A moving object tracking method based on over-complete angle dictionary optimization technology

Abstract

The application discloses a moving target tracking method based on an overcomplete angle dictionary optimization technology, which comprises the following steps: a Doppler through-wall radar module is used to acquire echo signals of a moving target; a windowed time-frequency analysis method is used to estimate and process the echo signals to acquire instantaneous frequency values; a high-order polynomial model is used to fit and process the instantaneous frequency values to acquire a fitting curve; the fitting curve is used to solve an instantaneous frequency tilt angle, and then an overcomplete instantaneous frequency tilt angle dictionary is constructed; the tilt angle dictionary is used to perform time-frequency analysis and processing on the echo signals to acquire an optimal parameter domain distribution; a signal demodulation technology is used to process the optimal parameter domain distribution, and an eigenvalue classification technology is used to extract and process the demodulated signals to construct an instantaneous frequency component set of the echo signals; and through the instantaneous frequency component set, a trajectory of the moving target is synthesized to complete tracking processing on the moving target. The application has high target positioning precision and good tracking effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of moving target tracking, and particularly relates to a moving target tracking method based on over-complete angle dictionary optimization technology. BACKGROUND

[0002] In recent years, with the continuous improvement of people's living standards, science and technology are also developing forward unceasingly, and radar positioning technology has been widely applied in various fields. Doppler through-wall radar (DTWR) is a device for effectively positioning moving targets, and is currently widely used in the above fields due to its simple operation, high positioning accuracy, strong anti-interference ability and other advantages. DTWR realizes the positioning analysis of the target position through the Doppler effect of electromagnetic wave propagation, and then obtains the motion trajectory of the target.

[0003] In order to accurately obtain the motion trajectory of the target, the traditional positioning and tracking method of the moving target first needs to perform time-frequency analysis processing on the echo signal to obtain the time-frequency distribution of the echo signal, and then uses the peak search method to extract the instantaneous frequency component (IF) of the target from the time-frequency distribution of the echo signal, and synthesizes the motion trajectory according to the extracted instantaneous frequency component of the target. When a windowed time-frequency transform is selected to perform time-frequency analysis processing on the echo signal, there is usually a significant frequency ambiguity phenomenon, and the main reason for this phenomenon is that the windowed time-frequency transform is limited by the principle of accurate measurement, which cannot meet the requirement of optimal time resolution and time-frequency resolution at the same time. Therefore, when the processed echo signal contains instantaneous frequency crossing or too close signals, the time-frequency distribution obtained by the windowed time-frequency transform processing contains time-frequency aliasing phenomenon. When the time-frequency distribution with aliasing phenomenon is used to estimate the instantaneous frequency curve of the target, there will be a large error between the estimated instantaneous frequency curve and the true frequency curve in the frequency ambiguity area, which will cause the synthesized motion trajectory to have a relatively obvious deviation problem.

[0004] In order to obtain high-precision target motion trajectory, researchers have proposed a large number of positioning algorithms for moving targets, such as target positioning methods based on straight line model, circle model, ellipse model and Bezier model. Although the above target positioning methods based on fixed model can improve the positioning accuracy of the target to different degrees, such methods cannot adaptively adjust the type of mathematical model according to the characteristics of the echo signal, and cannot accurately select and process in the case of complex motion state of the target positioning, so such methods have strong limitations. SUMMARY

[0005] The application aims to provide a moving target tracking method based on over-complete angle dictionary optimization technology, which has high target positioning accuracy and good tracking effect.

[0006] The moving target tracking method based on over-complete angle dictionary optimization technology provided by the application comprises the following steps:

[0007] S1. Obtain echo signals of a moving target.

[0008] S2. Estimate the echo signals obtained in step S1 by using a windowed time-frequency analysis method, and calculate the instantaneous frequency value of the echo signals.

[0009] S3. Fit the instantaneous frequency value obtained in step S2 by using a high-order polynomial model, and obtain a fitting curve of the instantaneous frequency.

[0010] S4. Solve the instantaneous frequency tilt angle by using the fitting curve of the instantaneous frequency obtained in step S3, and construct an over-complete instantaneous frequency tilt angle dictionary by using the solved instantaneous frequency tilt angle.

[0011] S5. Perform time-frequency analysis processing on the echo signals obtained in step S1 by using the instantaneous frequency tilt angle dictionary constructed in step S4, and obtain an optimal parameter domain distribution.

[0012] S6. Process the optimal parameter domain distribution obtained in step S5 by using a signal demodulation technology, extract the processed signal by using an eigenvalue classification technology, and construct an instantaneous frequency component set of the echo signals.

[0013] S7. Synthesize the trajectory of the moving target by using the instantaneous frequency component set constructed in step S6, and complete the tracking processing of the moving target.

[0014] The step S1 of obtaining the echo signals of the moving target specifically comprises:

[0015] The echo signal data of the moving target is collected by using a Doppler through-wall radar module, one-dimensional target echo signals are obtained, and the target signal x(t) received by the radar receiver is expressed by the following formula:

[0016]

[0017] wherein, A i (t) is the signal amplitude of the target i, f i (t) is the instantaneous frequency function of the target i, and M represents the number of targets in the detection environment.

[0018] The step S2 of estimating the echo signals obtained in step S1 by using a windowed time-frequency analysis method, and calculating the instantaneous frequency value of the echo signals specifically comprises:

[0019] (1) The windowed time-frequency analysis method is used to perform time-frequency analysis and estimation processing on the target echo signal obtained in step S1 to obtain the two-dimensional time-frequency parameter domain of the moving target. The windowed time-frequency analysis method is expressed by the following formula:

[0020] TFD(t,f)=∫x(η)·h(η-t)·exp(-j2πfη)dη

[0021] Where TFD(t,f) is the time-frequency two-dimensional parameter domain of the target signal, f is the frequency, t is the time, x(·) is the received target signal, and h(·) is the window function for time-frequency analysis;

[0022] (2) The peak search method is used to extract the instantaneous frequency value of the i-th target in the two-dimensional time-frequency parameter domain. The peak search method is expressed by the following formula:

[0023]

[0024] in, It is the instantaneous frequency value obtained from the estimation process.

[0025] Step S3, which involves using a higher-order polynomial model to fit the instantaneous frequency values ​​obtained in step S2 to obtain a fitting curve for the instantaneous frequency, specifically includes:

[0026] A higher-order polynomial model is used for the instantaneous frequency values ​​obtained in step S2. The fitting process is expressed using the following formula:

[0027]

[0028] in, This is the fitted instantaneous frequency curve, where N is the order of the higher-order polynomial, {b0,b1,...,b...} N-1} represents the coefficients of the higher-order polynomial, and t represents time.

[0029] Step S4 involves using the fitting curve of the instantaneous frequency obtained in step S3 to solve for the instantaneous frequency tilt angle, and constructing an overcomplete instantaneous frequency tilt angle dictionary using the obtained instantaneous frequency tilt angle, specifically including:

[0030] 1) Solve for the instantaneous frequency tilt angle:

[0031] The instantaneous frequency fitting curve obtained in step S2 The slope of the curve is calculated to obtain the change in the instantaneous frequency tilt angle of the i-th target in the two-dimensional time-frequency parameter domain. The following formula is used for the calculation:

[0032]

[0033]

[0034] Where, k(t) n ) represents the slope of the instantaneous frequency fitting curve, n = 1, ..., L; t n Let L be the length of the echo signal at time n during the sampling duration, and θ(t) be the time n of the sampling duration. n T is the tilt angle of the instantaneous frequency. x It is the sampling time, F s It is the sampling frequency;

[0035] 2) Construct a complete dictionary of instantaneous frequency tilt angles:

[0036] The tilt angle θ(t) of the instantaneous frequency obtained from step 1) n The overcomplete instantaneous frequency tilt angle dictionary Φ is constructed using the following formula. (2W+1)×L :

[0037]

[0038] Where W is the dictionary expansion coefficient; 2W+1, L and λ are the number of atoms in the dictionary, the length of the echo signal and the instantaneous frequency tilt angle expansion factor, respectively.

[0039] Step S5 involves using the instantaneous frequency tilt angle dictionary constructed in step S4 to perform time-frequency analysis processing on the echo signal obtained in step S1 to obtain the optimal parameter domain distribution, specifically including:

[0040] The instantaneous frequency tilt angle dictionary Φ described in step S4 is used. (2W+1)×L The echo signal x(t) obtained in step S1 is reprocessed using time-frequency analysis, and the optimal parameter domain distribution (TFD) is obtained according to the energy convergence criterion. best (t,f);

[0041] Within a set time interval η, the instantaneous frequency of the echo signal is treated as a linear function and expressed by the following formula:

[0042] IF i (η) = IF i (t)+IF′ i (t)·(η-t),t∈η

[0043] Among them, IF i (t) is the instantaneous frequency value at time t, IF′ i (t) is the first derivative of the instantaneous frequency at time t;

[0044] The mathematical model of the echo signal within a set time η is expressed by the following formula:

[0045] x i (η)=A i (η)exp{j2π[∫IF i (η)dτ]}

[0046] =A i (η)exp{j2π[IF i (t)η+1 / 2·IF′ i (t)(η-t) 2 ]}

[0047] The echo signal within the set time η is processed by using the windowed time-frequency transform, and is represented by the following formula:

[0048] TFD(t,f)

[0049] =∫x i (η)·h(η-t)·exp(-j2πfη)dη

[0050] =∫A i (η)·exp{j2π[IF i (t)η+1 / 2·IF′ i (t)(η-t) 2 ]}·h(η-t)·exp(-j2πfη)dη

[0051] Wherein, TFD(t,f) is the time-frequency two-dimensional parameter domain of the echo signal;

[0052] For the time-frequency point (t,f) in the above formula, if the 1 / 2·IF′ i (t)(η-t) 2 term in the formula is eliminated, the time-frequency energy obtained will be more concentrated, and the interference will be less, thereby better suppressing the time-frequency aliasing phenomenon.

[0053] The 1 / 2·IF′ (2W+1)×L (t)(η-t) α term in the above formula is eliminated by using the dictionary atom Φ i in the overcomplete angle dictionary Φ 2 , the time-frequency energy concentration of the echo signal is improved, and is represented by the following formula:

[0054]

[0055] Wherein, Φ α (α∈[1,2W+1]) is the αth atom in the overcomplete angle dictionary Φ (2W+1)×L , is the dictionary atom Φ αThe obtained optimization parameter domain distribution, where t is time, f is frequency, and F S It is the sampling frequency;

[0056] Using the angle dictionary Φ (2W+1)×L Time-frequency analysis of the echo signal yielded 2W+1 time-frequency distribution TFDs. ILCT Based on the energy convergence criterion, the optimal energy corresponding to each time-frequency point (t,f) is obtained from 2W+1 parameter domain distributions, thus yielding the optimal parameter domain distribution TFD. best (t,f) is represented by the following formula:

[0057]

[0058] Step S6 involves using signal demodulation technology to process the optimal parameter domain distribution obtained in step S5, and using eigenvalue classification technology to extract and process the demodulated signal, constructing a set of instantaneous frequency components for the echo signal. Specifically, this includes:

[0059] ① The peak search method is used to target the optimal parameter domain distribution (TFD) obtained in step S5. best The instantaneous frequency of the i-th target is extracted using the following formula: (t,f)

[0060]

[0061] in, It is the instantaneous frequency of the i-th target;

[0062] ②Use the extracted instantaneous frequency Feature classification and extraction processing is performed on the echo signal to obtain the echo component of the i-th target:

[0063] The echo signal acquired by Doppler radar is a typical non-stationary signal with low autocorrelation between the signals. It is impossible to directly perform feature classification and extraction processing on the acquired signal. Signal demodulation processing is used to convert the echo signal of the i-th target into an autocorrelation signal as a preprocessing step before feature classification and extraction.

[0064] A. Signal demodulation processing:

[0065] The demodulation process of a signal is represented by the following formula:

[0066]

[0067] Where, x do (t) is the demodulated signal. Through instantaneous frequency The constructed demodulation factor;

[0068] The demodulated signal x do (t) is constructed into a two-dimensional matrix to facilitate the separation and processing of autocorrelation signals in the echo signal. The constructed two-dimensional matrix to be processed is represented by the following formula:

[0069]

[0070] Wherein, matrix E m×n The number of rows m satisfies the following conditions: when L is odd, m = (L+1) / 2; when L is even, m = L / 2+1; matrix E m×n The number of rows and columns n satisfies the following condition: n = L - m + 1; E m×n It is the matrix to be processed, x do (t) is the demodulated signal;

[0071] B. Feature classification and extraction processing:

[0072] The two-dimensional matrix E to be processed m×n This can be expressed using the following formula:

[0073]

[0074] Among them, U m×n Let P be the eigenvalue matrix of the signal, where all values ​​except those on the diagonal are 0; m×m and Q n×n All are unitary matrices, and the vectors within them are mutually orthogonal. It is Q n×n The conjugate transpose of;

[0075] The demodulated target signal exhibits high autocorrelation, retaining only the eigenvalue matrix U. m×n The first eigenvalue in the matrix is ​​used to set the values ​​at other locations to 0, thus obtaining the extraction matrix of the i-th target echo. Expressed using the following formula:

[0076]

[0077] C. Construct the instantaneous frequency component set of the echo signal:

[0078] The extraction matrix obtained from feature extraction The inverse process of constructing a two-dimensional matrix involves summing the overlapping positions in the matrix and taking the average to obtain the echo demodulated signal of the i-th target. Using the constructed inverse demodulation factor Obtain the echo signal of the i-th target Expressed using the following formula

[0079]

[0080] extracting the echo signal of the ith target from the received target echo signal x(t), while the residual signal is returned to the echo signal obtained in step S1 as a new signal, participating in the extraction of the next signal component, which is expressed by the following formula:

[0081]

[0082] where x new (t) is the signal to be processed after removing the extracted target component.

[0083] The instantaneous frequency component set constructed in step S6 is used in step S7 to synthesize the trajectory of the moving target, completing the tracking processing of the moving target, which specifically includes:

[0084] a. Calculate the estimated target distance and angle of arrival:

[0085] The Doppler through-wall radar is a dual-frequency continuous wave radar, the transmitter transmits carrier frequencies f1 and f2, and the interval between the two receivers is d. Receiver 1 is used to estimate the distance change of the target, and the following formula is used to calculate the distance:

[0086]

[0087] where R(t) is the distance of the target distance radar module, C is the speed of electromagnetic wave propagation in vacuum, IF 1,1 (t) and IF 2,1 (t) are the instantaneous frequencies of the echo signals received by receiver 1 at carrier frequencies f1 and f2;

[0088] Receiver 1 and receiver 2 are used to estimate the angle of arrival of the target, and the following formula is used to calculate the angle of arrival:

[0089]

[0090] where angel(t) is the angle of arrival of the target signal, λ is the wavelength of the carrier, IF 1,2 (t) is the instantaneous frequency of the echo signal received by receiver 2 at carrier frequency f1;

[0091] b. Synthesize the motion trajectory of the moving target:

[0092] According to the distance and angle of arrival calculated in step a, the coordinates of the target motion are synthesized, and the motion trajectory is synthesized; which is described by the following formula:

[0093] x(t)=R(t)·sin(angel(t))

[0094] y(t)=R(t)·cos(angel(t))

[0095] Based on the calculated x-axis and y-axis coordinates, lines are drawn in a two-dimensional Cartesian coordinate system to achieve target tracking and motion trajectory estimation.

[0096] The moving target tracking method based on overcomplete angle dictionary optimization technology provided by this invention processes the acquired echo signal using windowed time-frequency analysis and a high-order polynomial model to obtain a fitting curve of the instantaneous frequency, and then constructs an overcomplete instantaneous frequency tilt angle dictionary for time-frequency analysis of the echo signal to obtain the optimal parameter domain distribution. Feature classification extraction technology is then used to process the optimal parameter domain distribution to construct an instantaneous frequency component set, synthesize the trajectory of the moving target, and complete the tracking process. Furthermore, this invention offers high target positioning accuracy and better tracking performance. Attached Figure Description

[0097] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0098] Figure 2 This is a schematic diagram of the Doppler radar structure of the method of the present invention.

[0099] Figure 3 This is a schematic diagram comparing the time-frequency parameter domain distributions of analog signals processed by traditional methods and the method of this invention.

[0100] Figure 4 This is a schematic diagram comparing the instantaneous frequency curves of analog signals after estimation using conventional methods and the method of this invention.

[0101] Figure 5 This diagram illustrates the comparison of the effects of processing sample data using traditional methods and the method of this invention. Detailed Implementation

[0102] like Figure 1 The diagram shown is a flowchart of the method of the present invention: The moving target tracking method based on overcomplete angle dictionary optimization technology provided by the present invention includes the following steps:

[0103] S1. Acquire the echo signal of the moving target; specifically including:

[0104] Adopting such Figure 2 The Doppler through-wall radar structure shown acquires echo signal data from moving targets, obtaining a one-dimensional target echo signal. The target signal x(t) received by the radar receiver is expressed by the following formula:

[0105]

[0106] wherein A i (t) is the signal amplitude of target i, f i (t) is the instantaneous frequency function of target i, M represents the number of targets in the detection environment;

[0107] S2. Using a windowed time-frequency analysis method to estimate the echo signal obtained in step S1, the instantaneous frequency value of the echo signal is calculated; specifically including:

[0108] (1) Using a windowed time-frequency analysis method to estimate the echo signal obtained in step S1, the time-frequency two-dimensional parameter domain of the moving target is obtained, and the windowed time-frequency analysis method is expressed by the following formula:

[0109] TFD(t,f)=∫x(η)·h(η-t)·exp(-j2πfη)dη

[0110] Wherein, TFD(t,f) is the time-frequency two-dimensional parameter domain of the target signal, f is the frequency, t is the time, x(·) is the received target signal, and h(·) is the window function of time-frequency analysis;

[0111] (2) Using a peak search method to extract the instantaneous frequency value of the i-th target in the time-frequency two-dimensional parameter domain, and the peak search method is expressed by the following formula:

[0112]

[0113] Wherein, is the instantaneous frequency value obtained by estimation processing;

[0114] S3. Using a high-order polynomial model to fit the instantaneous frequency value obtained in step S2, a fitting curve of the instantaneous frequency is obtained; specifically including;

[0115] Using a high-order polynomial model to fit the instantaneous frequency value obtained in step S2 , which is expressed by the following formula:

[0116]

[0117] Wherein, is the fitting curve of the instantaneous frequency after fitting, N is the order of the high-order polynomial, and {b0,b1,…,b N-1} is the coefficient of the high-order polynomial, and t is the time;

[0118] S4. The fitting curve of the instantaneous frequency obtained in step S3 is used to solve the instantaneous frequency tilt angle, and an over-complete instantaneous frequency tilt angle dictionary is constructed by the solved instantaneous frequency tilt angle; {b0, b1, …, b N-1} are the coefficients of the high-order polynomial.

[0119] S4. The fitting curve of the instantaneous frequency obtained in step S3 is used to solve the instantaneous frequency tilt angle, and an over-complete instantaneous frequency tilt angle dictionary is constructed by the solved instantaneous frequency tilt angle; {b0, b1, …, b

[0120] 1) Solving the instantaneous frequency tilt angle:

[0121] The instantaneous frequency fitting curve obtained in step S2 is The curve slope is solved, so as to obtain the change of the instantaneous frequency tilt angle of the i-th target in the time-frequency two-dimensional parameter domain, which is solved by the following formula:

[0122]

[0123]

[0124] Wherein, k(t n ) is the slope of the instantaneous frequency fitting curve, n = 1, …, L; t n is the n-th moment in the sampling time length, L is the length of the echo signal, θ(t n ) is the tilt angle of the instantaneous frequency, T x is the sampling time, F s is the sampling frequency;

[0125] 2) Constructing an over-complete instantaneous frequency tilt angle dictionary:

[0126] According to the tilt angle θ(t n ) of the instantaneous frequency solved in step 1), an over-complete instantaneous frequency tilt angle dictionary Φ (2W+1)×L is constructed by the following formula:

[0127]

[0128] Wherein, W is the expansion coefficient of the dictionary; 2W+1, L and λ are the number of atoms in the dictionary, the length of the echo signal and the instantaneous frequency tilt angle expansion factor respectively;

[0129] S5. The instantaneous frequency tilt angle dictionary constructed in step S4 is used for time-frequency analysis and processing of the echo signal obtained in step S1 to obtain the optimal parameter domain distribution; specifically including:

[0130] The instantaneous frequency tilt angle dictionary Φ (2W+1)×LThe echo signal x(t) obtained in step S1 is reprocessed by time-frequency analysis, and the optimal parameter domain distribution TFD is obtained according to an energy convergence criterion best (t,f).

[0131] The instantaneous frequency of the echo signal is equivalent to a linear function within a set time interval η, and is expressed by the following formula:

[0132] IF i (η)=IF i (t)+IF′ i (t)·(η-t),t∈η

[0133] where IF i (t) is the instantaneous frequency value at time t, and IF′ i (t) is the first derivative value of the instantaneous frequency at time t.

[0134] The mathematical model of the echo signal within the set time interval η is expressed by the following formula:

[0135] x i (η)=A i (η)exp{j2π[∫IF i (η)dτ]}

[0136] =A i (η)exp{j2π[IF i (t)η+1 / 2·IF′ i (t)(η-t) 2 ]}

[0137] The echo signal within the set time interval η is processed by windowed time-frequency transform, and is expressed by the following formula:

[0138] TFD(t,f)

[0139] =∫x i (η)·h(η-t)·exp(-j2πfη)dη

[0140] =∫A i (η)·exp{j2π[IF i (t)η+1 / 2·IF′ i (t)(η-t) 2 ]}·h(η-t)·exp(-j2πfη)dη

[0141] where TFD(t,f) is a two-dimensional parameter domain of the echo signal.

[0142] For the time-frequency point (t,f) in the above formula, if 1 / 2·IF′i (t)(η-t) 2 If the term is eliminated, the time-frequency energy will be more concentrated, and the interference will be less, so that the aliasing phenomenon is better suppressed.

[0143] An overcomplete angular dictionary Φ (2W+1)×L The dictionary atom Φ α Eliminate 1 / 2·IF' in the above formula i (t)(η-t) 2 The term, realize the concentration of echo signal time-frequency energy, using the following formula:

[0144]

[0145] Where, Φ α (α∈[1,2W+1]) is the first α atom in the overcomplete angular dictionary Φ (2W+1)×L is the optimal parameter domain distribution obtained by using the dictionary atom Φ α t is time, f is frequency, F S is the sampling frequency;

[0146] Using the angular dictionary Φ (2W+1)×L The echo signal is analyzed by time-frequency analysis to obtain 2W+1 time-frequency distribution TFD ILCT (t,f,Φ), based on the energy convergence criterion, the best energy corresponding to each time-frequency point (t,f) is obtained from the 2W+1 parameter domain distribution, and then the optimal parameter domain distribution TFD best (t,f) is obtained, which is represented by the following formula:

[0147]

[0148] S6. The signal demodulation technology is used to process the optimal parameter domain distribution obtained in step S5, and the eigenvalue classification technology is used to extract the processed signal, and the instantaneous frequency component set of the echo signal is constructed; specifically including:

[0149] ① The peak search method is used to extract the instantaneous frequency of the i-th target from the optimal parameter domain distribution TFD best (t,f) obtained in step S5, which is represented by the following formula:

[0150]

[0151] Where, is the instantaneous frequency of the i-th target;

[0152] ② The extracted instantaneous frequency ​The echo signal is classified and extracted to obtain the echo component of the ith target:

[0153] The echo signal received by the Doppler radar is a typical non-stationary signal, and the signals have low autocorrelation. The signal cannot be directly classified and extracted, and the echo signal of the ith target is converted into an autocorrelated signal by signal demodulation processing as a preprocessing before feature classification and extraction.

[0154] A. Signal demodulation processing:

[0155] The demodulation operation of the signal is represented by the following formula:

[0156]

[0157] Where x do (t) is the demodulated signal, is a demodulation factor constructed by the instantaneous frequency ;

[0158] The demodulated signal x do (t) is constructed into a two-dimensional matrix to facilitate the separation of autocorrelation signals in the echo signal. The constructed two-dimensional processing matrix is represented by the following formula:

[0159]

[0160] Where the number of rows m of the matrix E m×n satisfies the condition: m = (L+1) / 2 when L is odd, and m = L / 2+1 when L is even; the number of columns n of the matrix E m×n satisfies the following condition: n = L-m+1; E m×n is the constructed processing matrix, and x do (t) is the demodulated signal;

[0161] B. Feature classification and extraction processing:

[0162] The two-dimensional processing matrix E m×n is represented by the following formula:

[0163]

[0164] Where U m×n is the eigenvalue matrix of the signal, and the values in the matrix other than the diagonal line are all 0; P m×m and Q n×n are unitary matrices, and the vectors in the matrix are mutually orthogonal, and is the conjugate transpose of Q n×n ;

[0165] The demodulated target signal has high autocorrelation, only the first eigenvalue in the eigenvalue matrix U is reserved, and the values at other positions are set to 0 to obtain the extraction matrix of the i-th target echo m×n The following formula is used to represent

[0166]

[0167] C. Constructing the instantaneous frequency component set of the echo signal:

[0168] The extraction matrix obtained by feature extraction The inverse process of constructing a two-dimensional matrix is used, the overlapping positions in the matrix are added and the mean value is obtained to obtain the echo demodulation signal of the i-th target The constructed inverse demodulation factor is used to obtain the echo signal of the i-th target The following formula is used to represent

[0169]

[0170] The extracted echo signal of the i-th target is removed from the received target echo signal x(t), and the residual signal is returned to the echo signal obtained in step S1 and participates in the extraction of the next signal component, and the following formula is used to represent:

[0171]

[0172] Where x new (t) is the signal to be processed after removing the extracted target component. The time-frequency parameter domain and the instantaneous frequency curve obtained by processing the analog signal using the method described in the present application and the conventional method are shown in Figure 3 and Figure 4 ; wherein Figure 3 (a) is the parameter domain distribution diagram after windowed time-frequency transform processing, Figure 3 (b) and Figure 3 (c) are the parameter domain distribution diagrams after processing according to the present application; Figure 4 (a) is the signal instantaneous frequency curve extracted after windowed time-frequency transform processing, Figure 4 (b) is the signal instantaneous frequency curve extracted after processing according to the present application;

[0173] S7. Using the instantaneous frequency component set constructed in step S6, the trajectory of the moving target is synthesized, and the tracking processing of the moving target is completed; specifically including:

[0174] a. Calculate the estimated target distance and angle of arrival:

[0175] ​The Doppler through-the-wall radar is a dual-frequency continuous wave radar, the carrier frequencies transmitted by the transmitter are defined as f1 and f2, the interval between the two receivers is defined as d, the receiver 1 is used to estimate the distance change of the target, and the distance is calculated by the following formula:

[0176]

[0177] Wherein, R(t) is the distance of the target distance radar module, C is the speed of electromagnetic wave propagation in vacuum, IF 1,1 (t) and IF 2,1 (t) are the instantaneous frequencies of the echo signals received by the receiver 1 at the carrier frequencies f1 and f2;

[0178] The receiver 1 and the receiver 2 are used to estimate the angle of arrival of the target jointly, and the angle of arrival is calculated by the following formula:

[0179]

[0180] Wherein, angel(t) is the angle of arrival of the target signal, λ is the wavelength of the carrier, IF 1,2 (t) is the instantaneous frequency of the echo signals received by the receiver 2 at the carrier frequency f1;

[0181] b. Synthesizing the motion trajectory of the moving target:

[0182] According to the distance and the angle of arrival calculated in step a, the coordinates of the target motion are synthesized, and the motion trajectory is synthesized; and the following formula is used for description:

[0183] x(t) = R(t) · sin(angel(t))

[0184] y(t) = R(t) · cos(angel(t))

[0185] According to the x-axis and y-axis coordinates calculated, a line is drawn in the two-dimensional rectangular coordinate system, so as to realize the target tracking and the motion trajectory estimation. The instantaneous frequency curves and the target positioning effects obtained by processing the example data by using the method of the present application and the conventional method are shown in Figure 5 , Figure 5 (a) is the target instantaneous frequency curve estimated by the windowed time-frequency transform method, Figure 5 (b) is the target motion trajectory synthesized by the windowed time-frequency transform method, Figure 5 (c) is the target instantaneous frequency curve estimated by the method of the present application, Figure 5 (d) is the target motion trajectory synthesized by the method of the present application; and Figure 5 It can be seen that the target positioning accuracy of the method of the present application is high, and the tracking effect is better.

Claims

1. A moving target tracking method based on overcomplete angle dictionary optimization technology, comprising the following steps: S1. Acquire the echo signal of the moving target; S2. The windowed time-frequency analysis method is used to estimate the echo signal obtained in step S1 and calculate the instantaneous frequency value of the echo signal; S3. Use a high-order polynomial model to fit the instantaneous frequency values ​​obtained in step S2 to obtain the fitting curve of the instantaneous frequency; S4. Using the fitted curve of the instantaneous frequency obtained in step S3, solve for the instantaneous frequency tilt angle, and construct an overcomplete instantaneous frequency tilt angle dictionary using the obtained instantaneous frequency tilt angle; specifically including: 1) Solve for the instantaneous frequency tilt angle: The instantaneous frequency fitting curve obtained in step S2 The slope of the curve is calculated to obtain the change in the instantaneous frequency tilt angle of the i-th target in the two-dimensional time-frequency parameter domain. The following formula is used for the calculation: in, It is the slope of the instantaneous frequency fitting curve. ; For the nth time in the sampling duration, It is the length of the echo signal. It is the tilt angle of the instantaneous frequency. It is the sampling time. It is the sampling frequency; 2) Construct a complete dictionary of instantaneous frequency tilt angles: The tilt angle obtained from the instantaneous frequency in step 1) An overcomplete instantaneous frequency tilt angle dictionary is constructed using the following formula. : Where W is the dictionary expansion coefficient; 2W+1, L and These are the number of atoms in the dictionary, the length of the echo signal, and the instantaneous frequency tilt angle spread factor, respectively. S5. Using the instantaneous frequency tilt angle dictionary constructed in step S4, perform time-frequency analysis processing on the echo signal obtained in step S1 to obtain the optimal parameter domain distribution; specifically including: within a set period of time Within this framework, the instantaneous frequency of the echo signal is treated as a linear function and expressed using the following formula: in, yes The instantaneous frequency value at time 1. yes The first derivative of the instantaneous frequency at time t; Set time The echo signal within is processed using windowed time-frequency transformation; A complete angle dictionary was used. dictionary atoms Eliminating the transformed formula item; Use angle dictionary Time-frequency analysis of the echo signal yielded 2W+1 time-frequency distributions. Based on the energy convergence criterion, each time-frequency point is obtained from the 2W+1 parameter domain distribution. The corresponding optimal energy is then used to obtain the optimal parameter domain distribution. ; S6. The optimal parameter domain distribution obtained in step S5 is processed using signal demodulation technology, and the demodulated signal is extracted using eigenvalue classification technology to construct the instantaneous frequency component set of the echo signal. S7. Using the instantaneous frequency component set constructed in step S6, synthesize the trajectory of the moving target to complete the tracking process of the moving target.

2. The moving target tracking method based on overcomplete angle dictionary optimization technology according to claim 1, characterized in that... Step S1, which involves acquiring the echo signal of a moving target, specifically includes: A Doppler through-wall radar module is used to collect echo signal data of moving targets, obtaining a one-dimensional target echo signal. The target signal received by the radar receiver is then converted into a single signal. The following formula is used to express this: in, It is the signal amplitude of target i. It is the instantaneous frequency function of target i. This indicates the number of targets in the detection environment.

3. The moving target tracking method based on overcomplete angle dictionary optimization technology according to claim 2, characterized in that... Step S2 describes using a windowed time-frequency analysis method to estimate the echo signal obtained in step S1 and calculate the instantaneous frequency value of the echo signal. Specifically, this includes: (1) The windowed time-frequency analysis method is used to perform time-frequency analysis and estimation processing on the target echo signal obtained in step S1 to obtain the two-dimensional time-frequency parameter domain of the moving target. The windowed time-frequency analysis method is expressed by the following formula: in, It is the time-frequency two-dimensional parameter domain of the target signal. It's frequency. It is time. It is the received target signal. It is a window function for time-frequency analysis; (2) The peak search method is used to extract the instantaneous frequency value of the i-th target in the two-dimensional time-frequency parameter domain. The peak search method is expressed by the following formula: in, It is the instantaneous frequency value obtained from the estimation process.

4. The moving target tracking method based on overcomplete angle dictionary optimization technology according to claim 3, characterized in that... Step S3, which involves using a higher-order polynomial model to fit the instantaneous frequency values ​​obtained in step S2 to obtain a fitting curve for the instantaneous frequency, specifically includes: A higher-order polynomial model is used for the instantaneous frequency values ​​obtained in step S2. The fitting process is expressed using the following formula: in, This is the fitted instantaneous frequency curve, where N is the order of the higher-order polynomial. These are the coefficients of a higher-order polynomial. It's time.

5. The moving target tracking method based on overcomplete angle dictionary optimization technology according to claim 4, characterized in that... Step S5 involves using the instantaneous frequency tilt angle dictionary constructed in step S4 to perform time-frequency analysis processing on the echo signal obtained in step S1 to obtain the optimal parameter domain distribution, specifically including: The instantaneous frequency tilt angle dictionary described in step S4 is used. Regarding the echo signal acquired in step S1 Perform time-frequency analysis again and obtain the optimal parameter domain distribution based on the energy convergence criterion. ; within a set period of time Within this framework, the instantaneous frequency of the echo signal is treated as a linear function and expressed using the following formula: in, yes The instantaneous frequency value at time 1. yes The first derivative of the instantaneous frequency at time t; Set time The mathematical model of the echo signal within is expressed by the following formula: Set time The echo signal within is processed using windowed time-frequency transform and expressed by the following formula: in, It is the time-frequency two-dimensional parameter domain of the echo signal; A complete angle dictionary was used. dictionary atoms Eliminate the above formula The term, which enhances the time-frequency energy concentration of the echo signal, is expressed by the following formula: in, It is a complete angle dictionary The first in One atom, , It uses dictionary atoms The obtained optimization parameter domain distribution, It is time. It's frequency. It is the sampling frequency; Use angle dictionary Time-frequency analysis of the echo signal yielded 2W+1 time-frequency distributions. Based on the energy convergence criterion, each time-frequency point is obtained from the 2W+1 parameter domain distribution. The corresponding optimal energy is then used to obtain the optimal parameter domain distribution. It is expressed by the following formula: 。 6. The moving target tracking method based on overcomplete angle dictionary optimization technology according to claim 5, characterized in that... Step S6 involves using signal demodulation technology to process the optimal parameter domain distribution obtained in step S5, and using eigenvalue classification technology to extract and process the demodulated signal, constructing a set of instantaneous frequency components for the echo signal. Specifically, this includes: ① The peak search method is used to target the optimal parameter domain distribution obtained in step S5. The instantaneous frequency of the i-th target is extracted using the following formula: in, It is the instantaneous frequency of the i-th target; ②Use the extracted instantaneous frequency Feature classification and extraction processing is performed on the echo signal to obtain the echo component of the i-th target: Signal demodulation processing is used to convert the echo signal of the i-th target into an autocorrelation signal, which serves as a preprocessing step before feature classification and extraction. A. Signal demodulation processing: The demodulation process of a signal is represented by the following formula: in, It is the demodulated signal. Through instantaneous frequency The constructed demodulation factor; The demodulated signal A two-dimensional matrix is ​​constructed to facilitate the separation and processing of autocorrelation signals in the echo signal. The constructed two-dimensional matrix to be processed is represented by the following formula: Among them, matrix The number of rows m of the matrix satisfies the following conditions: when L is odd, m = (L+1) / 2; when L is even, m = L / 2 + 1. The number of rows and columns n satisfies the following condition: n = L - m + 1; It is a two-dimensional matrix to be processed. It is the demodulated signal; B. Feature classification and extraction processing: The two-dimensional matrix to be processed This can be expressed using the following formula: in, Let be the eigenvalue matrix of the signal, and all values ​​in the matrix except for the diagonal lines are 0; and All are unitary matrices, and the vectors within them are mutually orthogonal. yes The conjugate transpose of; The extraction matrix of the i-th target echo is expressed by the following formula. : C. Construct the instantaneous frequency component set of the echo signal: The extraction matrix obtained from feature extraction The inverse process of constructing a two-dimensional matrix involves summing the overlapping positions in the matrix and taking the average to obtain the echo demodulated signal of the i-th target. Using the constructed inverse demodulation factor Obtain the echo signal of the i-th target The following formula is used to express it. : The echo signal of the i-th target will be extracted. From the received target echo signal The residual signal is removed and treated as a new signal, then added back to the echo signal obtained in step S1 to participate in the next signal component extraction. This is expressed by the following formula: in, It is the signal to be processed after removing the extracted target component.

7. The moving target tracking method based on overcomplete angle dictionary optimization technology according to claim 6, characterized in that... Step S7, which uses the instantaneous frequency component set constructed in step S6 to synthesize the trajectory of the moving target and complete the tracking process of the moving target, specifically includes: a. Calculate the estimated target distance and angle of arrival: The Doppler through-wall radar is a dual-frequency continuous wave radar. The carrier frequencies transmitted by the transmitter are defined as f1 and f2, and the interval between the two receivers is d. Receiver 1 is used to estimate the target's range change, and the range is calculated using the following formula: in, It is the distance between the target and the radar module. It is the speed at which electromagnetic waves propagate in a vacuum. and It is the instantaneous frequency of the echo signal when receiver 1 receives the echo signal with carrier frequencies f1 and f2; The target's angle of arrival (AHA) is estimated using receivers 1 and 2 working together, and is calculated using the following formula: in, It is the angle of arrival of the target signal. It is the wavelength of the carrier wave. It is the instantaneous frequency of the echo signal when receiver 2 receives the echo signal with a carrier frequency of f1; b. The trajectory of the composite moving target: Based on the distance and angle of arrival calculated in step a, the coordinates of the target's motion are synthesized, and then the motion trajectory is synthesized; the following formula is used to describe it: Based on the calculated x-axis and y-axis coordinates, lines are drawn in a two-dimensional Cartesian coordinate system to achieve target tracking and motion trajectory estimation.

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