Radar multi-component signal separation method based on optimized time-frequency distribution

Abstract

The application relates to a radar multi-component signal separation method based on an optimized time-frequency distribution, and relates to a radar multi-component signal separation method. The application aims to solve the problems that most of the existing IF estimation algorithms assume that radar signal components do not cross in the time-frequency domain; the radar components may be tracked after the intersection point, error switching occurs, the frequency extraction precision is reduced under the influence of noise in the low signal-to-noise ratio condition; and the current signal overlapping area is still disturbed by the cross term, resulting in distortion of the recovered signal and a large error between the original signal. The process is as follows: 1, obtaining an instantaneous frequency estimation; 2, obtaining an instantaneous frequency estimation; 3, detecting a straight line segment in each block; 4, obtaining a corrected instantaneous frequency estimation; 5, obtaining an instantaneous frequency diagram; 6, determining a time-varying filter; and 7, radar multi-component signal separation. The application is used in the field of radar multi-component signal separation.

Description

TECHNICAL FIELD

[0001] The present application relates to a radar multi-component signal separation method. BACKGROUND

[0002] The frequency of non-stationary signal changes with time, and the traditional Fourier transform in time-frequency domain is no longer applicable. Instantaneous frequency (IF) is usually used for the analysis of non-stationary signal. In the military field of electronic countermeasures, signals are usually complex and overlap with each other, so it is necessary to study the IF estimation of multi-component signal and separate each signal from the mixed signal on this basis. In the aspect of instantaneous frequency extraction, the existing IF estimation algorithm has good performance in estimating single-component signal, but has the following problems in estimating multi-component signal: signal components may overlap in time-frequency domain, and most of the existing IF estimation algorithms assume that signal components do not cross in time-frequency domain. If the signal components cross each other, these methods may track the wrong components after the intersection point, resulting in false switching. In the case of low signal-to-noise ratio, the frequency extraction accuracy is reduced due to the influence of noise, or at the two ends of the time-frequency diagram, the signal energy concentration decreases and the energy is dispersed. In the aspect of mixed signal separation, the current algorithm using frequency information for filtering is still disturbed by the cross term when processing the signal overlap area, resulting in distortion of the recovered signal and large error between the original signal. SUMMARY

[0003] The purpose of the present application is to solve the problems that most of the existing IF estimation algorithms assume that radar signal components do not cross in time-frequency domain, if the radar signal components cross each other, these methods may track the wrong radar components after the intersection point, resulting in false switching, and in the case of low signal-to-noise ratio, the frequency extraction accuracy is reduced due to the influence of noise, or at the two ends of the time-frequency diagram, the radar signal energy concentration decreases and the energy is dispersed, and the current algorithm using frequency information for filtering is still disturbed by the cross term when processing the signal overlap area, resulting in distortion of the recovered signal and large error between the original signal, and proposes a radar multi-component signal separation method based on optimized time-frequency distribution.

[0004] The specific process of the radar multi-component signal separation method based on optimized time-frequency distribution is as follows:

[0005] Step one: using Viterbi algorithm to process the radar multi-component signal to obtain the estimation of instantaneous frequency

[0006] Step two: based on step one, using improved Viterbi algorithm to process the radar multi-component signal to obtain the estimation of instantaneous frequency

[0007] Step three: the time-frequency distribution of radar multi-component signal is segmented, and a Hough transform is performed on each small block after segmentation; the most likely straight line segment in each block is detected;

[0008] Step four: the results of step two and step three are modified by using a modified improved Viterbi algorithm to obtain a modified instantaneous frequency estimation value;

[0009] Step five: the modified instantaneous frequency estimation value obtained in step four is smoothed to obtain the final instantaneous frequency estimation result of each time of the radar multi-component signal, that is, an instantaneous frequency diagram is obtained;

[0010] Step six: determine the time-varying filter;

[0011] Step seven: taking the instantaneous frequency of each time of the radar multi-component signal obtained in step five as the center, and based on the time-varying filter introduced in step six, the frequency range of each time of each component signal of the radar is obtained; the radar multi-component signal separation is performed by using the generalized S transform combined with the obtained frequency range of each time of each component signal of the radar.

[0012] The beneficial effects of the present application are:

[0013] Most of the existing aliasing signal separation algorithms, such as filtering using frequency information, are interfered by cross terms when processing the signal overlap area, resulting in distortion of the recovered signal and large error between the original signal, and the radar multi-component signal separation method based on optimized time-frequency distribution is proposed. The whole IF extraction and signal separation process is called radar multi-component signal separation technology based on optimized time-frequency distribution.

[0014] The present application is based on the time-frequency distribution of the signal, and an improved Viterbi algorithm (IVA) is first proposed, and then a Hough transform is introduced to modify the results of the IVA algorithm, forming a set of multi-component signal IF extraction method with high precision, called Modified-Improved Viterbi Algorithm (M-IVA). On the basis of the instantaneous frequency extracted by M-IVA, the multi-component signal is separated by using the parameter-optimized generalized S transform and adaptive time-varying filter, and good separation effect can be achieved. The whole frequency extraction and signal separation process is called multi-component signal separation technology based on optimized time-frequency distribution.

[0015] The application relates to a modified improved Viterbi algorithm, which is based on instantaneous frequency estimation of the Viterbi algorithm, and a new constraint is proposed to obtain a new penalty function, and the new scheme is called the improved Viterbi algorithm, the step makes the cross-region switching in the IF extraction of the multi-component signal with time-frequency cross not have errors, and the component analysis can still be ensured to be correct under a low signal-to-noise ratio environment, in order to improve the accuracy of the signal at both ends, the time-frequency distribution is divided into blocks, a Hough transform is introduced to detect straight lines in each block distribution, and a short line is used to fit and approximate a continuous IF curve. The result of the Viterbi algorithm is separated from the result of the Hough transform to guide the separation, and the result of the Hough transform is used to modify the Viterbi algorithm, so that a modified IVA instantaneous frequency estimation value is obtained. On the basis of obtaining the signal instantaneous frequency, in the aspect of filter strategy selection, a time-varying filter with a better adaptive window is selected to better determine the passband range of the signal from the instantaneous frequency diagram, which is helpful for separating the signal; in the aspect of time-frequency analysis method selection, in order to better utilize the previously obtained instantaneous frequency, an S transform is adopted, which establishes a connection between a window function and the instantaneous frequency, and is extended to a generalized S transform, the parameter of the adjusting window function is optimized, the gradient descent method is used to find the optimal parameter of the generalized S transform window function, and the multi-component signal is separated. The application solves the error problem of the cross-region switching in the IF extraction, improves the accuracy of the signal at both ends, and improves the amplitude distortion problem at the cross in the common signal separation technology. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The flow chart of the application;

[0017] Figure 2 The flow chart of the core part of the instantaneous frequency extraction of the application;

[0018] Figure 3a The time-frequency distribution diagram of a three-component signal under a noiseless environment;

[0019] Figure 3b The time-frequency distribution diagram of a three-component signal under a 5db environment;

[0020] Figure 3c The time-frequency distribution diagram of a three-component signal under a 0db environment;

[0021] Figure 3d The IF estimation diagram of the Viterbi algorithm for a three-component signal under a noiseless environment;

[0022] Figure 3e The IF estimation diagram of the Viterbi algorithm for a three-component signal under a 5db environment;

[0023] Figure 3f The IF estimation diagram of the Viterbi algorithm for a three-component signal under a 0db environment;

[0024] Figure 4a The IF estimation figure of IVA algorithm for three-component signals under 5db environment;

[0025] Figure 4b The IF estimation figure of IVA algorithm for three-component signals under 0db environment;

[0026] Figure 5a The time-frequency distribution shown in Fig. 1 is divided into 8x8 time-frequency blocks as shown in Fig. 2; Figure 3b

[0027] Figure 5b The IF estimation result of Hough transform under 5dB environment;

[0028] Figure 5c The partial enlarged view of Fig. 8; Figure 5b

[0029] The IF estimation result figure of Hough transform under 0dB environment; Figure 5d

[0030] The partial enlarged view of Fig. 14; Figure 5e Figure 5d

[0031] The IF estimation result figure of Hough transform under 5dB environment after IVA correction; Figure 6a

[0032] The final instantaneous frequency estimation curve after smoothing processing of Fig. 18; Figure 6b Figure 6a The IF estimation result figure of Hough transform under 0dB environment after IVA correction;

[0033] Figure 6c The final instantaneous frequency estimation curve after smoothing processing of Fig. 26;

[0034] Figure 6d Figure 6c The RMSE performance comparison figure of separating signals by using five time-frequency analysis methods;

[0035] Figure 7 The time-domain amplitude distortion of signal components after STFT filtering;

[0036] Figure 8a The time-domain amplitude distortion of signal components after GST filtering;

[0037] Figure 8b The time-domain amplitude distortion of signal components after fractional order STFT (STFRFT) filtering;

[0038] Figure 8c The time-domain amplitude distortion of signal components after fractional order STFT (STFRFT) filtering;

[0039] Figure 8d ​​​​Time domain amplitude distortion of signal component after fractional GST (GFRST) filtering;

[0040] Figure 9a Actual radar signal time-frequency distribution diagram;

[0041] Figure 9b Figure 9a M-IVA instantaneous frequency estimation result;

[0042] Figure 9c Component 1 obtained by generalized S transform adaptive filtering;

[0043] Figure 9d Component 2 obtained by generalized S transform adaptive filtering. DETAILED DESCRIPTION

[0044] Embodiment one: the process of the radar multi-component signal separation method based on the optimized time-frequency distribution is as follows:

[0045] Step one: the radar multi-component signal is processed by using the Viterbi algorithm (VA) to obtain the instantaneous frequency estimation

[0046] Step two: the radar multi-component signal is processed by using the improved Viterbi algorithm (IVA) based on step one to obtain the instantaneous frequency estimation

[0047] Step three: the time-frequency distribution diagram of the radar multi-component signal is segmented, and a Hough transform is performed on each small block after segmentation; the most likely straight line segment in each block is detected, and these short lines can simulate the position and trend of the real instantaneous frequency of the radar signal in the overall trend;

[0048] Step four: the result of step two and step three is corrected by using the modified improved Viterbi algorithm (M-IVA) to obtain the corrected (improved Viterbi algorithm (IVA)) instantaneous frequency estimation value;

[0049] Step five: the corrected instantaneous frequency estimation value obtained in step four is smoothed to obtain the final instantaneous frequency estimation result of each time of the radar multi-component signal, that is, the instantaneous frequency diagram is obtained;

[0050] Step six: the time-varying filter is determined;

[0051] Step seven: taking the instantaneous frequency of each time of the radar multi-component signal obtained in step five as the center, and based on the time-varying filter introduced in step six, the frequency range of each component signal of the radar at each time is obtained; the radar multi-component signal separation is performed by using the generalized S transform combined with the obtained frequency range of each component signal of the radar at each time. ​

[0052] Specific implementation two: the difference between this embodiment and the first embodiment is that the step one uses the Viterbi algorithm (VA) to process the radar multi-component signal to obtain the estimation of the instantaneous frequency The specific process is:

[0053] Two penalty functions are added to the VA used in the radar multi-component signal, and the ideas of the two constraints of the IF estimation in the VA are as follows: (1) The frequency estimation should first consider that the time-frequency point with large amplitude is the point corresponding to the IF of the radar signal. The noise is scattered and disordered, and the energy is dispersed on the time-frequency plane, and the energy of each point is small, while the energy of the radar signal is concentrated on the ridge line, and the signal amplitude is large. (2) There is no sudden change between two consecutive IF points. This is because the true instantaneous frequency is continuous and there is no jump, and at the same time this constraint can suppress the influence of noise on the signal to a certain extent.

[0054] The constraint (1) is realized by the penalty function q(), and the constraint (2) is realized by the penalty function g(). After defining the two penalty functions corresponding to the two constraints, the estimation of the instantaneous frequency can be written as the minimum path penalty function corresponding to the route

[0055] The penalty function q() is inversely proportional to the amplitude of the energy of the radar multi-component signal.

[0056] The penalty function q() is realized by sorting the energy values of all points along the frequency axis in the time-frequency distribution diagram.

[0057] Assuming that there are M×N points in the time-frequency distribution diagram, M represents the frequency, and N represents the time, then the path from n=1 to n=N has M N bars;

[0058] For a given time point n, the penalty function q() is to sort the TF values into a decreasing sequence:

[0059] TF(n,f n,1 )≥TF(n,f n,2 )≥…≥TF(n,f n,j )≥…TF(n,f n,M )

[0060] Where, TF represents the energy value of the frequency corresponding to the time point n; f n,j represents the jth frequency value at the time point n, that is, the vertical coordinate changes on the time-frequency distribution diagram, j=1,2,...,M;

[0061] Therefore, in order to make the penalty function q() of the point with the largest amplitude minimum, a simple function is designed to satisfy the assumption:

[0062] q(TF(n,fn,j )) = j - 1

[0063] At time point n, q(TF(n, f n,1 )) = 0, q(TF(n, f n,2 )) = 1,..., q(TF(n, f n,M )) = M - 1;

[0064] The penalty function g() is defined as:

[0065] g(l(n, n + 1)) = 0 for |f n,j -f n+1,i | < Δ

[0066] g(l(n, n + 1)) = c|f n,j -f n+1,i | - Δ otherwise

[0067] Where l(n, n + 1) is all the paths between time point n and n + 1 on the connected time-frequency distribution, n = 1, 2,..., N - 1; f n,j represents the jth frequency value at time point n, f n+1,i represents the ith frequency value at time point n + 1, and i = 1, 2,..., M, j = 1, 2,..., M; Δ is a threshold value (frequency unit) set in the program, representing the maximum expected value of IF change between two consecutive time points; c represents the penalty constant given when the IF difference between two consecutive time points does not satisfy the threshold value.

[0068] The selection of Δ along the c direction determines the maximum expected value of IF change between consecutive points. In the experiment, the selection of Δ is based on the frequency resolution of TFD. When a high-resolution time-frequency distribution is used, taking the corresponding Δ and c of adjacent points can obtain better results.

[0069] Then the estimate of the instantaneous frequency can be written as:

[0070]

[0071] Where n represents the time point in the time-frequency distribution, and N represents the total time points in the time-frequency distribution.

[0072] The total path is the path passing through from the first time point to the last time point, and the estimate of the instantaneous frequency is the path corresponding to the minimum cost function value;

[0073] The specific meaning of the function is that at the first time, the point with the maximum energy at each frequency is found as the starting point of the path, and the penalty function q() works; from the next time, all frequency points at this time are traversed to find a path combined with the point fixed at the previous time, so that the penalty function g()+q() is minimized. Until the frequency point position at the last time is determined, that is, the curve where the IF is located is found.

[0074] The other steps and parameters are the same as in the first embodiment.

[0075] The third embodiment is different from the first or second embodiment in that the step two is based on step one to process the radar multi-component signal by using an improved Viterbi algorithm (IVA) to obtain the estimation of the instantaneous frequency The specific process is as follows:

[0076] On the basis of the constraint in step one, the application proposes a new constraint that the continuous points on the IF estimation have a small change in their directions. This constraint is realized by introducing a penalty function h(), and the improved scheme is called the improved Viterbi algorithm. The algorithm is used to extract the IF from the obtained time-frequency distribution. The method used to solve the above optimization problem is to recursively select the best path from the previous moment to estimate the IF at a given time.

[0077] The constraint related to the best angle is robust to noise because the estimation process involves correlation with the direction filter, and the best angle of the noise is random, while the real signal presents continuity in the angle. The penalty function h() is introduced and defined as follows:

[0078]

[0079]

[0080] where θ(n, f n,j ) represents the energy direction at the (n, f n,j ) position (the point may be a signal or noise); d represents the penalty constant when the difference between the energy direction (θ(n, f n,j )) at (n, f n,j ) and the energy direction (θ(n+1, f n+1,i )) at (n+1, f n+1,i ) is greater than or equal to the threshold value;

[0081] The modified instantaneous frequency estimation is represented as:

[0082] where θ(n, f n,j ) represents the energy direction at the (n, f n,j ) position (the point may be a signal or noise); d represents the penalty constant when the difference between the energy direction (θ(n, f n,j )) at (n, f n,j ) and the energy direction (θ(n+1, f n+1,i )) at (n+1, f n+1,i ) is greater than or equal to the threshold value;

[0081] The modified instantaneous frequency estimation is represented as:

[0082] where θ(n, f n,j ) represents the energy direction at the (n, f n,j ) position (the point may be a signal or noise); d represents the penalty constant when the difference between the energy direction (θ(n, f n,j )) at (n, f n,j ) and the energy direction (θ(n+1, f n+1,i )) at (n+1, f n+1,i ) is greater than or equal to the threshold value;

[0081] The modified instantaneous frequency estimation is represented as:

[0082]

[0083] Other steps and parameters are the same as those in embodiment one or two.

[0084] Embodiment four: The difference between this embodiment and one of the embodiments one to three is that the time-frequency distribution of the radar multi-component signal is segmented in step three, and a Hough transform is performed on each small block after segmentation; the most likely straight line segment in each block is detected, and these short lines can simulate the position and trend of the real instantaneous frequency of the radar signal in the overall trend; the specific process is as follows:

[0085] The time-frequency distribution of the radar multi-component signal is segmented into 32x32 time-frequency blocks, i.e., the size of each time-frequency block is 8x8, a Hough transform is performed on each time-frequency block, and the most likely straight line segment in each time-frequency block is detected to obtain 32x32 straight line segments.

[0086] Other steps and parameters are the same as those in one of the embodiments one to three.

[0087] Embodiment five: The difference between this embodiment and one of the embodiments one to four is that a modified improved Viterbi algorithm (M-IVA) is used in step four to modify the results of steps two and three to obtain a modified (improved Viterbi algorithm (IVA)) instantaneous frequency estimation value; the specific process is as follows:

[0088] The M-IVA is a modified improved Viterbi algorithm (M-IVA);

[0089] The results of the improved Viterbi algorithm in step two are used to separate and guide the results of the Hough transform, and the results of the Hough transform are used to modify the improved Viterbi algorithm to obtain a modified IVA instantaneous frequency estimation value.

[0090] The specific process of obtaining the modified IVA instantaneous frequency in step four is shown in the accompanying Figure 2 The modification process and judgment criteria have the following five points:

[0091] Step four one: the improved instantaneous frequency estimation obtained in step two is subjected to a binaryzation process, if there is a line in the improved instantaneous frequency estimation graph at a certain frequency point at any time point t, it is considered that the frequency point in the binaryzation processed improved instantaneous frequency estimation graph is the instantaneous frequency estimation value at that time, and is set to 1, otherwise it is considered not to be the instantaneous frequency estimation value at that time, and is set to 0;

[0092] Step four two: the Hough transform graph obtained in step three is binarized, if there is a line in the Hough transform graph corresponding to a frequency point at any time point t, it is considered that the frequency point in the binarized Hough transform graph is the instantaneous frequency estimation value at the time, and is set to 1; otherwise, it is considered that it is not the instantaneous frequency estimation value at the time, and is set to 0;

[0093] Step four three: at time t, if there is a position of a point determined to be a frequency estimation value in step four one in the upper and lower range of the position of the point determined to be a frequency estimation value in step four two (i.e. there is a point with a value of 1), it is considered that the determination result of step four one is correct, and the position of the point determined to be a frequency estimation value in step four one and the position of the point determined to be a frequency estimation value in step four two are averaged; is a threshold value;

[0094] Step four four: at time t, if there is no position of a point determined to be a frequency estimation value in step four two in the upper and lower range of the position of the point determined to be a frequency estimation value in step four one, it is determined that the determination result of step four one is wrong, and the position of the point determined to be a frequency estimation value in step four two closest to the position of the point determined to be a frequency estimation value in step four one is searched, and it is considered that the position (the position of the point determined to be a frequency estimation value in step four two closest to the position of the point determined to be a frequency estimation value in step four one) is the position of the real frequency point;

[0095] Step four five: all the corrected frequency positions at all times (if all the times select the results of step four three, all the times corresponding to the frequency points of step four three are integrated; if all the times select the results of step four four, all the times corresponding to the frequency points of step four four are integrated; if all the times select both the results of step four three and the results of step four four, all the times corresponding to the frequencies of step four three and step four four are integrated) are integrated to obtain the corrected instantaneous frequency estimation value.

[0096] The other steps and parameters are the same as those in one of the first to fourth embodiments.

[0097] Embodiment six: the embodiment six is different from one of the first to fifth embodiments in that a time-varying filter is determined in step six, and the specific process is as follows:

[0098] a time-varying filter B i (n, k) is searched for a passband range of the i th component signal of the radar in the instantaneous frequency graph, and a self-adaptive filter is selected based on the short-time Fourier transform to be the final time-varying filter B i (n, k);

[0099] In the time-frequency diagram, the horizontal axis represents time and the vertical axis represents frequency. In the case of known instantaneous frequency, the position of a signal component in the time-frequency diagram is known. The time-frequency analysis results at these positions are taken out separately and inverse transformed to obtain the time-domain information of the signal. In actual time-frequency distribution, the signal energy does not correspond to only one frequency point at a time. The points with large energy around the frequency point should belong to the passband range of the filter. In this way, the error caused by inaccurate frequency estimation can be reduced. Taking STFT as an example, a time-varying filtering scheme is used to search around the position of the frequency.

[0100] For the radar signal z(t), the short-time Fourier transform of the radar signal z(t) is

[0101]

[0102] where F z (t, w) is the short-time Fourier transform spectrum of the radar signal z(t) at time t, t is the size of the window function moving on the time axis, w is the frequency, z(u) is the radar time-domain signal, is the time-domain analysis window function, and the radar signal is multiplied by the analysis window function which is equivalent to taking a slice of the signal near the analysis time point t. R is a real number domain representing the integral interval, is the imaginary unit.

[0103] Correspondingly, The inverse transform of

[0104]

[0105] For convenience of calculation, the window function is set to 1. The inverse transform of the short-time Fourier transform value at a certain time is the signal sampling value at this time, and the radar signal value is obtained by dividing the window function;

[0106] The STFT of the discrete form of the radar signal z(t) is

[0107]

[0108]

[0109] In the formula, F(n, k) is the short-time Fourier transform spectrum at the nth point after discretization, n is the number of points of the window function moving on the time axis, k is the discrete frequency point, z(m) is the discrete time-domain signal, is the selected time-domain analysis window function, N is the window length of the selected window function, and DFT represents the discrete Fourier transform, is the restored signal, and the value of the window function is limited for convenience of calculation;

[0110] To recover the radar signal, for the i-th component of the radar, the transformed value belonging to the i-th component of the radar is found, and this process is written in the form of a filter

[0111]

[0112] wherein, B is the i-th recovered signal component, and i (n, k) is a filter for extracting the i-th signal component of the radar from the time-frequency diagram;

[0113] When the signal is affected by noise, the amplitude of the noise can be comparable to that of the signal, in which case the position of the signal cannot be simply determined by the high energy of some points. The important basis for determining the position of the signal in the present application is the position in the time-frequency diagram pointed to by the instantaneous frequency. The vicinity of the instantaneous frequency curve is considered to be the passband of the filter of the signal component. A simple implementation method is to consider the points within the range L in the vicinity of the point corresponding to the instantaneous frequency of the signal component at a certain time as the energy of the signal component. The points B i (n, k) = 1, and the other positions B i (n, k) = 0.

[0114] This filtering method is equivalent to considering the points within the range L in the vicinity of the instantaneous frequency diagram obtained in step five as the signal component, and is a fixed window width filter. In order to enhance the filtering effect, a method of adaptive filtering at each time is considered, and the implementation is as follows:

[0115] (1) Assuming that the frequency value of the n-th time point of the i-th component of the radar on the instantaneous frequency diagram is An energy threshold is set

[0116] wherein a is a coefficient, and TF represents the energy value of the frequency corresponding to the time point n;

[0117] (2) Searching for possible frequency points on both sides of (looking up and down from the time-frequency diagram);

[0118] If the energy difference between the energy of the searched possible frequency point A and the energy of the frequency point B is greater than ΔTF, then the frequency point A does not belong to the frequency point of the i-th component of the radar;

[0119] If the energy difference between the energy of the searched possible frequency point and the energy of the frequency point B is less than or equal to ΔTF, then the frequency point belongs to the frequency point of the i-th component of the radar;

[0120] (3) repeat (1), (2) to obtain time-varying filter B(n, k) of all components at all time points;

[0121] The k is a discrete frequency point.

[0122] The other steps and parameters are the same as one of the first to fifth embodiments.

[0123] The seventh embodiment is different from one of the first to sixth embodiments in that the step seven obtains the frequency range (the value of k represents the frequency range) of each component signal of the radar at each time point based on the time-varying filter introduced in the step six, with the instantaneous frequency of each time point of the radar multi-component signal obtained in the step five as the center; the radar multi-component signal separation is performed by using the generalized S transform combined with the obtained frequency range of each component signal of the radar at each time point; and the specific process is as follows:

[0124] The gradient descent method is used to find the optimal parameters λ and p of the generalized S transform, and the S transform window function corresponding to each time point is calculated; the signal separation is performed by using the parameter-optimized generalized S transform; and the specific process is as follows:

[0125] The S transform of the radar signal z(t) is

[0126]

[0127]

[0128]

[0129] wherein S(τ, f) is the S transform result of the signal z(t) at the time τ, τ represents the distance size of the window function moving along the time axis, f is the frequency, t represents the time, σ is the adjustment factor of the kernel function of the S transform, w(τ-t, σ) is the kernel function used by the S transform and the time shift is τ, w(t, σ) is the original kernel function of the S transform, and σ(f) represents that the adjustment factor of the kernel function is related to the frequency f.

[0130] The w(t, σ) is the kernel function used by the S transform, which is a Gaussian function, and the function adjustment factor σ therein is the inverse of the frequency f modulus value. Therefore, the window function of the S transform changes with the frequency, and the relationship between the window function and the frequency is established, which is a feature that other time-frequency analysis methods do not have. The instantaneous frequency estimation of the signal has been obtained before the time-varying filtering, so the frequency is replaced by the estimated frequency, and the window function is designed by using the frequency of each component at each time point, so that the work results of the step five can be used to the greatest extent.

[0131] One feature of the S transform is that the integral of the transform result is the Fourier transform of the radar signal

[0132]

[0133] where Z(f) is the Fourier transform of the radar signal;

[0134] Therefore The inverse transform of

[0135]

[0136] Using this property, the S transform can be implemented by the fast Fourier transform;

[0137] The present application uses an improved form of the generalized S transform (GST)

[0138]

[0139] Where GST(τ,f) is the generalized S transform result of the radar signal z(t), τ is the distance size of the window function moving along the time axis, f is the frequency, z(t) is the radar signal (time domain signal), t represents time, λ and p are two adjustment factors added respectively, when λ=p=1, the generalized S transform is equivalent to the S transform, and in other cases, λ and p are used to adjust the shape of the window function;

[0140] The values of λ and p increase, and the amplitude of the window function of GST also increases, but the window function is more affected by p.

[0141] In practice, there is little prior knowledge of the received radar signal, and in order to obtain a good separation effect by using the generalized S transform filtering, the parameters λ and p need to be set well, and the gradient descent method is used to find the best parameter setting in the present application, so as to generalize the generalized S transform to a more practical situation.

[0142] The S transform can be understood as a short-time Fourier transform to some extent, except that the window function becomes a frequency-adjusted Gaussian function, so the mathematical expression of the time-varying filtering in the GST case is directly given by analogy;

[0143] Discrete transform is performed on GST(τ,f) to obtain GST z (n,k), based on GST z (n,k) and time-varying filter B i (n,k), each component of the radar multi-component signal after separation is obtained

[0144]

[0145] Where, is each component of the radar multi-component signal after separation, GST z (n,k) is the spectrum of the generalized S transform at the nth time point, B i (n,k) is the time-varying filter of the i-th component;

[0146] Time-varying filter B i (n, k) is the adaptive filter in step six, the process is very similar to the filtering method of the STFT in step six, the difference lies in the process of transformation.

[0147] The other steps and parameters are the same as one of the first to sixth embodiments.

[0148] The beneficial effects of the present application are verified by the following embodiments:

[0149] Embodiment one:

[0150] The specific process of the radar multi-component signal separation method based on the optimized time-frequency distribution is as follows:

[0151] Step one: the radar multi-component signal is processed by using the Viterbi algorithm (VA) to obtain the instantaneous frequency estimate

[0152] Step two: the radar multi-component signal is processed by using the improved Viterbi algorithm (IVA) based on step one to obtain the instantaneous frequency estimate

[0153] Step three: the time-frequency distribution diagram of the radar multi-component signal is segmented, and a Hough transform is performed on each small block after segmentation; the most likely straight line segment in each block is detected, and these short lines can simulate the position and trend of the real instantaneous frequency of the radar signal in the overall trend;

[0154] Step four: the results of step two and step three are corrected by using the modified improved Viterbi algorithm (M-IVA) to obtain the corrected (improved Viterbi algorithm (IVA)) instantaneous frequency estimate value;

[0155] Step five: the corrected instantaneous frequency estimate value obtained in step four is smoothed to obtain the final instantaneous frequency estimate result of the radar multi-component signal at each time, that is, the instantaneous frequency diagram is obtained;

[0156] Step six: determine the time-varying filter B i (n, k);

[0157] Step seven: taking the instantaneous frequency of the radar multi-component signal at each time obtained in step five as the center, and based on the time-varying filter introduced in step six, the frequency range of each component signal of the radar at each time is obtained; the radar multi-component signal separation is performed by using the parameter-optimized generalized S transform combined with the obtained frequency range of each component signal of the radar at each time.

[0158] Embodiment two:

[0159] The simulation signal uses three components: two LFM signals and one SFM signal. The start-cutoff frequencies of the two LFM signals are 35MHz-9MHz and 5MHz-20MHz, respectively, while the lowest-highest frequency of the SFM signal is 15MHz-28MHz, with a modulation period of 3μs. Its sampling frequency F... s The frequency response time (FRT) is 100MHz, the number of sampling points N is 256, and the amplitude of each component is 1V. The time-frequency distribution diagrams of the three components under noise-free, 5dB, and 0dB SNR environments are shown below. Figure 3a , Figure 3b , Figure 3c As shown in the figure. Two constraints are added to the Viterbi algorithm shown in step one for instantaneous frequency estimation. The results obtained under three different noise environments are as follows. Figure 3d , Figure 3e , Figure 3f As shown. It is demonstrated that when VA estimates a three-component signal, the shape of the estimated IF value deviates from the theoretical value, and errors are extremely prone to occur during cross-term switching. Based on this, a new constraint proposed in this invention is added, requiring that continuous points in the IF estimation have small changes in their directions. The optimal path is recursively selected from the previous instant to estimate the IF at a given time. The instantaneous frequency extraction results of IVA in 5dB and 0dB environments are shown below. Figure 4a and Figure 4b As shown in the diagram. Observations show that IVA did not exhibit errors during switching in the crossover region, and component analysis remained correct even in low signal-to-noise ratio environments; however, the accuracy at both ends of the signal still needs further improvement. The time-frequency distribution of the three-component signal is 256×256 in size. Dividing the time-frequency distribution into 32×32 time-frequency blocks (each block being 8×8) is illustrated in the diagrams below. Figure 5a As shown. Under a 5dB environment, a Hough transform was performed on each block to detect the most likely line segment within that block, resulting in 32×32 line segments, as shown below. Figure 5b As shown, its enlarged partial view is as follows: Figure 5c It can be seen that these short lines simulate the position and trend of the signal's actual instantaneous frequency in the overall trend. Repeating the experiment in a 0dB environment yielded the following results: Figure 5d and Figure 5e As shown in the figure. The results of the Hough transform and the IVA are combined for correction. The corrected IF estimation results under 5dB and 0dB environments are shown in the figure. Figure 6a and 6c As shown, the curve exhibits some jitter, but it can be observed that most of the frequency estimates are correctly positioned. After fitting and smoothing, the final instantaneous frequency estimation curve is as follows. Figure 6b and 6d As shown, it is very close to the actual curve.

[0160] Example 3:

[0161] The simulation signal used was the same as the three-component signal in Example 2, with the same signal amplitude. Five time-frequency analysis algorithms were employed to separate the signal and compare their performance: Short-Time Fourier Transform (STFT), Short-Time Fractional Fourier Transform (STFRFT), Synchronous Compressed Wavelet Transform (SWT), Generalized S-Transform (GST), and Fractional Generalized S-Transform (GFRST). The root mean square error (RMSE) was used as the evaluation metric for signal recovery by different algorithms.

[0162]

[0163] Where RMSE is the root mean square error between the original signal and the recovered signal. Where z is the length of the signal, and z(n) represents the original signal. This represents the recovered signal; the smaller the value of this index, the closer the reconstructed time-domain signal is to the true signal. (Appendix) Figure 7 The results are Monte Carlo simulation experiments of repeated experiments to calculate RMSE under different signal-to-noise ratios. It can be seen that both GST and GFRST have good temporal reconstruction effects. Figure 8a , Figure 8b , Figure 8c , Figure 8d The time-domain waveforms of the signals obtained by filtering one LFM signal using STFT, GST, STFRFT, and GFRST are compared with the original signal waveform. The signal intersects with other components around 1.8µs. When using STFT filtering, the recovered signal amplitude reaches 2V near the intersection, which is significantly distorted compared to the original signal's 1V. The signal amplitude recovered using GST is at most 1.5V, showing a reduced error. Extending both algorithms to the fractional domain, experimental results still show that the fractional S-transform exhibits less amplitude distortion.

[0164] Example 4:

[0165] As attached Figure 9a As shown, an SFM signal of equivalent strength is added to the actual received LFM radar signal. The artificially added SFM component has a modulation index of 3, a modulation frequency of 0.5MHz, and a sampling frequency of 200MHz. Signal separation is then performed using the multi-component signal separation technique based on optimized time-frequency distribution proposed in this invention. Figure 9b The instantaneous frequency is estimated by the improved Viterbi algorithm with Hough transform correction. Figure 9c , Figure 9d These are the signal components obtained by the generalized S-transform after parameter optimization. Experimental results show that the algorithm proposed in this invention remains effective in processing real signals.

[0166] The present application can have other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application, and these corresponding changes and modifications shall all belong to the protection scope of the claims of the present application.

Claims

1. A radar multi-component signal separation method based on optimized time-frequency distribution, characterized in that: The method specifically comprises the following steps: Step one: using Viterbi algorithm to process the radar multi-component signal to obtain the estimation of the instantaneous frequency Step two: based on step one, the improved Viterbi algorithm is used to process the radar multi-component signal to obtain the estimation of the instantaneous frequency Step three: the time-frequency distribution of the radar multi-component signal is segmented, and a Hough transform is performed on each small block after segmentation; the most likely straight line segment in each block is detected; Step four: the results of step two and step three are corrected by using a modified Viterbi algorithm to obtain a corrected instantaneous frequency estimation value; the specific process is as follows: Step four one: the improved instantaneous frequency estimation obtained in step two is subjected to binaryzation processing; if there is a line in the improved instantaneous frequency estimation graph corresponding to a frequency point at any time point t, it is considered that the frequency point in the binaryzation processed improved instantaneous frequency estimation graph is the instantaneous frequency estimation value at the time point, and is set to 1; otherwise, it is considered that it is not the instantaneous frequency estimation value at the time point, and is set to 0; Step four two: the Hough transform graph obtained in step three is subjected to binaryzation processing; if there is a line in the Hough transform graph corresponding to a frequency point at any time point t, it is considered that the frequency point in the binaryzation processed Hough transform graph is the instantaneous frequency estimation value at the time point, and is set to 1; otherwise, it is considered that it is not the instantaneous frequency estimation value at the time point, and is set to 0; Step four three: At time t, if the position of the point considered to be the frequency estimate value in step four one is within the upper and lower ranges of the position of the point determined to be the frequency estimate value in step four two, consider the result of step four one to be correct, and average the position of the point considered to be the frequency estimate value in step four one and the position of the point determined to be the frequency estimate value in step four two; is the threshold value; Step four four: At time t, if the position of the point considered as the frequency estimation value in step four one is not within the upper and lower range of the position of the point determined as the frequency estimation value in step four two, it is determined that the result of step four one is wrong, and the position of the point determined as the frequency estimation value in step four two nearest to the position of the point considered as the frequency estimation value in step four one is searched, and the position is considered as the position of the real frequency point. Step four five: all the corrected frequency positions at all time points are integrated to obtain the corrected instantaneous frequency estimation value; Step five: the corrected instantaneous frequency estimation value obtained in step four is subjected to smoothing processing to obtain the final instantaneous frequency estimation result of each time point of the radar multi-component signal, that is, an instantaneous frequency graph is obtained; Step six: a time-varying filter is determined; Step seven: taking the instantaneous frequency of each time point of the radar multi-component signal obtained in step five as the center and based on the time-varying filter introduced in step six, the frequency range of each time point of each component signal of the radar is obtained; the radar multi-component signal is separated by using a generalized S transform in combination with the obtained frequency range of each time point of each component signal of the radar.

2. The radar multi-component signal separation method based on optimized time-frequency distribution according to claim 1, characterized in that: The step one uses the Viterbi algorithm to process the radar multi-component signal to obtain an estimation of the instantaneous frequency The specific process is as follows: Assuming there are M x N points in the time-frequency distribution, M represents frequency and N represents time, then there are M N bars between the time points from n = 1 to n = N. For a given time point n, the penalty function q() is to sort the TF values into a decreasing sequence: TF(n, f n,1 ) ≥ TF(n, f n,2 ) ≥... ≥ TF(n, f n,j ) ≥... TF(n, f n,M ) wherein TF represents the energy value of the frequency corresponding to the time point n; f n,j represents the jth frequency value at the time point n, i.e. the ordinate of the time-frequency distribution, j = 1, 2,..., M; In order to make the point with the maximum amplitude have the minimum penalty function q(), a simple function is designed to satisfy the assumption: q(TF(n,f n,j )) = j-1 At time point n, q(TF(n, f n,1 )) = 0, q(TF(n, f n,2 )) = 1,..., q(TF(n, f n,M )) = M-1; The penalty function g() is defined as: g(l(n, n + 1)) = 0 for |f n,j -f n+1,i |<Δ g(l(n, n + 1)) = c | f n,j - f n+1,i - Δ otherwise Wherein, l(n,n+1) is all the paths connecting two time points n and n+1 on the time-frequency distribution graph, n = 1, 2,..., N - 1; f n,j denotes the jth frequency value at time point n, f n+1,i denotes the ith frequency value at time point n + 1, and i = 1, 2,..., M, j = 1, 2,..., M; Δ is a threshold value; c denotes a penalty constant; An estimate of the instantaneous frequency may be written as: Wherein, n represents a time point in the time-frequency distribution graph, and N represents the total time points in the time-frequency distribution graph.

3. The radar multi-component signal separation method based on optimized time-frequency distribution according to claim 2, characterized in that: The step two is based on the step one to process the radar multi-component signal by using the improved Viterbi algorithm to obtain the estimation of the instantaneous frequency The specific process is as follows: The penalty function h() is introduced and defined as follows: h(l(n,n+1)) = 0 Where θ(n,f) n,j ) indicates that in (n,f n,j The direction of energy at the location; The threshold representing the difference in angles between two consecutive time points; d represents the threshold value for (n, f) n,j The energy direction at point (n+1, f) is parallel to that at point (n+1, f). n+1,i The penalty constant when the energy direction difference at point () is greater than or equal to the threshold; The modified instantaneous frequency estimation quantity is represented as:

4. The radar multi-component signal separation method based on optimized time-frequency distribution according to claim 3, characterized in that: In step three, the time-frequency distribution of the radar multi-component signal is segmented, and a Hough transform is performed on each small block after segmentation; the most likely straight line segment in each block is detected; the specific process is as follows: The time-frequency distribution of the radar multi-component signal is segmented into 32x32 time-frequency blocks, that is, the size of each time-frequency block is 8x8, a Hough transform is performed on each time-frequency block, and the most likely straight line segment in each time-frequency block is detected to obtain 32x32 straight line segments.

5. The radar multi-component signal separation method based on optimized time-frequency distribution according to claim 4, characterized in that: In step six, the time-varying filter is determined; the specific process is as follows: (1) Assume that the frequency value of the i-th component of the radar at the n-th time point on the instantaneous frequency map is Setting an energy threshold Wherein, a is a coefficient, and TF represents the energy value of the frequency corresponding to the time point n; (2) in Search both sides for possible frequency points; If the energy If the difference between the energy of the searched possible frequency point A is greater than ΔTF, then the frequency point A does not belong to the frequency points of the i-th component of the radar. If energy With the possible frequency points of the search If the energy difference is less than or equal to ΔTF, then the frequency point The frequency point belonging to the i-th component of the radar; (3) repeating (1) and (2) to obtain the time-varying filter B(n,k) of all components at all time points; The k is a discrete frequency point.

6. The radar multi-component signal separation method based on optimized time-frequency distribution according to claim 5, characterized in that: The step seven is centered on the instantaneous frequency of each moment of the radar multi-component signal obtained in step five, and based on the time-varying filter introduced in step six, the frequency range of each moment of each component signal of the radar is obtained; the radar multi-component signal separation is performed by using the generalized S transform combined with the obtained frequency range of each moment of each component signal of the radar; the specific process is as follows: An improved form of the generalized S transform Wherein, GST(τ,f) is the generalized S transform result of the radar signal z(t), τ is the distance size of the window function moving along the time axis, f is the frequency, z(t) is the radar signal, t represents time, and λ and p are respectively two adjusting factors, when λ=p=1, the generalized S transform is equivalent to the S transform, and in other cases, λ and p are used to adjust the shape of the window function. Discrete transform of GST(τ, f) gives GST z (n, k) based on GST z (n, k) and time-varying filter B i (n, k) gives each component after radar multi-component signal separation wherein GST (n, k) is the generalized S-transform at the nth time point z (n, k) is the generalized S-transform at the nth time point i (n, k) is the time-varying filter for the i-th component.

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