A GNSS-based forward scattering radar echo parameter extraction method

Abstract

The application discloses a forward scattering radar echo parameter extraction method based on GNSS, and comprises the following steps: 1, forward scattering signal extraction; 2, using the Rényi entropy of the smooth pseudo-Wigner-Ville distribution to judge whether the forward scattering signal contains a target scattering signal; 3, using a sliding window to analyze the frequency domain characteristics of each signal segment of the target scattering signal, and judging whether a target crossing event occurs; 4, using a smaller sliding window to analyze the signal segment of the crossing event in sections, calculating the time domain statistical characteristic value of the signal segment in the sliding window, and extracting an optimal signal; 5, using the optimal signal to estimate the target crossing Doppler slope; and 6, using the optimal signal to estimate the target crossing time. The application can realize preliminary judgment of the relative position relationship between a target and a baseline, can realize target crossing Doppler slope estimation and target crossing time estimation of a forward scattering radar echo, and can be popularized to a forward scattering radar network of platforms such as the ground, the sea surface and the air.

Description

TECHNICAL FIELD

[0001] The application relates to a forward scattering radar echo parameter extraction method based on GNSS, in particular to an echo parameter extraction method capable of realizing optimal signal selection and detection of a target, and accurate estimation of a target crossing moment and a Doppler slope, and belongs to the technical field of radar detection. BACKGROUND

[0002] An external radiation source radar based on a global navigation satellite system (GNSS) has advantages of all-weather, all-day, global coverage and good concealment, and the main defect is that a target scattering signal is weak, and long-time accumulation technology or a high-gain antenna needs to be used to realize remote target detection. A characteristic that a target radar cross section (RCS) rapidly increases in a forward scattering area can effectively make up for the problem that the target scattering signal is weak, so that the combination of a forward scattering radar (FSR) and the global navigation satellite system is a feasible air target detection system.

[0003] The signal shadowing phenomenon caused by the target crossing the baseline can realize the air target detection, and the signal extraction process based on the GNSS forward scattering radar signal has been studied (I.Suberviola, I. Mayordomo, and J. Mendizabal. Experimental results of air target detection with a GPS forward-scattering radar [J]. IEEE Geoscience and Remote Sensing Letters, 2012, 9 (1): 47-51. I.Suberviola, I. Mayordomo, and J. Mendizabal. GPS forward scattering radar air target detection experimental results [J]. IEEE Geoscience and Remote Sensing Letters, 2012, 9 (1): 47-51.), and the extracted forward scattering signal is similar to the linear frequency modulation (Linear Frequency Modulation, LFM) signal. The relative position relationship between the target and the baseline will affect the parameter value of the processed forward scattering signal, and by estimating the forward scattering signal parameters such as the Doppler slope and the crossing time, the motion target parameter estimation can be further realized. The relative position relationship between the target and the baseline can be used as a measure of whether the signal parameter estimation value is available or a reference for motion parameter estimation error compensation. At present, there is little work on the combination of forward scattering signal selection and signal parameter estimation, and by using a method that can preliminarily identify the relative position of the target and the baseline, the purpose of selecting the required optimal signal is achieved, and the parameter estimation is realized on the basis of the optimal signal, which can effectively improve the reliability of the parameter estimation value.

[0004] Therefore, the application provides a GNSS-based forward scattering radar echo parameter extraction method, when a forward scattering signal is obtained, whether the current contains a target signal is judged by a signal detection method, then the relationship between the target and the baseline position is judged by using the time-frequency domain statistical characteristics and the optimal signal selection is realized, and finally the Doppler slope and the target crossing time estimation are realized based on the optimal signal. SUMMARY

[0005] The application aims to provide a GNSS-based forward scattering radar echo parameter extraction method, which has the characteristics of simple use, real-time and high efficiency, and solves the problem of forward scattering echo parameter extraction process design.

[0006] The application is based on the receiver processed forward scattering signal for detection, optimal signal selection, characteristic value calculation of representing the relative position relationship between the target and the baseline, target crossing time and Doppler slope estimation. The method is aimed at the area continuously covered by the space-based radiation source and the receiver array, determines whether there is a target appearing in the forward scattering area through the effective detection algorithm, when the target crosses the baseline, realizes the relative position calculation between the target and the baseline through the time-frequency domain statistical characteristic value of the target forward scattering echo, realizes the signal parameter estimation including the Doppler slope and the target crossing time through the extracted optimal signal, and provides data support for the target motion parameter estimation.

[0007] The technical scheme of the application is that firstly, based on the existing GNSS-based forward scattering radar signal extraction technology, the echo received by the receiver is processed to obtain the forward scattering signal, secondly, the signal detection is carried out, the existing signal detection method is improved, the detection method based on the Rényi entropy of the smoothed pseudo Wigner-Ville distribution (SPWVD) is proposed, then the signal section is selected by sliding window, and the frequency domain statistical characteristic value of the current signal section is calculated to determine whether it corresponds to the target crossing baseline time period, a new type of optimal signal selection method is realized, the time domain characteristic value is calculated to identify the relative position relationship between the target and the baseline, and finally the optimal signal is used to obtain the target crossing Doppler slope and crossing time estimation value. A complete processing flow of extracting parameters through the target forward scattering echo is provided.

[0008] The application is a GNSS-based forward scattering radar echo parameter extraction method, and the specific steps are as follows:

[0009] Step 1, forward scattering signal extraction;

[0010] The forward scattering radar receiver is a single-channel processing, and it can be considered that the satellite direct wave and the target scattering signal almost arrive at the receiver at the same time, and the received signal is the coherent superposition of the direct wave and the target scattering wave. The receiver radio frequency front end completes a series of mixing, filtering, down-conversion and sampling quantization operations on the received signal to obtain an intermediate frequency signal. After the carrier synchronization and the pseudo code synchronization are realized in the GNSS tracking loop, the signal is de-modulated, and the code correlation is performed. The in-phase (I) integrator of the tracking loop starts to output data bits (navigation message), and the output amplitude is modulated by the forward scattering echo. After the navigation message is filtered out, the forward scattering signal is obtained.

[0011] Step 2, using the SPWVD-based Rényi entropy detection method to determine whether the processed received signal obtained in step 1 contains the target scattering signal;

[0012] Step 3, the frequency domain characteristics of each signal segment of the target scattering signal obtained in step 2 are analyzed by using a sliding window, and whether the target crossing baseline event occurs is judged;

[0013] The Doppler of the forward scattering signal changes linearly with time, when the target crosses the baseline, the Doppler frequency is zero, and this characteristic is true when the target is in a certain range near the baseline, so the frequency of the signal segment corresponding to the crossing event should be near zero frequency, and the frequency distribution is used to characterize the frequency domain statistical characteristics of the crossing event. Preliminary representation whether the event occurs.

[0014] Step 4, the time domain statistical characteristic value of the signal segment in the sliding window is calculated by using a smaller sliding window to analyze the signal segment of the crossing event, and the optimal signal is extracted;

[0015] The time domain characteristics that can characterize the energy of the forward scattering signal are selected, which can realize the preliminary judgment of the relative position relationship between the target and the baseline when the target crosses.

[0016] Step 5, the optimal signal obtained in step 4 is used to estimate the Doppler slope of the target crossing;

[0017] Step 6, the optimal signal obtained in step 4 is used to estimate the target crossing time.

[0018] The following technical effects can be achieved by adopting the present application

[0019] 1. The present application provides a forward scattering radar echo parameter extraction method based on GNSS, which can be applied to target detection of the forward scattering radar network.

[0020] 2. The present application proposes to use time and frequency domain statistical characteristics to describe the target crossing characteristics, which can realize the preliminary judgment of the relative position relationship between the target and the baseline.

[0021] 3. The present application can realize the Doppler slope estimation of the target crossing of the forward scattering radar echo and the target crossing time estimation.

[0022] 4. The present application can be popularized to the forward scattering radar network of different platforms such as ground, sea and air. DETAILED DESCRIPTION

[0023] Figure 1 The flow chart of the forward scattering signal extraction in the embodiment of the present application.

[0024] Figure 2 The schematic diagram of the three-dimensional space target crossing forward scattering area in the embodiment of the present application.

[0025] Figure 3 The signal detection flow chart based on time-frequency distribution Rényi entropy in the embodiment of the present application.

[0026] Figure 4 Figure for performance analysis of the SPWVD-based Renyi entropy detection method in the simulation example of the present application.

[0027] Figure 5 Figure for results of the difference value of the frequency domain feature of the forward scattering signal in the simulation example of the present application.

[0028] Figure 6 Figure for results of the difference value of the time domain feature of the forward scattering signal in the simulation example of the present application.

[0029] Figure 7 Figures (a), (b) and (c) are simulation result figures of target crossing Doppler slope estimation in the simulation example of the present application.

[0030] Figure 8 Figure is an estimation simulation result figure in the matching filter two-dimensional search method in the simulation example of the present application.

[0031] Figure 9 Figure is a target crossing time estimation simulation result figure in the simulation example of the present application.

[0032] Figure 10 Figure is a flow chart of the method of the present application. DETAILED DESCRIPTION

[0033] In order to better understand the technical solutions of the present application, the following describes the present application in conjunction with the accompanying drawings. Figures 1-10 The embodiments of the present application are further described.

[0034] The present application is a forward scattering radar echo parameter extraction method based on GNSS, which comprises the following specific steps: Figure 10

[0035] Step one, forward scattering signal extraction

[0036] First, the receiver radio frequency front end completes a series of mixing, filtering, down-conversion and sampling quantization operations on the received signal to obtain an intermediate frequency signal. Taking the Beidou system as an example, the Beidou is a code division multiple access system, and the signals radiated by multiple satellites use the same frequency, so it is necessary to determine the satellite number corresponding to the received signal, search the approximate carrier frequency and pseudo code phase of the signal, and this process is called signal acquisition. Then, the signal is tracked to further obtain more accurate estimates of the carrier frequency and pseudo code phase. After realizing carrier synchronization and pseudo code synchronization, the signal is de-carriered and code-correlated, and the in-phase (I) integrator of the tracking loop starts to output data bits (navigation message), the output amplitude of which is modulated by the forward scattering echo. After the navigation message is filtered out, the forward scattering signal is obtained. The extraction process is shown in Figure 1

[0037] The forward scattering signal is represented as: ​​

[0038]

[0039] Among them, U tg (t) is the target echo amplitude, which depends on the target shape and target position, R T (t) and R R (t) represents the distance from the target to the transmitter and receiver, R D (t) is the distance between the satellite and the receiver, is the scattering phase of the target, and f is the carrier frequency.

[0040] The flat plate target in the FSR baseline coordinate system is as follows Figure 2 As shown, the receiver is located at the origin and the transmitter is located on the y-axis. The target trajectory is parallel to the xOy plane, so the z-axis is perpendicular to the target trajectory and the baseline. The distance from the intersection of the target trajectory projection on the xOy plane and the baseline to the origin is d R The three-dimensional position coordinates of the rectangular target in the baseline coordinate system are (x(t), y(t), z P ), where z P is the height of the target relative to the xOy plane, and is also the shortest distance from the target trajectory to the baseline. The angle between the target trajectory projection and the baseline is θ t Angle α h , α v and β h , β v Represents the azimuth and elevation of the target relative to the receiver and transmitter respectively.

[0041] In the baseline coordinate system, the expression of the forward scattered signal is

[0042]

[0043] Where λ is the signal wavelength, K r ' is the Doppler slope in Hz / s, expressed as

[0044]

[0045] Step 2: Use the Rényi entropy detection method based on SPWVD to determine whether there is a target scattered signal

[0046] The decision criterion is expressed as

[0047]

[0048] Where P is the sampling time, Q is the sampling frequency, α>0 is the order of Rényi entropy, C s (p,q) is the time-frequency distribution corresponding to the signal, ∑ p' ∑ q'C(p',q') is the sum of the time-frequency distribution results, p' and q' are the coordinate variables of the time-frequency distribution horizontal and vertical axes respectively, and η is the decision threshold.

[0049] For a large enough sampling time number P and sampling frequency number Q, according to the central limit theorem, X approximately obeys a normal distribution with mean m and variance σ 2 . Given the false alarm probability P f , the decision threshold is

[0050] η = σQ -1 (P f ) + m (5)

[0051] Where Q(x) is the right tail probability function of a random variable obeying N(0, 1) distribution.

[0052] The detection probabilities under various time-frequency distributions are compared, and a signal detection method based on the Rényi entropy of SPWVD is proposed, as shown in the flowchart Figure 3 . If there is a target echo, step three is performed.

[0053] Step three, analyze the frequency domain characteristics of each signal segment using a sliding window to determine whether a target crossing baseline event occurs

[0054] By sliding window, the signal segment is intercepted, and the frequency domain characteristic values of each signal segment are calculated, including the center of gravity frequency, mean square frequency and frequency variance, as shown in Table 1 below. Find the signal segment whose frequency domain characteristic value is closest to zero frequency, if the frequency domain characteristic values of the signal segments on both sides show an increasing trend, it can be considered that the signal segment corresponds to the time period when the target crossing event occurs. The frequency domain characteristic value calculation can be used as a new method to determine whether a target crossing baseline event occurs.

[0055]

[0056] Table 1 Frequency domain characteristic values Note: P(f) is the signal power spectrum

[0057] Step four, use a smaller sliding window to analyze each signal segment for the crossing event, extract the optimal signal, and calculate the time domain statistical characteristic values of each signal segment

[0058] After finding the signal segment where the crossing event occurs, further subdivide the time period, and use the sliding window to find the signal segment where the instantaneous frequency curve is symmetric about the zero frequency center. The amplitude of this signal segment is modulated by the RCS peak region, which maximizes the signal-to-noise ratio and is the optimal signal. This optimal signal finding method can improve the reliability of the parameter estimation value of the target crossing baseline signal segment, and provides a supplement to the preprocessing process before signal parameter estimation.

[0059] Define the minimum distance between the target crossing baseline and the baseline as z P , zP The value of z will affect the signal phase and signal amplitude, therefore, the time domain characteristic value describing the signal energy and amplitude is used to describe the shortest distance z between the target and the baseline when the target crosses the baseline P The time domain characteristic value is shown in Table 2.

[0060]

[0061] Table 2 Note: is the average value, x n represents the amplitude of the signal at time n, and N is the number of signal sampling points

[0062] The forward scattering signal of a specific aircraft target crossing the baseline under different conditions can be obtained in advance, and the frequency domain and time domain characteristic values are calculated to construct a characteristic database, which provides support for the state judgment of the actual target crossing the baseline.

[0063] Step five, using the obtained optimal signal to estimate the Doppler slope of the target crossing

[0064] The instantaneous frequency of the forward scattering signal changes linearly. First, the SPWVD of the forward scattering signal is calculated, and the frequency corresponding to the maximum value of the spectrum at each time is taken as the estimated value of the instantaneous Doppler frequency. Second, the Doppler slope can be obtained by linear fitting, or the parameter estimation can be realized by using Radon transform (or other transform can be used instead) based on time-frequency analysis, the essence of which is to extract the linear feature of the forward scattering signal in the time-frequency distribution. Further, a two-dimensional search method based on the matching filter idea can be used to select an appropriate step size to obtain a high-precision estimate of the Doppler slope. In a certain interval, a reference signal is generated with a suitable Doppler slope step size, and the initial phase range is set to 0-360°. By using a two-dimensional search method, a high-precision estimate value is obtained. Assuming that the initial estimate value of the Doppler slope is K', the search range is set to [K' -5 , K' +5 ], and the step size can be selected according to the requirement.

[0065] The matching signal is constructed based on the Doppler slope and the initial phase as follows:

[0066]

[0067] wherein K is the Doppler slope of the reference signal, and is the initial phase of the reference signal.

[0068] The matching filter can be expressed as

[0069]

[0070] wherein θ is the parameter to be estimated, T s is the duration of the signal x(t), and Sref (t, θ) is a reference signal constructed according to a signal model.

[0071] Step six, using the obtained optimal signal, target crossing time estimation is carried out

[0072] After confirming that the shortest distance between the target and the baseline meets the requirement of the crossing time estimation accuracy, the time point when the Doppler frequency is zero can be considered as the target crossing baseline time.

[0073] For the crossing time estimation, the following methods can be adopted:

[0074] 1. Obtain the instantaneous Doppler frequency through SPWVD, and the time point closest to zero frequency is regarded as the target crossing baseline time;

[0075] 2. Obtain the instantaneous Doppler frequency through SPWVD, and the time point corresponding to the zero frequency is regarded as the target crossing time by using the instantaneous frequency fitting method;

[0076] 3. Obtain the instantaneous Doppler frequency through SPWVD, and the time point closest to zero frequency on the straight line estimated by Hough transform in the time-frequency graph is regarded as the target crossing baseline time.

[0077] The effect of the present application can be illustrated by simulation experiments, and the simulation parameter settings are shown in Table 3. The detection probability under different signal-to-noise ratios is shown in Table 3 by using the forward scattering signal expression (2). It can be seen that the Rényi entropy detection method based on SPWVD has good detection performance. Figure 4

[0078]

[0079]

[0080] Table 3 Forward scattering signal simulation parameters

[0081] Secondly, the frequency domain characteristic values of each signal segment are analyzed by using a sliding window, the duration of each signal segment is set to 0.4s, the sliding window length is 0.04s, the target moves vertically to the baseline, z P =0, and it is assumed that the vertical distance from the midpoint of the target trajectory to the baseline is d, which changes in the range of [-50, +50]m, and the positive and negative signs are used to distinguish the left and right sides of the baseline. It can be known that when d=0, the target trajectory is symmetric about the baseline, and the signal frequency should be most concentrated at zero frequency. The characteristic difference value is defined as

[0082] FVD=10log 10 (FF / FF0) (8)

[0083] ​Among them, FF is the frequency domain eigenvalue obtained by the current calculation, and FF0 is the frequency domain eigenvalue when the target trajectory is symmetric about the baseline (d=0), corresponding to Table 1.

[0084] Figure 5 The frequency domain feature difference values ​​under different conditions are shown. When the target trajectory is not symmetrical about the baseline, the frequency domain features of the forward scattered signal are quite different. This feature can be used to find a more symmetrical signal to maximize the signal energy. The frequency domain feature values ​​proposed in this method can well distinguish signals under different parameters.

[0085] Next, the Monte Carlo simulation is performed 1000 times to calculate z P = 0:1:100m when the time domain feature difference value, such as Figure 6 The feature difference value is defined as

[0086] FVD=10log 10 (TF / TF0) (9)

[0087] Among them, TF is the time domain eigenvalue obtained by current calculation, TF0 is the target crossing baseline (z P =0), corresponding to Table 3. The farther the FVD value is from zero, the greater the difference.

[0088] It can be seen that for general aircraft targets, it can be considered that z P When the distance is less than 40m, the time domain eigenvalue changes monotonically, and this characteristic can be used to achieve a preliminary analysis of the relative position relationship between the target motion trajectory and the baseline.

[0089] The Doppler slope estimation result is as follows: Figure 7 (a), (b), (c) and Figure 8 As shown, Figure 7 (a) is the SPWVD result diagram of the forward scattered signal; Figure 7 (b) is the instantaneous frequency fitting result, Figure 7 (c) shows the Doppler slope estimation result using the Hough transform. Using the Doppler slope estimate obtained using the Hough transform as the initial value, the interval is divided into 300 intervals with a step size of 0.0334 Hz / s. The estimated result is 33.0031 Hz / s, with a relative error of (33.0344 - 33.0031) / 33.0344 = 0.095%, demonstrating high estimation accuracy.

[0090] Using method 3 in step 6, we can get the time corresponding to zero frequency, such as Figure 9 As shown, the estimated value of the crossing time is -0.002s, which can achieve a high estimation accuracy, and the error level of the crossing time estimation is on the order of milliseconds.

[0091] Based on the above, the feasibility of the GNSS-based forward scattering radar echo parameter extraction method proposed in the application can be proved.

Claims

1. A GNSS-based forward scattering radar return parameter extraction method, characterized in that: The method comprises: Step 1, forward scattering signal extraction; Step 2, using a SPWVD-based Renyi entropy detection method to determine whether the forward scattering signal obtained in step 1 contains a target scattering signal; Step 3, using a sliding window to analyze the frequency domain characteristics of each signal segment of the target scattering signal obtained in step 2 to determine whether a target baseline crossing event occurs; Step 4, using a smaller sliding window to analyze the signal segment by segment for the signal segment in which the baseline crossing event occurs, calculating the time domain statistical characteristic value of the signal segment in the sliding window, and extracting an optimal signal; Step 5, using the optimal signal obtained in step 4 to estimate the target crossing Doppler slope; Step 6, using the optimal signal obtained in step 4 to estimate the target crossing time; In step 4, the optimal signal is extracted by selecting a time domain characteristic capable of describing the energy size of the forward scattering signal to preliminarily determine the relative position relationship between the target crossing time and the baseline; after finding the signal segment in which the crossing event occurs, the time period is further subdivided, and a signal segment in which the instantaneous frequency curve is symmetric about the zero frequency center is found by using the sliding window, the amplitude of the signal segment is modulated by the RCS peak value region, and the signal-to-noise ratio is maximized to obtain the optimal signal; Define the minimum distance between the target crossing the baseline and the baseline as z P , z P The value of z will affect the signal phase and signal amplitude, therefore, the time domain characteristic value describing the signal energy and amplitude size is used to characterize the minimum distance z P between the target crossing the baseline and the baseline, and the time domain characteristic value is as follows: Maximum: x max = max(x n ); Minimum: x min = min(x n ); Peak-to-Peak: x p = max(x n ) - min(x n ); Mean: Variance: Standard Deviation: Root Mean Square: wherein is the average value, x n denotes the amplitude of the signal at time n, N is the number of signal samples; In step 5, the instantaneous frequency of the forward scattering signal changes linearly; first, the SPWVD of the forward scattering signal is calculated, and the frequency corresponding to the maximum value of the frequency spectrum at each time is taken as the instantaneous Doppler frequency estimation value; second, the Doppler slope is obtained by linear fitting, or the Radon transform is used to realize parameter estimation on the basis of time-frequency analysis to extract the straight line feature of the forward scattering signal in the time-frequency distribution; a two-dimensional search method based on the matching filter idea is adopted, an appropriate step size is selected, and a high-precision estimation value of the Doppler slope is obtained; the initial phase range is set to 0-360°, and a high-precision estimation value is obtained by two-dimensional search; let the initial estimation value of the Doppler slope be K', the search range be set to [K'-5, K'+5], and the step size be selected according to requirements; The matching signal is constructed based on the Doppler slope and the initial phase as follows: wherein K is the Doppler slope of the reference signal, is the initial phase of the reference signal; The matching filter is represented as: where θ is the parameter to be estimated, T s is the duration of the signal x(t), S ref (t, θ) is a reference signal constructed according to the signal model.

2. The GNSS-based forward-scattering radar return parameter extraction method of claim 1, wherein: The forward scattering signal extraction has the following specific process: First, the receiver RF front end performs mixing, filtering, down-conversion and sampling quantization operations on the received signal to obtain an intermediate frequency signal; then, the signal is tracked to further obtain more accurate estimation values of the carrier frequency and the pseudo-code phase; after carrier synchronization and pseudo-code synchronization, the signal is de-carrier and code-correlated, and the in-phase (I) integrator of the tracking loop starts to output data bits, i.e., the navigation message; the output amplitude of the navigation message is modulated by the forward scattering echo, and the forward scattering signal is obtained after the navigation message is filtered out.

3. The GNSS-based forward-scattering radar return parameter extraction method of claim 1, wherein: The specific process of step two is as follows: The decision criterion is represented as where P is the number of sampling time, Q is the number of sampling frequency, α>0 is the order of Rényi entropy, C s (p,q) is the time-frequency distribution corresponding to the signal, ∑ p' ∑ q' C(p',q') is the sum of time-frequency distribution results, p' and q' are the coordinate variables of the horizontal axis and the vertical axis of the time-frequency distribution respectively, and η is a decision threshold. For a sufficiently large number of samples P and a sufficiently large sampling frequency Q, according to the central limit theorem, X is approximately normally distributed with mean m and variance σ 2 ; given a false alarm probability P f , the decision threshold is η = σQ -1 (P f )+m Wherein, Q(x) is the right tail probability function of a random variable subject to N(0, 1) distribution.

4. The GNSS-based forward-scattering radar return parameter extraction method of claim 1, wherein: The frequency domain characteristics include the center of gravity frequency, the mean square frequency and the frequency variance; the signal segment in which the frequency domain characteristic value is closest to zero frequency is found, and if the frequency domain characteristic values of the signal segments on both sides show an increasing trend, it is considered that the signal segment corresponds to the time period in which the target crossing event occurs.

5. The GNSS-based forward-scattering radar return parameter extraction method of claim 1, wherein: The crossing moment estimation takes the following methods: 1) Obtain the instantaneous Doppler frequency by SPWVD, and the moment closest to zero frequency is regarded as the target crossing baseline moment; 2) Obtain the instantaneous Doppler frequency by SPWVD, and the moment corresponding to zero frequency is regarded as the target crossing moment by using the instantaneous frequency fitting method; 3) Obtain the instantaneous Doppler frequency by SPWVD, and the moment closest to zero frequency on the straight line is regarded as the target crossing baseline moment by using the Hough transform to estimate the straight line in the time-frequency graph.

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