonlinear eigenvector ○ nonlin The linear combination of is expressed as follows:

[0041]

[0042] Where c is a constant;

[0043] The Doppler frequency prediction module uses the input total eigenvector to complete the Doppler frequency prediction, which is expressed as follows:

[0044] Y=W out ·○ total,n

[0045] Among them, W out is the linear mapping weight to be learned; Y is the output of the STFT initial prediction model.

[0046] Step S4 is specifically as follows:

[0047] If the target enters the fuzzy state at time step n, the output of the initial STFT prediction model at time step n+1 is expressed as:

[0048] Y n+1 =W out ·○ total,n+1

[0049] Using Tikhonov regularization, the output Y of the STFT initial prediction model is compared with the expected output Y d Match, then the linear mapping weight W out Use the following formula to get:

[0050] W out =Y d ○ total,n T (○ total,n ○ total,n T +αI) -1

[0051] Wherein, α is the regularization parameter; I is the identity matrix; according to the above steps, the STFT initial prediction model is trained using unambiguous data to obtain the STFT prediction model.

[0052] Step S5 is as follows: if the target enters the fuzzy state at time step n=i, the last linear mapping weight update in the training phase of the STFT initial prediction model occurs at time step i-1, using W out (i-1) indicates; use W out (i-1) The STFT prediction model is used to predict the data of half a window in the fuzzy state starting from the total time step i. The prediction result is expressed as X p1 (n),n=i,i+1,...,i+window / 2-1,X p1 (n) is the prediction result of the STFT prediction model at time step n=i,i+1,...,i+window / 2-1;

[0053] Then use the linear mapping weight W out (i-window-1) The STFT prediction model is used to predict the time step i-window to the time step i+window / 2-1, and the prediction result is expressed as X p2 (n),n=i-window,...,i-1,i,i+1,...,i+window / 2-1; take X p2Calculate the error vector ΔX between the data in (n) when n=i-window, i-window+1,...,i-1 and the input vector X(n) p2 (n):

[0054] ΔX p2 (n) = X p2 (n)-X(n)

[0055] The obtained error vector is used as error vector data.

[0056] Step S7 specifically includes the following steps:

[0057] Use the NGRC error prediction model to predict the fuzzy region X p2 (n) Perform error prediction to obtain the prediction error ΔX' p2 (n), used to compensate for the X in the blurred area p2 The predicted output of (n) is expressed using the following formula:

[0058] X' p2 (n) = X p2 (n)+ΔX' p2 (n)

[0059] Among them, n=i,i+1,...,i+window-1; X' p2 (n) is the X in the fuzzy area p2 (n) Corrected prediction output;

[0060] The Doppler frequency after correcting the current ambiguity interval is expressed using the following formula:

[0061] X p (c,n)=c·X' p2 (n)+(1-c)·X p1 (n)

[0062] Where c is the frequency correction factor. Adjust the correction factor c so that the estimated target energy is concentrated in the baseband to the maximum extent. Then the instantaneous frequency of the estimated target is:

[0063]

[0064] in, is the optimal correction factor, and its value range is [0,1]; the instantaneous frequency of the target is obtained As input to the STFT prediction model to update the linear mapping weight W of the current window out (i+window / 2-1), and then predict the next interval according to the above steps until the fuzzy area is traversed and the target instantaneous Doppler frequency of the entire prediction period is obtained;

[0065] The target position is estimated as the integral of the instantaneous Doppler frequency using the following formula:

[0066]

[0067]

[0068]

[0069] Where R is the distance between the target and the wall-penetrating radar; θ EL is the elevation angle of the target relative to the position of the through-wall radar; θ AZ is the azimuth of the target relative to the position of the through-wall radar; is the carrier frequency f corresponding to the radar receiver Rxj i The target Doppler frequency; φ θEL is the elevation angle θ EL The initial phase of φ θAZ is the azimuth angle θ AZ The initial phase of φ R is the initial phase at distance R; λ1 is the wavelength of carrier frequency f1; Δf is the difference between carrier frequencies f1 and f2; b is the antenna spacing; and C is the speed of light.

[0070] This invention discloses a multi-batch through-the-wall radar target tracking and positioning method. It uses short-time Fourier transforms to identify the Doppler frequency ambiguity region of radar echoes. It also proposes a NGRC error prediction model for estimating the Doppler frequency in the ambiguity region. This model includes an error predictor with adaptive error compensation to eliminate prediction errors. This method effectively suppresses accumulated errors and improves the target tracking performance of Doppler through-the-wall radars. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 Schematic diagram of the process of the present invention;

[0072] Figure 2 Comparison of instantaneous Doppler frequency estimation results and target tracking results under different algorithms; (a) STFT estimation of target instantaneous frequency; (b) STFT tracking of target trajectory; (c) GRU algorithm estimation of target instantaneous frequency; (d) GRU algorithm tracking of target trajectory; (e) traditional NGRC algorithm estimation of target instantaneous frequency; (f) traditional NGRC algorithm tracking of target trajectory; (g) estimation of target instantaneous frequency by the method of the present invention; (h) tracking of target trajectory by the method of the present invention. DETAILED DESCRIPTION

[0073] The present invention provides a Doppler through-wall radar target tracking and positioning method, the flow chart of which is as follows: Figure 1As shown, the following steps are included:

[0074] S1. Acquire the radar echo signal and demodulate it to obtain the demodulated radar echo signal. Specifically, use a Doppler wall-penetrating radar to transmit signals with carrier frequencies f1 and f2, and obtain the radar echo signal through a radar receiver Rxj, where j∈{1,2,3};

[0075] The demodulated radar echo signal is expressed using the following formula:

[0076]

[0077] Where h is the attenuation factor of the target echo component; v(t) is the instantaneous radial velocity between the target and the radar; φ i is the phase constant of the echo component; f di is the carrier frequency f i The Doppler frequency of the corresponding target; C is the speed of light; p is the number of carrier frequency points; a i is the target surface scattering coefficient; j is the imaginary unit.

[0078] S2. Process the radar echo signal obtained in step S1, determine the echo data status, obtain the Doppler frequency unambiguous state data, and then construct the input vector, specifically:

[0079] First, the radar echo signal obtained in step S1 is subjected to short-time Fourier transform processing, which is expressed by the following formula:

[0080]

[0081] Among them, R ij (t+τ) is the corresponding carrier frequency f at the radar receiver Rxj i Echo signal at time (t+τ); STFT_R ij (t,f) is the time-frequency distribution of the corresponding echo signal; h(τ) is the window function; τ is the time delay; the frequency corresponding to the energy peak at each moment in the time-frequency distribution is extracted as a rough estimate of the target instantaneous frequency, expressed using the following formula:

[0082]

[0083] Among them, STFT_f ij (t,f) is the corresponding carrier frequency f at the radar receiver Rxj i The target instantaneous frequency;

[0084] The number of targets to be identified at each time step t is counted, and the maximum number of targets within the detection cycle is used as the estimated value, which is expressed using the following formula:

[0085] l(n)=l(n·Δt)=max[l1(n·Δt), l2(n·Δt)]

[0086]

[0087] Among them, l j (n·Δt),j=1,2 is the number of time-frequency distribution peaks at each time step n·Δt at the radar receiver Rxj, that is, the number of targets to be identified at each time step; Δt is the sampling interval; L is the estimated number of targets; if the number of time-frequency distribution peaks l j (n·Δt), j = 1, 2 are both equal to the target number estimate L, then the echo data of the step size is in the Doppler frequency unambiguous state, otherwise the echo data is in the Doppler frequency ambiguous state;

[0088] The three-dimensional input vector is expressed using the following formula:

[0089]

[0090] Among them, x, y, z are three-dimensional input vectors; is the Doppler frequency estimate of the target at the radar receiver Rx1 corresponding to the frequency f1; is the Doppler frequency estimate of the target at the radar receiver Rx1 corresponding to the frequency f2; is the Doppler frequency estimation value of the target corresponding to the frequency f1 at the radar receiver Rx2; STFT is the STFT frequency estimation method.

[0091] S3. Construct the STFT initial prediction model and the NGRC initial error prediction model;

[0092] The STFT initial prediction model includes a feature vector extraction module and a Doppler frequency prediction module;

[0093] The feature vector extraction module processes the input three-dimensional input vector X to obtain the total feature vector, specifically:

[0094] Linear eigenvector lin,i It consists of 3k sample observations input at the current time step and the previous k-1 time steps, and is calculated using the following formula:

[0095]

[0096] Where X(n) is the value of the input vector X at the current time step n; It is a vector stacking operation;

[0097] Nonlinear eigenvector nonlin is a linear eigenvector○ lin,n The quadratic nonlinear function is calculated by the following formula:

[0098]

[0099] Among them, the operator Calculate ○ first lin,n The outer product p of all elements out , and then for p out The unique monomials in the vector composed of p are collected, out Use the following calculation:

[0100]

[0101] in, To calculate the outer product of all elements; p out For (3k) 2 A symmetric matrix of elements; nonlin is a symmetric matrix p out (3k)(3k+1) / 2 upper triangular elements;

[0102] Total eigenvector total,n is a constant, linear eigenvector○ lin,n and nonlinear eigenvector ○ nonlin The linear combination of is expressed as follows:

[0103]

[0104] Where c is a constant;

[0105] The Doppler frequency prediction module uses the input total eigenvector to complete the Doppler frequency prediction, which is expressed as follows:

[0106] Y=W out ·○ total,n

[0107] Among them, W out is the linear mapping weight to be learned; Y is the output of the STFT initial prediction model.

[0108] S4. Use the Doppler frequency unambiguous state data obtained in step S2 to train the STFT initial prediction model obtained in step S3 to obtain an STFT prediction model, specifically:

[0109] If the target enters the fuzzy state at time step n, the output of the initial STFT prediction model at time step n+1 is expressed as:

[0110] Y n+1 =W out ·○ total,n+1

[0111] Using Tikhonov regularization, the output Y of the STFT initial prediction model is compared with the expected output Y d Match, then the linear mapping weight W out Use the following formula to get:

[0112] W out =Y d ○ total,n T (○ total,n ○ total,n T +αI) -1

[0113] Wherein, α is the regularization parameter; I is the identity matrix; according to the above steps, the STFT initial prediction model is trained using unambiguous data to obtain the STFT prediction model.

[0114] S5. Using the STFT prediction model obtained in step S4, calculate the error vector data, specifically:

[0115] If the target enters the fuzzy state at time step n=i, the last linear mapping weight update in the training phase of the STFT initial prediction model occurs at time step i-1, using W out (i-1) indicates; use W out (i-1) The STFT prediction model is used to predict the data of half a window in the fuzzy state starting from the total time step i. The prediction result is expressed as X p1 (n),n=i,i+1,...,i+window / 2-1,X p1 (n) is the prediction result of the STFT prediction model at time step n=i,i+1,...,i+window / 2-1;

[0116] Then use the linear mapping weight W out (i-window-1) The STFT prediction model is used to predict the time step i-window to the time step i+window / 2-1, and the prediction result is expressed as X p2 (n),n=i-window,...,i-1,i,i+1,...,i+window / 2-1; take X p2 The data in (n) when n=i-window,i-window+1,...,i-1, that is, the first window data, calculate the error vector ΔX between it and the input vector X(n) p2 (n):

[0117] ΔX p2 (n) = X p2 (n)-X(n)

[0118] The obtained error vector is used as error vector data.

[0119] S6. Using the error vector data obtained in step S5 to train the NGRC initial error prediction model obtained in step S3, a NGRC error prediction model is obtained;

[0120] S7. Use the STFT prediction model obtained in step S4 and the NGRC error prediction model obtained in step S6 to predict the target Doppler frequency ambiguity state data and complete the through-wall radar target tracking and positioning, specifically:

[0121] Use the NGRC error prediction model to predict the fuzzy region X p2 (n) Perform error prediction to obtain the prediction error ΔX' p2 (n), used to compensate for the X in the blurred area p2 The predicted output of (n) is expressed using the following formula:

[0122] X' p2 (n) = X p2 (n)+ΔX' p2 (n)

[0123] Among them, n=i,i+1,...,i+window-1; X' p2 (n) is the X in the fuzzy area p2 (n) Corrected prediction output;

[0124] The Doppler frequency after correcting the current ambiguity interval is expressed using the following formula:

[0125] X p (c,n)=c·X' p2 (n)+(1-c)·X p1 (n)

[0126] Where c is the frequency correction factor. Adjust the correction factor c so that the estimated target energy is concentrated in the baseband to the maximum extent. Then the instantaneous frequency of the estimated target is:

[0127]

[0128] in, is the optimal correction factor, and its value range is [0,1]; the instantaneous frequency of the target is obtained As input to the STFT prediction model to update the linear mapping weight W of the current window out (i+window / 2-1), and then predict the next interval according to the above steps until the fuzzy area is traversed and the target instantaneous Doppler frequency of the entire prediction period is obtained;

[0129] The target position is estimated as the integral of the instantaneous Doppler frequency using the following formula:

[0130]

[0131]

[0132]

[0133] Where R is the distance between the target and the wall-penetrating radar; θ EL is the elevation angle of the target relative to the position of the through-wall radar; θ AZ is the azimuth of the target relative to the position of the through-wall radar; is the carrier frequency f corresponding to the radar receiver Rxj i The target Doppler frequency; φ θEL is the elevation angle θ EL The initial phase of φ θAZ is the azimuth angle θ AZ The initial phase of φ R is the initial phase at distance R; λ1 is the wavelength of carrier frequency f1; Δf is the difference between carrier frequencies f1 and f2; b is the antenna spacing; and C is the speed of light.

[0134] The method of the present invention is further described below with reference to an embodiment:

[0135] The existing algorithms including STFT algorithm, GRU algorithm, traditional NGRC algorithm and the method of the present invention are used to track the Doppler through-wall radar target to obtain the target instantaneous frequency estimation and tracking trajectory, such as Figure 2 As shown. Figure 2 It can be seen from the figure that the target instantaneous frequency estimation and tracking trajectory obtained by the method of the present invention have a higher degree of overlap with the true frequency and true trajectory. Compared with the existing algorithm, the tracking performance of the present invention is significantly improved.

Claims

1. A Doppler through-wall radar target tracking and positioning method, characterized in that: The following steps are involved: S1. Acquire and demodulate the radar echo signal to obtain a demodulated radar echo signal; S2. Process the radar echo signal obtained in step S1 to determine the echo data status, obtain the Doppler frequency unambiguous state data, and then construct the input vector; S3. Construct the STFT initial prediction model and the NGRC initial error prediction model; S4. Using the Doppler frequency unambiguous state data obtained in step S2 to train the STFT initial prediction model obtained in step S3, a STFT prediction model is obtained; S5. Using the STFT prediction model obtained in step S4, the error vector data is calculated; S6. Using the error vector data obtained in step S5 to train the NGRC initial error prediction model obtained in step S3, a NGRC error prediction model is obtained; S7. Use the STFT prediction model obtained in step S4 and the NGRC error prediction model obtained in step S6 to predict the target Doppler frequency ambiguity state data and complete the through-wall radar target tracking and positioning.

2. The Doppler through-wall radar target tracking and positioning method according to claim 1, characterized in that: Step S1 is specifically as follows: using a Doppler wall-penetrating radar to transmit signals with carrier frequencies f1 and f2, and obtaining radar echo signals through a radar receiver Rxj, j∈{1,2,3}; The demodulated radar echo signal is expressed using the following formula: Where h is the attenuation factor of the target echo component; v(t) is the instantaneous radial velocity between the target and the radar; φ i is the phase constant of the echo component; f di is the carrier frequency f i The Doppler frequency of the corresponding target; C is the speed of light; p is the number of carrier frequency points; a i is the target surface scattering coefficient; j is the imaginary unit.

3. The Doppler through-wall radar target tracking and positioning method according to claim 2, characterized in that: Step S2 is specifically as follows: first, the radar echo signal obtained in step S1 is subjected to short-time Fourier transform processing, which is expressed by the following formula: Among them, R ij (t+τ) is the corresponding carrier frequency f at the radar receiver Rxj i Echo signal at time (t+τ); STFT_R ij (t,f) is the time-frequency distribution of the corresponding echo signal; h(τ) is the window function; τ is the time delay; the frequency corresponding to the energy peak at each moment in the time-frequency distribution is extracted as a rough estimate of the target instantaneous frequency, expressed using the following formula: Among them, STFT_f ij (t,f) is the corresponding carrier frequency f at the radar receiver Rxj i The target instantaneous frequency; The number of targets to be identified at each time step t is counted, and the maximum number of targets within the detection cycle is used as the estimated value, which is expressed using the following formula: l(n)=l(n·Δt)=max[l1(n·Δt), l2(n·Δt)] Among them, l j (n·Δt), j = 1, 2 is the number of time-frequency distribution peaks at each time step n·Δt at the radar receiver Rxj; Δt is the sampling interval; L is the estimated number of targets; if the number of time-frequency distribution peaks l j (n·Δt), j = 1, 2 are both equal to the target number estimate L, then the echo data of the step size is in the Doppler frequency unambiguous state, otherwise the echo data is in the Doppler frequency ambiguous state; The three-dimensional input vector is expressed using the following formula: Among them, x, y, z are three-dimensional input vectors; is the Doppler frequency estimate of the target at the radar receiver Rx1 corresponding to the frequency f1; is the Doppler frequency estimate of the target at the radar receiver Rx1 corresponding to the frequency f2; is the Doppler frequency estimation value of the target corresponding to the frequency f1 at the radar receiver Rx2; STFT is the STFT frequency estimation method.

4. The Doppler through-wall radar target tracking and positioning method according to claim 3, characterized in that: In step S3, the STFT initial prediction model includes a feature vector extraction module and a Doppler frequency prediction module; The feature vector extraction module processes the input three-dimensional input vector X to obtain the total feature vector, specifically: Linear eigenvector lin,n It consists of 3k sample observations input at the current time step and the previous k-1 time steps, and is calculated using the following formula: Where X(n) is the value of the input vector X at the current time step n; It is a vector stacking operation; Nonlinear eigenvector nonlin is a linear eigenvector○ lin,n The quadratic nonlinear function is calculated by the following formula: Among them, the operator Calculate ○ first lin,n The outer product p of all elements out , and then for p out The unique monomials in the vector composed of p are collected, out Use the following calculation: in, To calculate the outer product of all elements; p out For (3k) 2 A symmetric matrix of elements; nonlin is a symmetric matrix p out (3k)(3k+1) / 2 upper triangular elements; Total eigenvector total,n is a constant, linear eigenvector○ lin,n and nonlinear eigenvector ○ nonlin The linear combination of is expressed as follows: Where c is a constant; The Doppler frequency prediction module uses the input total eigenvector to complete the Doppler frequency prediction, which is expressed as follows: Y=W out ·○ total,n Among them, W out is the linear mapping weight to be learned; Y is the output of the STFT initial prediction model.

5. The Doppler through-wall radar target tracking and positioning method according to claim 4, characterized in that: Step S4 is specifically as follows: When the target enters the fuzzy state at time step n, the output of the initial STFT prediction model at time step n+1 is expressed as: Y n+1 =W out ·○ total,n+1 Using Tikhonov regularization, the output Y of the STFT initial prediction model is compared with the expected output Y d Match, then the linear mapping weight W out Use the following formula to get: W out =Y d ○ total,n T (○ total,n ○ total,n T +αI) -1 Wherein, α is the regularization parameter; I is the identity matrix; according to the above steps, the STFT initial prediction model is trained using unambiguous data to obtain the STFT prediction model.

6. The Doppler through-wall radar target tracking and positioning method according to claim 5, characterized in that: Step S5 is as follows: if the target enters the fuzzy state at time step n=i, the last linear mapping weight update in the training phase of the STFT initial prediction model occurs at time step i-1, using W out (i-1) indicates; use W out (i-1) The STFT prediction model is used to predict the data of half a window in the fuzzy state starting from the total time step i. The prediction result is expressed as X p1 (n),n=i,i+1,...,i+window / 2-1,X p1 (n) is the prediction result of the STFT prediction model at time step n=i,i+1,...,i+window / 2-1; Then use the linear mapping weight W out (i-window-1) The STFT prediction model is used to predict the time step i-window to the time step i+window / 2-1, and the prediction result is expressed as X p2 (n),n=i-window,...,i-1,i,i+1,...,i+window / 2-1; take X p2 Calculate the error vector ΔX between the data in (n) when n=i-window, i-window+1,...,i-1 and the input vector X(n) p2 (n): ΔX p2 (n)=X p2 (n)-X(n) The obtained error vector is used as error vector data.

7. The Doppler through-wall radar target tracking and positioning method according to claim 6, characterized in that: Step S7 is specifically as follows: Use the NGRC error prediction model to predict the fuzzy region X p2 (n) Perform error prediction to obtain the prediction error ΔX' p2 (n), used to compensate for the X in the blurred area p2 The predicted output of (n) is expressed using the following formula: X' p2 (n)=X p2 (n)+ΔX' p2 (n) Among them, n=i,i+1,...,i+window-1; X' p2 (n) is the X in the fuzzy area p2 (n) Corrected prediction output; The Doppler frequency after correcting the current ambiguity interval is expressed using the following formula: X p (c,n)=c·X' p2 (n)+(1-c)·X p1 (n) Where c is the frequency correction factor. Adjust the correction factor c so that the estimated target energy is concentrated in the baseband to the maximum extent. Then the instantaneous frequency of the estimated target is: in, is the optimal correction factor, and its value range is [0,1]; the instantaneous frequency of the target is obtained As input to the STFT prediction model to update the linear mapping weight W of the current window out (i+window / 2-1), and then predict the next interval according to the above steps until the fuzzy area is traversed and the target instantaneous Doppler frequency of the entire prediction period is obtained; The target position is estimated as the integral of the instantaneous Doppler frequency using the following formula: Where R is the distance between the target and the wall-penetrating radar; θ EL is the elevation angle of the target relative to the position of the through-wall radar; θ AZ is the azimuth of the target relative to the position of the through-wall radar; is the carrier frequency f corresponding to the radar receiver Rxj i The target Doppler frequency; φ θEL is the elevation angle θ EL The initial phase of φ θAZ is the azimuth angle θ AZ The initial phase of φ R is the initial phase at distance R; λ1 is the wavelength of carrier frequency f1; Δf is the difference between carrier frequencies f1 and f2; b is the antenna spacing; and C is the speed of light.

Images