Wideband Multi-Target Translational Parameter Estimation and Compensation Method

Abstract

The present invention discloses a broadband multi-target translational parameter estimation and compensation method, belonging to the field of radar signal processing. Specifically: First, calculate the echo signals of N targets received by the radar, and based on the random Hough transform, separate and extract the corresponding trajectories of each target. Then, roughly estimate the initial positions, velocities, and accelerations of each target, and perform rough compensation. Use CLEAN to remove redundant scatterers and aliased tracks, so that each target only retains one continuous scatterer. Next, estimate the residual acceleration and residual translational velocity of the scatterer target based on the spectral characteristics, and calculate the final velocity estimate and acceleration estimate of the target. Finally, for the radar echo signal after fine compensation, based on the R-D imaging algorithm of the short-time Fourier transform, perform short-time Fourier time-frequency transformation on each row of range cells to obtain a three-dimensional Doppler-range-time matrix and obtain an R-D image slice. The present invention performs refined estimation and compensation of motion parameters in the time-frequency domain.

Description

Technical Field

[0001] The present invention belongs to the field of radar signal processing, and specifically relates to a method for estimating and compensating translational parameters of broadband multi-targets. Background Art

[0002] The modulation characteristics of different micro-motions of space targets on radar echoes are not the same, which will cause serious envelope migration of the scattering points of the target echoes. This migration is reflected in the echo delay and micro-Doppler characteristics, and is an important basis for space target feature recognition and imaging.

[0003] Therefore, the work based on micro-motion characteristics has important research value. However, most of the current research is based on the assumption that the translational components of the targets have been accurately compensated. In practice, high-speed moving space targets will produce complex modulation effects on radar echoes, including in-pulse broadening and inter-pulse walking.

[0004] When the radar detects space targets, there are often multiple targets within the same range gate, and the distances between them are relatively small, making it difficult to distinguish them in the range dimension. The multi-targets within the range gate fly by relying on their initial velocities, and under the action of aerodynamic force and earth's gravity, their force states are similar, resulting in similar motion states, and it is also difficult to distinguish them in the Doppler dimension. Conventional multi-target detection algorithms are only applicable to multi-steady targets and are difficult to apply to this scenario. Summary of the Invention

[0005] Aiming at the coupling and mutual interference problems in the separation of multi-target signals with complex motions, the present invention proposes a method for estimating and compensating translational parameters of broadband multi-targets. Based on the separation in the image domain and using the micro-motion information of the targets, the motion parameters are refinedly estimated and compensated in the time-frequency domain.

[0006] The specific steps are as follows:

[0007] Step 1: For the scenario where N targets are within the same range gate during radar space detection, calculate the echo signal received by the radar;

[0008] The calculation formula for the echo signal is:

[0009]

[0010] Wherein, is the fast time, t m is the slow time, t is the total time, f c is the carrier frequency, κ is the frequency modulation slope, A ij is the scattering intensity of the j-th scattering point on the i-th target, S i is the number of scattering points of the i-th target, T p is the pulse duration, and c is the speed of light. is the radial distance of the j-th scattering point on the i-th target relative to the radar, where Ri (t m ) is the radial distance from the radar site to the origin of the reference coordinate system corresponding to the i-th target, and its change is regarded as translational motion. R ij (t m ) is the distance from the j-th scatterer in the target to the coordinate origin, and its change is regarded as micro-motion; v represents the velocity.

[0011] Step 2: The echo signal of each target corresponds to a trajectory in the one-dimensional range profile. Based on region division and random Hough transform, the corresponding trajectories of each target are separated and extracted.

[0012] The specific steps are as follows:

[0013] ① Perform CFAR on the one-dimensional range profile sequences of each target, extract the target trajectories, and obtain a binary image;

[0014] ② Establish a Cartesian coordinate system (x, y) in the one-dimensional range profile sequence space, and evenly divide the coordinates of x and y into several time blocks;

[0015] ③ Perform classical random Hough transform in each small time block to extract straight lines, and map the results to the ρ-θ space;

[0016] ④ Perform threshold detection on the ρ-θ space to obtain the straight line expression of the original one-dimensional range profile sequence. Construct a corresponding mask according to the straight line expression and the sidelobe width of the echo signal, and separate the target signals from the one-dimensional image sequence.

[0017] Step 3: Use the least squares method to roughly estimate the initial position R, velocity and acceleration of each target respectively, and then perform rough compensation.

[0018] The compensation method is as follows.

[0019]

[0020] Among them, f r represents the sampling frequency point, f d represents the Doppler frequency, FFT(·) represents the Fourier transform, IFFT(·) represents the inverse Fourier transform, is the original echo signal.

[0021] Step 4: Use CLEAN to remove the redundant scatterers and aliased trajectories in the one-dimensional range profile sequence after rough compensation, so that each target only retains one continuous scatterer.

[0022] The CLEAN method is specifically as follows:

[0023] ① Perform one-dimensional CFAR on the one-dimensional range profile sequence of the target after rough compensation;

[0024] ②Perform envelope detection on the obtained result to obtain the range cell and time cell of the target's redundant scattering point;

[0025] ③First, obtain the straight-line equation of the aliased track through Hough transform, and then construct a mask with a width of only five range cells to select the aliased track;

[0026] ④Extract the amplitude A1 and phase of the peak within one slow time for the specific scattering point and the aliased track delay t1;

[0027] ⑤Inverse the target echo: And subtract it from the original one-dimensional image sequence;

[0028] ⑥Perform the same operation for each slow time until the specific scattering point and the aliased track are both eliminated by the CLEAN algorithm.

[0029] Step Five: Estimate the residual acceleration of each target with only one continuous scattering point remaining based on the spectral characteristics;

[0030] The steps are as follows:

[0031] ①Predict the magnitude of the residual acceleration according to the micro-momentum level prior, and evenly divide it to obtain the acceleration compensation sequence a com ;

[0032] ②Perform time-domain compensation on the coarsely compensated signal and transform it to the frequency domain to find its spectral peak:

[0033]

[0034] ③Then find the maximum value in the spectral peak vector, and the corresponding acceleration compensation value is the target residual acceleration:

[0035]

[0036] Step Six: Use the sliding window MUSIC to accurately estimate the instantaneous frequency, and estimate the residual translational velocity of each target with only one continuous scattering point remaining according to the spectral characteristics;

[0037] The algorithm steps are as follows:

[0038] ①Given the window length W, select an appropriate window function, truncate and window the signal;

[0039] ②Use the data to construct the autocorrelation matrix R x ;

[0040] ③For the autocorrelation matrix R xPerform eigen - decomposition, and sort the obtained eigenvalues λ and eigenvectors Q; the maximum value λ0 of the eigenvalue λ and the corresponding Q0 in Q span the signal subspace, and the remaining vectors in Q span the noise subspace Q N ;

[0041] ④ To measure the instantaneous normalized angular frequency of the signal, given the vector v(f) = exp(2πjft m ) in the Doppler dimension, thus constructing the spectral estimation formula: Search for the instantaneous frequency f within this time window s ;

[0042] ⑤ Slide the time window, and repeat steps ② to ⑤ until the search in the Doppler dimension is completed;

[0043] After refined processing, the instantaneous frequency of the scattering points of the target is obtained, thereby estimating its translational amount Δf, and thus obtaining the estimated value of the residual translational velocity:

[0044] Δv = Δf×f s / 2π

[0045] Step Seven: Use the residual acceleration and residual translational velocity of each target to calculate the final velocity estimate and acceleration estimate of this target;

[0046] The velocity estimation formula is:

[0047]

[0048] where is the roughly estimated velocity;

[0049] The acceleration estimation formula is:

[0050]

[0051] where is the roughly estimated acceleration.

[0052] Step Eight: For the radar echo signal after fine compensation, based on the R - D imaging algorithm of short - time Fourier transform, perform short - time Fourier time - frequency transform on each row of range cells to obtain a three - dimensional Doppler - range - time matrix, and each time slice of Doppler - range is the R - D image slice.

[0053] The advantages of the present invention are as follows:

[0054] 1). The broadband multi - target translational parameter estimation and compensation method. Compared with traditional parameter estimation, the present invention makes fuller use of the micro - motion characteristics of the target, and performs more accurate and appropriate parameter estimation and motion compensation on the target echo.

[0055] 2) Wideband multi-target translational parameter estimation and compensation method. For the case where multiple targets are within the same range gate and the distance between them is small, it is difficult for traditional methods to separate targets in both the range dimension and the Doppler dimension. The present invention avoids the coupling and mutual interference during the separation of complex signal models, and uses time-frequency domain refinement processing to suppress the track aliasing problem in the image domain separation itself. Brief Description of the Drawings

[0056] Figure 1 It is the overall flowchart of the wideband multi-target translational parameter estimation and compensation method of the present invention;

[0057] Figure 2 It is the flowchart of the R-D imaging algorithm based on the short-time Fourier transform of the present invention; Detailed Embodiment

[0058] The present invention will be further described in detail below in conjunction with the drawings and embodiments.

[0059] The wideband multi-target translational parameter estimation and compensation method of the present invention studies how to perform accurate and appropriate parameter estimation and motion compensation on multi-target echo signals based on image domain separation in the time-frequency domain; by adopting image domain separation, the coupling and mutual interference during the separation of complex signal models are avoided, and time-frequency domain refinement processing is used to suppress the track aliasing problem in the image domain separation itself.

[0060] The present invention studies the parameter estimation of wideband radar based on space targets and the method of time-frequency analysis. First, aiming at the non-stationary motion characteristics of space cone targets, the influence of translational velocity on radial distance is much greater than that of acceleration and micro-motion on radial distance within a certain observation time, and the characteristics of large computational complexity and non-real-time of traditional image detection algorithms; by extracting straight trajectories based on regional random Hough, constructing masks according to signal sidelobes and target non-stationary characteristics, and extracting target trajectories by low-order fitting. Secondly, extract the distance information of each slow time of the target, perform rough compensation on the translational parameters by least squares, and use the CLEAN algorithm for accurate estimation and elimination aiming at the sidelobe mutual interference between target scatterers and the influence of overlapping tracks on the micro-motion phase, so as to obtain a one-dimensional range image of a space cone target containing only one scatterer and this scatterer contains only residual translational and micro-motion information. Finally, perform fine compensation on the residual translation. First, estimate the residual acceleration of the target using the peak method according to the influence of micro-Doppler, residual translational velocity, and residual translational acceleration on the signal spectrum to make the micro-Doppler curve unbiased; then use the sliding window MUSIC to accurately cut the noise subspace and the signal-noise subspace to achieve high-precision estimation of the target instantaneous frequency robust to noise, and then obtain the time-frequency domain translation amount of the time-frequency curve to estimate the residual velocity of the target. Finally, the separation, coherent compensation, and R-D imaging of multiple non-stationary targets in space by wideband radar are realized.

[0061] The broadband multi-target translational parameter estimation and compensation method is as follows Figure 1 As shown in Figure 1 , first, use the region-division-based random Hough transform on the target one-dimensional image sequence to implement line detection, then perform low-order fitting, and construct a mask based on the fitting result for image domain separation. Perform least squares rough estimation and compensation on the separated result to obtain the coarsely compensated target one-dimensional image sequence. To simplify subsequent micro-motion information extraction and reduce the computational load, CLEAN is performed on the redundant scatter points and aliased tracks to reduce the coupling of sidelobes and aliased tracks and complete the rough compensation. After rough compensation, its motion information includes micro-motion, residual velocity, and residual acceleration. Based on the frequency domain characteristics of the signal, the precise estimation of the residual acceleration is achieved through the peak method, and then based on the TVAR model, the precise estimation result of the residual velocity is obtained by solving the instantaneous frequency. Finally, the instantaneous R-D imaging based on the short-time Fourier transform is performed.

[0062] The specific steps are as follows:

[0063] Step 1: For the scenario where N targets are within the same gate during radar space detection, calculate the echo signal received by the radar;

[0064] The transmitted signal of the broadband radar is:

[0065]

[0066] where is the fast time, t m is the slow time, T p is the pulse duration, f c is the carrier frequency, t is the total time, and κ is the frequency modulation slope;

[0067] The echo signal calculation formula is:

[0068]

[0069] where A ij is the scattering intensity of the j-th scatter point on the i-th target, S i is the number of scatter points of the i-th target, c is the speed of light, is the radial distance of the j-th scatter point on the i-th target relative to the radar, where R i (t m ) is the radial distance from the radar station location to the origin of the reference coordinate system corresponding to the i-th target, and its change is regarded as translational motion. R ij (t m ) is the distance from the j-th scatter point in this target to the coordinate origin, and its change is regarded as micro-motion. v represents velocity.

[0070] After the radar echo is matched and filtered, is expressed as:

[0071]

[0072] where f di = 2v i / λ represents the Doppler frequency shift corresponding to the i-th target, v i represents the velocity of the i-th target, λ is the signal wavelength, and α i = 1 - 2v i / c represents the time dilation factor, A ij represents the scattering intensity of the j-th scatterer on the i-th target after modulation, B represents the bandwidth, corresponds to the Sa function, and most processing results of microwave radar are the Sa function; the reason is that radar signal processing can only truncate the signal for finite-length processing, which is equivalent to adding a rectangular window to the signal, and its processing result corresponds to the frequency-domain envelope of the rectangular window, that is, the Sa function. The main lobe of this function is relatively narrow, but the sidelobes are very high, and a large amount of spectral energy leaks to the sidelobes, affecting target resolution and subsequent signal processing, and appropriate windowing needs to be added for suppression.

[0073] It can be seen from the processing results that: since the motion of the target includes acceleration and strong micro-motion, the echo signal is a non-stationary signal. At the same time, high-speed moving targets will have a great impact on the phase, pulse width, etc. of the echo. General target compensation methods such as envelope minimum entropy and special point method, although they can ultimately achieve compensation for non-stationary targets, generally have poor effects. Especially for coherent radar systems, the accuracy of polynomial-form coherent compensation is better than non-coherent compensation, and it also has less influence on the phase change caused by target micro-motion, which has important research value.

[0074] Step 2: The echo signal of each target corresponds to a trajectory in the one-dimensional range image. Based on region division and random Hough transform, the corresponding trajectories of each target are separated and extracted.

[0075] An image domain separation method is adopted. At the cost of a certain degree of aliasing, low-order fitting is performed in the image domain to construct a mask to separate the one-dimensional image sequence of the target. The Hough transform is a commonly used method for image domain fitting, but its computational complexity is huge and its value is relatively low. Therefore, we need to explore an improved Hough transform with lower computational complexity.

[0076] The Hough transform is an algorithm for straight line detection in an image through a "one-to-many" voting strategy. It essentially describes the corresponding relationship in two parameter spaces by defining the relationship between points in the image space and curves in the parameter space, so that problems that are difficult to solve in the image space can be well solved in the parameter space.

[0077] In a given x-y coordinate system, the expression of a straight line can be represented as,

[0078] y = k·x + b

[0079] Among them, x is the x-axis coordinate in the Cartesian coordinate system, y is the y-axis coordinate, k is the slope of the straight line, b is the y-intercept of the straight line. This equation can also be written as

[0080] b = -x·a + y

[0081] The above equation can be regarded as the straight line equation in the Cartesian coordinate system. According to the transformation relationship between the ρ-θ space and the Cartesian coordinate system,

[0082] x = ρcosθ

[0083] y = ρsinθ

[0084] Among them, ρ is the shortest distance from the origin to the straight line, θ is the angle between this straight line and the x-axis. Substituting these into the equation, we can get

[0085] ρ = xcosθ + ysinθ

[0086] The steps of the Hough algorithm are as follows.

[0087] ① First, detect the feature points of the image and extract the corresponding binary image of the feature points;

[0088] ② According to the preset intervals of ρ and θ, perform parameter conversion on each feature point, and add one to the pixel value corresponding to the conversion result;

[0089] ③ Detect the image in the ρ-θ space according to the preset threshold, and the points exceeding the threshold are considered to correspond to a straight line in the original image.

[0090] The main task of the Hough transform is to map the y-intercept and slope of the straight line to the ρ-θ space, and transform the detection of the straight line into the detection of peaks through a voting strategy.

[0091] However, this method has a large defect. Its mapping idea is "one-to-many", and each feature point needs to perform a large number of mapping operations, resulting in a large computational complexity of the algorithm. In view of this deficiency, Xu Lei et al. proposed the Randomized Hough Transform. This algorithm replaces the "one-to-many" mapping idea with a "many-to-one" mapping, greatly reducing the time complexity of the algorithm.

[0092] The basic idea of the classical Randomized Hough Transform is to determine the mapping relationship based on the geometric features of the image, and its basic measurement method is still the voting mechanism. Geometric features refer to the relationship between the feature point coordinates and the curve equation to be extracted. For example, two points can determine a straight line, so when extracting a straight line, randomly select two feature points to determine a straight line; three points can determine a circle, so when extracting a circle, randomly select three non-collinear feature points to determine the parameters of a circle.

[0093] The algorithm steps for extracting the straight line are as follows.

[0094] ① Extract feature points from the original image and randomly select two feature points;

[0095] ② Determine the unique straight line according to the coordinates (x1, x2), (y1, y2) of the two points: Convert to ρ-θ space: ρ = x1 cosθ + y1 sinθ;

[0096] ③ Increment by one at the corresponding ρ, θ coordinates and stop after a certain number of operations;

[0097] ④ Detect the ρ, θ space according to the preset threshold, and the points greater than the threshold are considered to correspond to a straight line in the original image.

[0098] Compared with the classical Hough, the computational complexity of the classical stochastic Hough is much lower, effectively improving the computational speed and space utilization rate of the algorithm. However, in fact, there are still a large number of redundant and meaningless random operations in the classical stochastic Hough. Their computational complexities are directly related to the number of feature points extracted. If the feature points cannot be pre-screened, the algorithm will waste a large amount of computing power on useless operations.

[0099] The HRRPs of multiple targets are often separable or partially overlapping. The trajectories of high-speed targets in space within a certain observation time can generally be fitted by a high-order polynomial. When the observation time window is short, the fitting effect of the second-order polynomial is sufficient. However, the parameter space corresponding to the Hough transform for the second-order fitting is three-dimensional, and the computational complexity is large. Secondly, high-precision estimation of target parameters is not required to separate target trajectories in the image domain. Therefore, to address the problem of cross-overlapping of multiple target trajectories, this paper adopts low-order fitting, that is, performs straight line detection on the binary image obtained by CFAR, and then constructs a rectangular mask according to the estimation results to separate the range images of targets one by one.

[0100] Therefore, this paper uses the region-division-based stochastic Hough transform for multiple targets, and the specific steps are as follows:

[0101] ⑤ Perform CFAR on the one-dimensional range image sequences of each target, extract the target trajectories, and obtain a binary image;

[0102] ⑥ Establish a Cartesian coordinate system (x, y) in the one-dimensional range image sequence space and evenly divide the coordinates of x and y into several time blocks;

[0103] Because what is processed here is the radar received signal, and its horizontal and vertical coordinates, namely the fast time dimension and the slow time dimension, are not balanced, so the number of time blocks for region division should be much larger in the fast time dimension;

[0104] ⑦Perform classical random Hough transform within each hour block to extract straight lines, and map the results to the ρ-θ space;

[0105] ⑧Perform threshold detection on the ρ-θ space to obtain the straight line expressions of the original one-dimensional range image sequence. Construct corresponding masks according to the straight line expressions and the sidelobe widths of the echo signals, and separate the target signals from the one-dimensional image sequence.

[0106] Points exceeding the threshold are considered to correspond to a straight line in the original image.

[0107] In practice, the one-dimensional range image sequences obtained often have target trajectory intersections. At this time, if edge detection algorithms such as Canny are used for trajectory extraction, the target trajectories are often broken. However, constructing masks by polynomial fitting to extract target trajectories will not cause trajectory breaks, but there will be some signal aliasing.

[0108] Step 3: Use the least squares method for the corresponding trajectories of each target to roughly estimate the initial positions R and velocities and accelerations Then perform rough compensation.

[0109] Obtain the distance information R corresponding to each chirp of the target through one-dimensional CFAR based on the target trajectory obtained in Step 1 w (t m ). The size of space targets is on the order of 1m - 2m, and the amplitude of their micro-motions should also be on this order. The velocities of space targets are mostly on the order of several kilometers per second. Therefore, the trajectory information R w (t m ) is mainly translational.

[0110] Assume that within a certain observation time T o the radar receives M echoes. Then the target distance information of all echoes can be expressed as,

[0111] R = [R w (t1)…R w (t M )] T

[0112] The Gaussian noise corresponding to each echo is,

[0113] e = [e1…e M )] T

[0114] The parameters to be estimated are,

[0115] P = [0.5a0, v0, R0] T / α

[0116] Where, a0 is the rough acceleration estimate value, v0 is the rough velocity estimate value, and R0 is the rough initial distance estimate value.

[0117] The corresponding time series is

[0118]

[0119] T = [T1…T M T

[0120] Then, according to the physical meaning, we have

[0121] R = TP + e

[0122] Among them, the cost function of the parameter P to be estimated under the least squares criterion is

[0123] Then we have

[0124]

[0125] Among them, inv(·) is to find the inverse of the matrix.

[0126] Generally, the measurement accuracies of velocity and distance in the obtained target one-dimensional image sequence are the 3dB width of the spectrum, that is, the Rayleigh resolution, which is determined by the specific parameters of the radar. The radar range resolution formula is The time of M pulses, that is, the observation time, is Then the maximum error of velocity is

[0127]

[0128] It can be seen that the more pulses participating in the operation, the higher the accuracy of the least squares method. However, due to the severe micro-motion of the space target, the final rough estimation errors of velocity and acceleration will be greater than the theoretical values.

[0129] The compensation method is as follows

[0130]

[0131] Among them, f r represents the sampling frequency point, f d represents the Doppler frequency, FFT(·) represents the Fourier transform, and IFFT(·) represents the inverse Fourier transform. is the roughly estimated velocity;

[0132] The remaining translational motion can be expressed as

[0133]

[0134] The residual translational motion phase is​

[0135]

[0136] Step 4: Use CLEAN to remove the redundant scatter points and aliased tracks in the one-dimensional range profile sequence after coarse compensation, so that each target only retains one continuous scatter point.

[0137] The target trajectory after coarse compensation is close to a straight line. The residual translational motion and micro-motion jointly determine the range and phase of the target's one-dimensional image. At this time, the residual translational motion and micro-motion interfere with each other, affecting the accurate estimation of each other. Starting from the characteristics of micro-motion and time-frequency curves, the present invention estimates and compensates the residual translational motion parameters with relatively high accuracy.

[0138] The micro-Doppler time-frequency curve without any translational component should be a periodic signal symmetric about the time axis. Therefore, the micro-motion scatter points extracted above do not need to distinguish their specific positions. The micro-motion periods at the cone top and cone bottom are the same, the amplitudes are different, and the residual translational motions are the same. So, there is no need to distinguish the positions of the scatter points on the cone.

[0139] For the signal after coarse compensation and CLEAN, extract the signals at each slow time point in a range cell. Since the compensation method is coherent compensation, the frequency of this row of signals can be extracted to solve the instantaneous frequency time-frequency curve of the target.

[0140] First, take the derivative of the residual phase formula and substitute the micro-Doppler expression of conical precession to obtain

[0141] f(t m ) = 2 / λ(Δv + Δat m + sinαsinθl p (t m )ω c cos(ω c t m ))

[0142] It can be seen that at this time, the influence of the residual velocity in the residual translational motion on the time-frequency curve is to shift the time-frequency curve up or down; the influence of the residual acceleration on the time-frequency curve is to make the time-frequency curve have a certain skew.

[0143] For the original signal, the spectrum without translational motion and micro-motion should be a single-frequency signal with concentrated energy. The influence of the residual velocity on the original signal is to shift the spectrum; the influence of the residual acceleration is to change the signal from a single frequency to a band frequency and disperse the energy.

[0144] In summary, the translational velocity can be better estimated from the time-frequency domain processing of micro-motion, and the residual acceleration can be better estimated from the frequency domain of the original signal. This estimation method of the residual acceleration Δa is called the peak method, and its steps are as follows.

[0145] ①Predict the magnitude of the residual acceleration a priori according to the micro-momentum level. In this paper, the range of the residual acceleration is taken as [-4m / s 2 ~4m / s 2 , and the acceleration compensation sequence a com ; is obtained by uniform division.

[0146] ②Perform time-domain compensation on the signal after coarse compensation , transform it to the frequency domain, and find its spectral peak:

[0147] ③Then find the maximum value in the spectral peak vector, and the corresponding acceleration compensation value is the target residual acceleration:

[0148] Then this paper needs to estimate the residual translational velocity Δv. First, it is necessary to plot the time-frequency diagram of the target to obtain the micro-Doppler of the target. The time-frequency resolution of STFT and CWD is relatively low, which is difficult to meet the requirements of high-precision translational compensation. Although the bilinear time-frequency transform avoids windowing and truncating the original signal, its time-frequency resolution ability is significantly better than that of the linear time-frequency analysis method. However, because it uses signal convolution operations, it is more sensitive to the cross-interference between multi-frequency component signals and will introduce "false signals", resulting in more serious interference terms for multi-component signals.

[0149] Therefore, a TVAR is adopted here to analyze the micro-motion. TVAR is a more generalized autoregressive model. Different from the traditional autoregressive model, the coefficients of the TVAR model are time-varying, so it has better analysis ability for non-stationary random signals. In addition. The TVAR model is generally used in the fields of finance and economy to analyze data changes, and now it is also often used to analyze the instantaneous frequency of non-stationary signals. For the determination of its time-varying coefficients, it is generally represented by the sum of a group of basis functions with linear weights, so as to realize the transformation from the non-stationary time-varying problem to the stationary linear time-invariant problem.

[0150] The difference equation of the TVAR model is as follows,

[0151]

[0152] where x(n) is the non-stationary time series at time n, n = 1, 2, 3,..., N, w(n) is Gaussian white noise, and a k (n) is the time-varying coefficient of the k-th order, and p is the model order. The time-varying autoregressive model is to use the time-varying linear combination of the past p samples of the sequence to fit and predict the sequence value at the current moment.

[0153] When the signal is a non-stationary signal, the instantaneous frequency changes with time, so time-varying coefficients are needed to describe this change. Generally, there are two methods to determine the time-varying coefficients: the adaptive method iteratively calculates the time-varying coefficients and the basis function method calculates the time-varying coefficients according to certain criteria.

[0154] The dynamic model of the adaptive method is as follows,

[0155]

[0156] The adaptive method is only suitable for the case where the signal frequency changes slowly. When the signal changes violently, it will be difficult for this method to track the time-varying coefficients. The consequence in practical applications is that the algorithm diverges when the signal frequency changes rapidly and cannot converge to the true value. In addition, this method is sensitive to noise.

[0157] In the method of solving time-varying coefficients with basis functions, the commonly used basis functions are: Legendre basis functions, Walsh basis functions, DCT basis functions, and Fourier basis functions. This method regards the time-varying coefficients as a linear combination of basis functions,

[0158]

[0159] where, g j (n) is the basis function, a ij is the transformed time-invariant coefficient, and M0 is the dimension of the basis function.

[0160] Substituting Equation (4.20) into the difference equation of the TVAR model, we can get,

[0161] Y N =X N Φ N +E N

[0162] where, the signal sequence is,

[0163] Y N =[x(p + 1), x(p + 2), …, x(N)] T

[0164] The time-invariant coefficient sequence is,

[0165] Φ N =[a 10 …a 1m , a 20 …a 2m …a p0 …a pm T

[0166] The Gaussian white noise sequence is,

[0167] E N ​=[e(p + 1), e(p + 2)…e(N)] T

[0168] The matrix composed of the signal sequence and the basis function sequence is

[0169]

[0170] The methods for estimating time-varying coefficients in the TVAR model include the least squares method, the mean square estimation method, etc. In this invention, the least squares method is used with Fourier basis functions as an example for the simulation of the target instantaneous frequency.

[0171] The formula for the Fourier basis function is

[0172] g n (k) = exp[-j2πnk / N]

[0173] g n The physical meaning of g(k) is to calculate the 2πn / N sine and cosine components in the signal at a sampling frequency of 2πk / N over 0 to 2π.

[0174] The model residuals of the least squares method are recorded as follows

[0175] E N = Y N - X N Φ N

[0176] The idea of the least squares method is to minimize the sum of the squares of the residuals under the least squares criterion, and its cost function is

[0177]

[0178] Therefore, the least squares estimate of the model time-varying coefficients is

[0179]

[0180] After estimating the time-varying coefficients of the TVAR model, the following complex polynomial equation can be constructed

[0181] z p + a1(n)z p-1 + a2(n)z p-2 +…+ a p = 0

[0182] where z = e -jω The physical meaning is the normalized instantaneous frequency of the signal at this moment.

[0183] After solving the polynomial, the z values of each component can be obtained, and its true instantaneous frequency can be calculated by the following formula

[0184] fk (n) = angle (z k (n))×f s / 2π

[0185] f k (n) is the instantaneous frequency of the k-th order component, f s is the sampling rate of the signal. It is worth mentioning that f s It is not the fast time sampling rate of an echo, because the signal processed is a signal of multiple chirps on a distance unit, so the corresponding sampling rate should be the pulse repetition frequency of the radar.

[0186] In the space target scenario, the target is tens or hundreds of kilometers away from the radar station, and the signal-to-noise ratio of the processed signal is relatively low. In particular, the micro-motion extracted by the broadband radar has a cross-range unit phenomenon, and the target signal in some time series is not the main lobe of the signal, but the side lobe of the signal, and the signal-to-noise ratio is relatively low. In addition, the energy concentration effect of micro-Doppler is poor at some time points when the frequency changes drastically, and the overall processing effect is not ideal. Therefore, it is necessary to find an instantaneous frequency estimation algorithm with good noise reduction performance.

[0187] The results obtained from the above steps include micromotion and residual translation. The magnitude of residual translation and micromotion are comparable. However, since most of the processing results of microwave radar are Sa functions, their side lobes are very high, which has a greater interference on the adjacent distance units, especially on the phase of the target. Although there is only one target, the spatial target is an extended target, and the spectrum leakage of adjacent scattering points is more serious, which has a greater impact on the extraction of micromotion. The translation of different scattering points is the same, so the translation compensation can be completed by processing a single scattering point. Therefore, the compensated one-dimensional image sequence is CLEANed to remove redundant scattering points, and only one continuous scattering point is retained for each target.

[0188] In addition, the radial distances between multiple targets are relatively close, and they are often indistinguishable in the distance dimension. Moreover, there will be cross-overlapping of target tracks within a coherent accumulation time. This overlap will affect subsequent signal processing, especially micro-motion extraction, which will directly affect the phase of the micro-motion signal, thereby affecting the refined processing of the signal and reducing the processing accuracy of the algorithm. Therefore, it is necessary to further remove the cross-aliasing of the multi-target tracks. The present invention also uses the CLEAN algorithm to process the aliased part to reduce its impact on micro-motion extraction. Because the scattering points of the same target are flattened after coarse compensation, they are mainly concentrated in several to a dozen distance units. The aliased signals of other targets will exist in the one-dimensional distance image sequence with the target in the form of a high slope, uncompensated, and nearly straight line. Therefore, Hough transform straight line detection is first performed on it, the target straight line equation is extracted, and then a mask with a very narrow width is constructed to perform a CLEAN operation on the aliased track.

[0189] The CLEAN method itself is just a principle that can be flexibly changed according to the usage requirements and does not have strict algorithmic steps. It is mainly used for noise reduction, sidelobe reduction, and weak target detection, and is widely applied in the fields of computer vision and microwave radar.

[0190] The specific steps of the CLEAN method are as follows:

[0191] 1. Perform one-dimensional CFAR on the one-dimensional range image sequence of the target after coarse compensation;

[0192] 2. Perform envelope detection on the obtained result to obtain the range cells and time cells of the redundant scatterers of the target;

[0193] 3. First, obtain the straight-line equation of the aliased track through Hough transform, and then construct a mask with a width of only five range cells to select the aliased track;

[0194] 4. Extract the amplitude A1 and phase delay t1 of the peak value within one slow time for the specific scatterer and the aliased track;

[0195] 5. Invert the target echo: And subtract it from the original one-dimensional image sequence;

[0196] 6. Perform the same operation for each slow time until the specific scatterer and the aliased track are both eliminated by the CLEAN algorithm.

[0197] After CLEAN, the sidelobe energy leaked by the redundant scatterers is effectively suppressed, and the aliased tracks are effectively cleared, removing obstacles for micro-motion extraction and subsequent further refinement processing.

[0198] Step Five: Estimate the residual acceleration of each target with only one continuous scatterer retained based on spectral characteristics;

[0199] First, take the derivative of the residual phase formula and substitute the conical precession micro-Doppler expression to obtain

[0200] f(t m ) = 2 / λ(Δv + Δat m + sinαsinθl p (t m )ω c cos(ω c t m ))

[0201] It can be seen that at this time, the influence of the residual velocity in the residual translation on the time-frequency curve is to shift the time-frequency curve up or down; the influence of the residual acceleration on the time-frequency curve is to cause a certain skew of the time-frequency curve.

[0202] For the original signal, the spectrum without translational and micro - motion should be a single - frequency signal with concentrated energy. The influence of the residual velocity on the original signal is to shift the spectrum; the influence of the residual acceleration is to change the signal from a single - frequency to a band - frequency signal, with energy dispersion.

[0203] In summary, the translational velocity can be estimated well from the time - frequency domain processing of micro - motion, and the residual acceleration can be estimated well from the frequency domain of the original signal. This method for estimating the residual acceleration Δa is called the peak method, and its steps are as follows.

[0204] The steps are as follows:

[0205] ④ Predict the magnitude of the residual acceleration according to the prior of the micro - motion level. In this embodiment, the range of the residual acceleration is selected as [-4m / s 2 ~4m / s 2 , and it is evenly divided to obtain the acceleration compensation sequence a com ;

[0206] ⑤ Perform time - domain compensation on the roughly compensated signal and transform it to the frequency domain, and find its spectral peak:

[0207]

[0208] ⑥ Then find the maximum value in the spectral peak vector, and the corresponding acceleration compensation value is the target residual acceleration:

[0209]

[0210] Step 6: Use the sliding - window MUSIC to accurately estimate the instantaneous frequency, and estimate the residual translational velocity of each target with only one continuous scattering point according to the spectral characteristics;

[0211] The present invention uses a sliding - window MUSIC method to denoise the micro - Doppler signal of the one - dimensional range profile sequence of the target scattering point. MUSIC decomposes the covariance matrix, cuts the signal subspace and the noise subspace, and then constructs a spectral estimation function to perform spectral peak search in the azimuth direction for parameter estimation. The basis for MUSIC to cut the signal - noise subspace and the noise subspace is that the correlation between the signal and the noise is very weak, the direction vectors of the signal in space are highly correlated, but the direction vectors of the signal and the noise are nearly orthogonal. By using this orthogonality to construct the spectral estimation function, the cutting of the noise and the signal can be realized, and the noise can be taken out almost completely, which is very robust to noise.

[0212] The algorithm steps are as follows:

[0213] 1. Given the window length W, select a suitable window function, truncate and window the signal;

[0214] 2. Use the data to construct the autocovariance matrix R x ;

[0215] 3. Perform eigen - decomposition on the autocovariance matrix R x and sort the obtained eigenvalues λ and eigenvectors Q; the maximum value λ0 of the eigenvalues λ is the signal subspace spanned by the corresponding Q0 in Q, and the remaining vectors in Q span the noise subspace Q N ;

[0216] 4. To measure the instantaneous normalized angular frequency of the signal, given the vector v(f) = exp(2πjft m ) in the Doppler dimension, thus constructing the spectral estimation formula: Search for the instantaneous frequency f within this time window s ;

[0217] 5. Slide the time window and repeat steps ② to ⑤ until the search in the Doppler dimension is completed;

[0218] After fine - processing, obtain the instantaneous frequency of the scattering points of the target, thereby estimating its translational amount Δf, and thus obtaining the estimated value of the residual translational velocity:

[0219] Δv = Δf × f s / 2π

[0220] Step Seven: Use the residual acceleration and residual translational velocity of each target to calculate the final velocity estimate and acceleration estimate of the target;

[0221] The velocity estimation formula is:

[0222]

[0223] where is the roughly estimated velocity;

[0224] The acceleration estimation formula is:

[0225]

[0226] where is the roughly estimated acceleration.

[0227] Step Eight: For the radar echo signal after fine - compensation, based on the range - Doppler (R - D) imaging algorithm using short - time Fourier transform, perform short - time Fourier time - frequency transform on each row of range cells to obtain a three - dimensional Doppler - range - time matrix, and each time slice of Doppler - range is the R - D image slice.

[0228] The flowchart of the R - D imaging algorithm based on short - time Fourier transform is as shown in Figure 2As shown, for the received radar echo, after fine compensation, only the micro-motion and a very low-level translational motion remain in the signal, which can be considered to not contain translational motion. At this time, two-dimensional R-D imaging of the signal matrix will be defocused due to the micro-motion of the target. Therefore, an R-D imaging algorithm based on the short-time Fourier transform is used to perform short-time Fourier time-frequency transformation on each row of range cells to obtain a three-dimensional Doppler-range-time matrix. Then, any one of the Doppler-range time slices is the R-D image slice.

Claims

1. A broadband multi-target translational parameter estimation and compensation method, characterized in that, The specific steps are as follows: Step 1: For the scenario where N targets are within the same range gate during radar space detection, calculate the echo signal received by the radar; The echo signal calculation formula is: Among them, is the fast time, t m is the slow time, t is the total time, f c is the carrier frequency, κ is the frequency modulation slope, A ij is the scattering intensity of the j-th scattering point on the i-th target, S i is the number of scattering points of the i-th target, T p is the pulse duration, c is the speed of light; is the radial distance of the j-th scattering point on the i-th target relative to the radar, where R i (t m ) is the radial distance from the radar site to the origin of the reference coordinate system corresponding to the i-th target, and its change is regarded as translational motion, R ij (t m ) is the distance from the j-th scattering point in this target to the coordinate origin, and its change is regarded as micro-motion; v represents the velocity; Step 2: The echo signal of each target corresponds to a trajectory in the one-dimensional range profile. Based on region division and random Hough transform, separate and extract the corresponding trajectories of each target; Step 3: Use the least squares method for the corresponding trajectories of each target to roughly estimate the initial position R and velocity of each target and acceleration Then perform rough compensation; The compensation method is as follows, Among them, f r represents the sampling frequency point, f d represents the Doppler frequency, FFT(·) represents the Fourier transform, and IFFT(·) represents the inverse Fourier transform, is the original echo signal; Step 4: Use CLEAN to remove the redundant scatterers and aliased tracks in the one-dimensional range profile sequence after coarse compensation, so that each target only retains one continuous scatterer; Step 5: Estimate the residual acceleration of each target that only retains one continuous scatterer based on spectral characteristics; The steps are as follows: ①Predict the magnitude of the residual acceleration according to the prior of the micro-momentum level, and evenly divide it to obtain the acceleration compensation sequence a com ; ②For the signal after coarse compensation Perform time-domain compensation, transform it to the frequency domain, and find the peak value of its spectrum: ③ Then find the maximum value in the spectral peak vector, and the corresponding acceleration compensation value is the target residual acceleration: Step 6: Use the sliding window MUSIC to accurately estimate the instantaneous frequency, and estimate the residual translational velocity of each target that only retains one continuous scatterer according to spectral characteristics; The algorithm steps are as follows: ① Given the window length W, select an appropriate window function, truncate and window the signal; ② Use the data to construct the autocovariance matrix R x ; ③Perform eigen - decomposition on the auto - covariance matrix R x to obtain the sorted eigenvalues λ and eigenvectors Q. The maximum eigenvalue λ0 of λ corresponds to the signal subspace spanned by Q0 in Q, and the remaining vectors in Q span the noise subspace Q N ; ④ To measure the instantaneous normalized angular frequency of the signal, a vector v(f) = exp(2πjft) in the Doppler dimension is given m ), thus constructing a spectral estimation formula: Search for the instantaneous frequency f within this time window s ; ⑤ Slide the time window, return to step ②, and repeat until the Doppler dimension search is completed; After refined processing, the instantaneous frequency of the target scatterer is obtained, thereby estimating its translation amount Δf, and thus obtaining the estimated value of the residual translational velocity: Δv = Δf × f s / 2π Step 7: Use the residual acceleration and residual translational velocity of each target to calculate the final velocity estimate and acceleration estimate of the target; The velocity estimation formula is: wherein is the roughly estimated speed; The acceleration estimation formula is: wherein is the roughly estimated acceleration; Step 8: For the radar echo signal after fine compensation, based on the R-D imaging algorithm of short-time Fourier transform, perform short-time Fourier time-frequency transform on each row of range cells to obtain a three-dimensional Doppler-range-time matrix, and each time slice of Doppler-range is the R-D image slice.

2. The broadband multi-target translational parameter estimation and compensation method according to claim 1, characterized in that, The specific content of step 2 is as follows: ① Perform CFAR on the one-dimensional range profile sequence of each target, extract the target track, and obtain a binary image; ② Establish a Cartesian coordinate system (x, y) in the one-dimensional range profile sequence space, and evenly divide the coordinates of x and y into several time blocks; ③ Perform classical random Hough transform to extract straight lines within each small time block, and map the results to the ρ-θ space; ④ Perform threshold detection on the ρ-θ space to obtain the straight line expression of the original one-dimensional range profile sequence, construct a corresponding mask according to the straight line expression and the sidelobe width of the echo signal, and separate the target signal from the one-dimensional image sequence.

3. The broadband multi-target translational parameter estimation and compensation method according to claim 1, wherein, The specific content of the CLEAN method in step 4 is as follows: ① Perform one-dimensional CFAR on the one-dimensional range profile sequence of the target after coarse compensation; ② Perform envelope detection on the obtained result to obtain the range cells and time cells of the redundant scatterers of the target; ③ First, perform Hough transform to obtain the straight line equation of the aliased track, and then construct a mask with a width of only five range cells to select the aliased track; ④Extract the amplitude A1 and phase of the peak within one slow time for specific scattering points and aliased tracks Delay t1; ⑤Inverse target echo: And subtract it from the original one-dimensional image sequence; ⑥ Perform the same operation for each slow time until all specific scatterers and aliased tracks are eliminated by the CLEAN algorithm.

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