Distance or Doppler migration compensation method based on Bayesian trajectory reasoning

Abstract

The invention relates to the field of array signal processing, in particular to a distance / Doppler migration compensation method based on Bayesian trajectory reasoning in long-time coherent accumulation processing. According to the method, firstly, the distance frequency of a pulse compression echo signal is overturned, so that a time-frequency signal describing the motion trail of multiple targets to be detected in a slow time dimension can be extracted from inverse Fourier transform obtained by multiplying an echo signal which is not overturned and an overturned echo signal; secondly, taking each target motion trail in the time-frequency signal as a state variable, taking the obtained time-frequency signal as observation, and establishing a state space model of the multi-target motion trail; and finally, a fast-slow time dimension combined two-dimensional matched filter can be constructed according to a target motion track inferred by Bayesian filtering so as to compensate unknown distance and / or Doppler migration caused by high-speed / maneuvering motion of the target. The invention provides a new method for detecting the moving target.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and particularly to a method for compensating range or Doppler migration based on Bayesian trajectory inference in long-time coherent integration processing. Background Art

[0002] To improve the detection ability of a radar for a target, coherent integration of echo signals is proven to be an effective method both theoretically and in practice. The moving target detection method is the most commonly used method in coherent processing. This method can achieve the focusing of echo energy in the Doppler domain through Fourier transform in the slow time dimension, and improve the signal-to-noise ratio of detection. However, in practical applications, such as when a pulsed Doppler radar detects a maneuvering target, during the long-time integration process, the target may cross range cells, causing range migration; the variable-speed motion of the target may also lead to Doppler frequency migration. These two problems will greatly reduce the gain of coherent integration. In addition, in recent years, with the rapid development of autonomous driving technology, the requirements for vehicle-mounted radars are getting higher and higher, and the joint processing of multiple pulse echo signals is also an important part of improving radar performance. However, in a vehicle-mounted radar system, since the target distance to be detected is relatively close to the radar and the radar has a high range resolution, this makes it possible for relatively slow ground targets to also generate relatively complex range / Doppler migration.

[0003] For the linear range migration caused by motion, the two most common processing methods are the Keystone transform and the Radon Fourier transform. The Keystone transform decouples the coupling relationship between the fast and slow time dimension frequencies through interpolation to compensate for the linear range migration in the target echo. The RFT compensates for range migration through joint search of range-velocity. However, they both ignore the possible acceleration motion of non-cooperative targets, so they cannot compensate for range and / or Doppler migration simultaneously.

[0004] To compensate for range and Doppler migration caused by high-order motion of a target, a series of improved algorithms have been reported in the literature in recent years. Theoretically, when the motion of the target can be accurately described by a third-order polynomial, the GRFT estimates the motion trajectory of the target through joint search in the four-dimensional motion parameter space of the target and achieves coherent integration. However, such a complex search process is almost impossible to implement in practice. To reduce the complexity, the Radon transform and the improved high-order LV distribution method have been proposed in recent years. However, these improved methods still require a multi-dimensional parameter joint search with a huge amount of computation.

[0005] In recent years, in view of the problem of high complexity of multi-dimensional search, some non-search algorithms have been reported in the literature, such as adjacent cross-correlation function, time reversal-nonparametric resampling sparse long-time coherent accumulation, etc. These algorithms generally rely on a carefully designed autocorrelation function and combine signal parameter estimation algorithms such as LV distribution to obtain the parameters describing the target polynomial motion model. However, these algorithms still require the maneuvering target to satisfy the strict assumption of third-order motion.

[0006] It is not difficult to find through the literature that the existing literature reports on range or Doppler migration calibration methods, either with high computational complexity, or with serious cross-term problems, or based on strong target maneuvering model assumptions. Summary of the Invention

[0007] The present invention is made to solve the above problems, and aims to provide a method that can compensate for range / Doppler migration in radar detection and has relatively lower computational complexity. The present invention adopts the following technical solutions:

[0008] The present invention provides a method for compensating range or Doppler migration based on Bayesian trajectory inference, which is characterized by including the following steps: Step S1, obtaining the range frequency of the echo signal of the radar after pulse compression; Step S2, flipping the range frequency of the echo signal after pulse compression, and extracting the slow-time dimension time-frequency signal from the inverse Fourier transform of the multiplication of the non-flipped and flipped echo signals; Step S3, taking each target motion trajectory in the slow-time dimension time-frequency signal as a state variable and the slow-time dimension time-frequency signal as an observation input model, thereby constructing a state space model of multi-target motion trajectories; Step S4, based on the state space model, inferring the target motion trajectory through Bayesian filtering; Step S5, based on the target motion trajectory, constructing a two-dimensional matched filter that combines the fast-slow time dimensions to compensate for the unknown range and / or Doppler migration caused by the high-speed / maneuvering motion of the target.

[0009] The method for compensating range or Doppler migration based on Bayesian trajectory inference provided by the present invention may also have the following technical features, wherein in Step S1, the echo signal is obtained by a pulsed Doppler radar after pulse compression within a coherent processing interval composed of M transmitted pulses, and the formula is expressed as:

[0010]

[0011] where r k (t m ) and are respectively the radial distance of the kth target and the amplitude after pulse compression; t, t mare the fast time and the slow time respectively, f0 is the carrier frequency, c is the speed of light in vacuum; sin c(x) = sin(πx) / (πx). Generally, r k (t m ) can be described as:

[0012] r k (t m ) = k，0 +Δr k (t m )

[0013] where r k,0 is the initial position of the target; Δr k (t m ) is the continuous distance increment of the target varying with the slow time. Among them, when the change amount Δr k (t m )(k = 1, 2,..., K) is greater than the range resolution, it will cause the range migration phenomenon; at the same time, when Δr k (t m )(k = 1, 2,..., K) changes non-linearly, it may cause the Doppler migration phenomenon. In step S2, the echo signal is subjected to Fourier transform, and the echo signal is transformed into the range frequency - slow time domain, expressed as:

[0014]

[0015] In the formula, f ∈ [-f s / 2, -f s (N - 1) / 2N,...., f s / 2] is the range frequency unit, f s is the sampling frequency, N represents the number of samplings in the fast time dimension, represents the amplitude of the k-th target in the frequency domain. Then, the echo signal is flipped up and down with 0 frequency as the center to obtain:

[0016]

[0017] Then, the unflipped echo signal is multiplied by the flipped echo signal and then subjected to inverse Fourier transform to obtain:

[0018]

[0019] In the formula, s self (τ, t m ) and s cross (τ, t m ) represent the auto-term and cross-term of the signal respectively.

[0020] Finally, the extracted slow-time dimension time-frequency signal is expressed as:

[0021]

[0022] wherein, is the amplitude of the k-th target; is the phase factor of this target.

[0023] The distance or Doppler migration compensation method based on Bayesian trajectory inference provided by the present invention may also have the following technical feature: wherein, the spatial model expression in step S3 is as follows:

[0024]

[0025] The distance or Doppler migration compensation method based on Bayesian trajectory inference provided by the present invention may also have the following technical feature: wherein, step S5 further includes the following sub-steps: step S5-1, there is a phenomenon of velocity ambiguity in the target motion, and the velocity ambiguity phenomenon is processed by means of fuzzy integers to obtain the correct target motion trajectory; step S5-2, a corresponding two-dimensional filter is matched based on the target motion trajectory, and through dot product calculation, the processed filtered signal is obtained; step S5-3, the processed filtered signal is first transformed into the fast-time domain, and then transformed into the slow-time domain for Fourier transform, so as to obtain the relevant parameters for compensating the unknown distance and / or Doppler migration brought by the high-speed / maneuvering motion of the target.

[0026] The distance or Doppler migration compensation method based on Bayesian trajectory inference provided by the present invention may also have the following technical feature: wherein, in step S5-1, for the K-th target, the trajectory function corresponding to the fuzzy integer p is:

[0027]

[0028] The distance or Doppler migration compensation method based on Bayesian trajectory inference provided by the present invention may also have the following technical feature: wherein, in step S5-2, the corresponding filter expression is as follows:

[0029]

[0030] Step S5-3, the processed filtered signal is first transformed into the fast-time domain, and then subjected to slow-time dimension Fourier transform, so as to obtain the relevant parameters for compensating the unknown distance and / or Doppler migration brought by the high-speed / maneuvering motion of the target. Specifically, after is multiplied by S(f,t m ), the obtained signal can be transformed into the fast-time domain, and then slow-time dimension Fourier transform is performed to obtain:

[0031]

[0032] In the formula, represents the residual remaining after compensating for the range migration; represents the output amplitude of the k-th target; represents the influence from the remaining components. And represents the normalized Doppler frequency. Thus, the output range focusing distribution is:

[0033]

[0034] In this way, the joint estimation of the target position and the ambiguity constant is:

[0035]

[0036] Correspondingly, the estimation of the instantaneous velocity is:

[0037]

[0038] wherein, v b = c / 2f0T r represents the blind velocity; is the ambiguous velocity. Generally speaking, the search range of the ambiguity integer is limited, so the above process can compensate for the range migration with a reasonable computational complexity.

[0039] Function and Effect of the Invention

[0040] According to the range or Doppler migration compensation method based on Bayesian trajectory inference of the present invention, since the motion trajectory of a maneuvering target is inferred using Bayesian trajectory inference, and a two-dimensional matched filter jointly in the fast-slow time dimension is constructed thereon to compensate for the unknown range and / or Doppler migration caused by the high-speed / maneuvering motion of the target, a new method for detecting a maneuvering target by Bayesian trajectory inference is provided; the present invention realizes the calibration of range or Doppler migration and coherent cumulative target detection of a maneuvering target in the manner of Bayesian trajectory inference, without the need for a three-dimensional and above parameter search with huge complexity, and has practical value; the algorithm of the present invention can also handle targets with unknown motion forms and process various forms of radar systems, so it has practical application value in occasions such as detecting or identifying non-cooperative maneuvering targets with unknown motion forms. Description of the Drawings

[0041] Figure 1 is a schematic flow chart of the range or Doppler migration compensation method based on Bayesian trajectory inference in an embodiment of the present invention;

[0042] Figure 2 is a schematic algorithm flow chart of the range or Doppler migration compensation method based on Bayesian trajectory inference in an embodiment of the present invention;

[0043] Figure 3 It is a schematic diagram of the result of pulse compression in an embodiment of the present invention;

[0044] Figure 4 It is a STFT schematic diagram of the slow-time dimension signal in an embodiment of the present invention;

[0045] Figure 5 It is a schematic diagram of the instantaneous velocity correlation result based on STFT in an embodiment of the present invention;

[0046] Figure 6 It is a schematic diagram of the instantaneous velocity estimation result of the frame inference in an embodiment of the present invention;

[0047] Figure 7 It is a schematic diagram of the coherent integration detection result of MDT in an embodiment of the present invention;

[0048] Figure 8 It is a schematic diagram of the coherent integration detection result of the algorithm in an embodiment of the present invention;

[0049] Figure 9 It is a schematic diagram of the radar simulation parameters in an embodiment of the present invention;

[0050] Figure 10 It is a schematic diagram of the radar simulation target parameters in an embodiment of the present invention. Specific implementation manner

[0051] In order to make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the distance or Doppler migration compensation method based on Bayesian trajectory inference of the present invention will be specifically described below in conjunction with embodiments and drawings.

[0052] <Embodiment>

[0053] This embodiment provides a distance or Doppler migration compensation method based on Bayesian trajectory inference, and the radar types targeted include but are not limited to pulse Doppler radar, vehicle-mounted frequency modulated continuous wave radar, vehicle-mounted millimeter wave radar, inverse synthetic aperture radar, etc. The characteristic is to infer the motion trajectory of the Bayesian trajectory inference mobile target, and on this basis, construct a two-dimensional matched filter for the joint fast-slow time dimension to compensate for the unknown distance or Doppler migration caused by the high-speed or mobile motion of the target. The following will specifically illustrate its implementation steps taking the pulse Doppler radar as an example.

[0054] Figure 1 It is a schematic diagram of the process of the distance or Doppler migration compensation method based on Bayesian trajectory inference in an embodiment of the present invention.

[0055] As Figure 1 shown, the distance or Doppler migration compensation method based on Bayesian trajectory inference includes the following steps:

[0056] Step S1, obtain the range frequency of the echo signal of the radar after pulse compression;

[0057] Step S2, slow-time dimension signal extraction: Flip the range frequency of the echo signal after pulse compression, and extract the time-frequency signal (hereinafter simply referred to as the slow-time dimension time-frequency signal) describing the motion trajectories of the multiple targets to be measured from the inverse Fourier transform of the multiplication of the un-flipped and flipped echo signals.

[0058] In this embodiment, through a pulsed Doppler radar within a coherent processing interval composed of M transmitted pulses, after pulse compression (PC), the two-dimensional received echo signal can be expressed as:

[0059]

[0060] where, represents the amplitude of the k-th target after pulse compression, t, t m are the fast time and slow time respectively, f0 is the carrier frequency, c is the speed of light in vacuum, r k,0 is the initial position of the target, Δr k (t m ) is the increment of the motion trajectory of the target, which can be any continuous function, such as: a certain third-order polynomial where: the coefficients of each term represent the velocity, constant acceleration, and jerk acceleration of the k-th moving target respectively.

[0061] It can be seen from Equation (1) that when the motion trajectory Δr k (t m ) (k = 1, 2,..., K) is greater than the range resolution, range migration phenomenon will occur; at the same time, when Δr k (t m ) (k = 1, 2,..., K) changes non-linearly, Doppler migration may occur.

[0062] Perform Fourier transform (FT) on Equation (1), that is, transform the signal to the range-frequency versus slow-time domain to obtain:

[0063]

[0064] In the formula, f ∈ [-f s / 2, -f s (N - 1) / 2N,...., f s / 2] is the range frequency unit, f sis the sampling frequency, and N represents the number of samplings in the fast time dimension. represents the amplitude of the k-th target in the frequency domain. Then, the two-dimensional signal in the formula is flipped up and down with the 0 frequency as the center to obtain:

[0065]

[0066] Subsequently, the unflipped echo signal is multiplied by the flipped echo signal S(f, t m ) and then subjected to the Inverse Fourier Transform (IFT) to obtain:

[0067]

[0068] where s self (τ, t m ) and s cross (τ, t m ) represent the auto-term and cross-term of the signal respectively, and the expressions are:

[0069]

[0070]

[0071] Among them, a k represents the amplitude of the auto-term of the k-th target; b k，ρ represents the amplitude of the cross-term between the k-th and ρ-th targets, and B represents the bandwidth of the waveform signal.

[0072] From the above analysis, it can be seen that: in the signal s2(τ, t m ), there is only and exactly s self (τ, t m ) concentrated near t = 0, then there is:

[0073]

[0074] Among them, is the amplitude of the k-th target; is the phase factor of this target. It can be found that: Equation (6) is only the time-frequency signal related to multi-target motion in the slow time dimension.

[0075] Step S3, Bayesian trajectory inference: Regarding the motion trajectories of the respective targets in the slow time dimension time-frequency signal as state variables, and using the slow time dimension time-frequency signal as the object of observation and speculation to input into the model, thereby constructing a state space model of the multi-target motion trajectory;

[0076] In this embodiment, in order to facilitate the description of the relevant content of Bayesian trajectory inference, a variable is introduced:

[0077]

[0078] The state transition model of the phase in Equation (7) is as follows:

[0079]

[0080] where Dg(l) (l = 1, 2, …, L) are the coefficients of a finite impulse response (FIR) filter, and L represents the number of taps of the filter; denotes the state transition matrix. In addition, when the amplitude in Equation (6) is described using a random walk model, it can be written as:

[0081]

[0082] where denotes the instantaneous amplitude at time t m ; ζ a (t m-1 ) is Gaussian noise with zero mean and its covariance is If it is assumed that the target amplitude and phase in Equation (6) are independent of each other, then there is the following equation:

[0083] x k (t m ) = Fx k (t m-1 ) + ζ k (t m-1 ) , (10)

[0084] where denotes the joint state vector; denotes the following state transition matrix:

[0085]

[0086] is the error when using a piecewise low-order polynomial to approximate the model in Equation (6). This error represents Gaussian noise with zero mean, and its covariance matrix is a diagonal matrix where σ l , l = 1, 2,...., L is the perturbation intensity of the signal phase. In summary, Equation (6) can be described by the following state space model:

[0087]

[0088] In the formula, η(t m ) is measurement noise with zero mean, and y(t m ) represents the observation of the time-frequency signal in Equation (6).

[0089] After establishing the state space model of the multi-target motion trajectory, a filtering algorithm based on non-linear Bayesian inference, such as the Extended Kalman Filter (EKF) or the Unscented Kalman Filter (UKF), can be used to infer the state space model.

[0090] In addition, considering that the number of targets in the target echo is generally unknown, the method based on Sparse Iterative Covariance-based Estimation (SPICE) is used in this embodiment. First, SPICE will solve the following problem of Weighted Covariance Fitting (WCF):

[0091]

[0092] where represents the first D << M observed data of the slow-time dimension signal in Equation (3), which can generally be considered approximately stationary, meaning that y0 can be described by a line spectrum model at this time; ||×|| F represents the Frobenius norm of the matrix. The covariance matrix R of the observation is modeled as:

[0093]

[0094] where are the model parameters of the covariance. When I is the number of discretized frequency points, represents the steering matrix of its frequency, and each column is the steering vector of the discrete frequency w i ; is the noise vector of the observation.

[0095] SPICE can be solved by an iterative algorithm. When the algorithm converges or reaches the preset number of iterations, the fitted covariance can be obtained from Equation (14) Based on this covariance, using methods such as the Discriminant Functions Estimator (DFE), the estimated value K of the number of observed targets in Equation (10) can be obtained.

[0096] It can also be found from Equation (14) that: when the covariance estimation is completed, q s = [q1, q2,..., q I T is the power spectrum of the signal. This also means that: K targets correspond to the K largest local peaks in qs. Let and represent the estimates of the k-th target amplitude and frequency respectively, then the estimates of the k-th target initial amplitude and phase factor are respectively:

[0097]

[0098]

[0099] Considering the relationship of each phase in the state vector x k (t1) as follows:

[0100] 2(θ k (t 1-(l-1) ) - θ k (t 1-l )) = ω k (t1)T r , 1 = 1, ..., L (17)

[0101] Taking θ k (t1) = 0, the initial values of each phase in x k (t1) can be obtained by the recurrence relation of Equation (17).

[0102] Step S4, based on the state space model, infer the target motion trajectory through Bayesian filtering;

[0103] Step S5, range / Doppler migration compensation: Based on the target motion trajectory, construct a two-dimensional matched filter jointly in the fast-slow time dimension to compensate for the unknown range and / or Doppler migration caused by the high-speed / maneuvering motion of the target.

[0104] In this embodiment, step S5 includes the following sub-steps:

[0105] Step S5-1, coherently accumulate the target through a search method to obtain an estimate of the correct target motion trajectory.

[0106] Step S5-2, obtain the corresponding two-dimensional matched filter based on the estimate of the target motion trajectory, and obtain the processed filtered signal by performing dot product calculation with and S(f, t m ).

[0107] Specifically, the motion of the target may cause the phenomenon of velocity ambiguity. In this way, the high-speed motion of the k-th target often causes the phenomenon of velocity ambiguity. Generally, the ambiguity integer is unknown. For this reason, the present invention uses a search method to coherently accumulate the target.

[0108] For the k-th target, the trajectory estimate corresponding to p is

[0109]

[0110] Its corresponding two-dimensional matched filter is:

[0111]

[0112] Step S5-3: First transform the processed filtered signal into the fast time domain, and then perform a slow-time dimensional Fourier transform to obtain the relevant parameters for compensating the unknown range and / or Doppler migration caused by the high-speed / maneuvering motion of the target.

[0113] Specifically, after multiplying with S(f, t m ), the resulting signal is transformed into the fast time domain, and then a slow-time dimensional Fourier transform is performed to obtain:

[0114]

[0115] In Equation (20), represents the residual remaining after compensating for the range migration; represents the output amplitude of the k-th target; represents the influence from the remaining components. And represents the normalized Doppler frequency. Thus, the output range focus distribution is:

[0116]

[0117] In this way, the joint estimation of the target's position and the ambiguity constant is:

[0118]

[0119] Correspondingly, the estimation of the instantaneous velocity is:

[0120]

[0121] where v b = c / 2f0T r represents the blind velocity; is the ambiguous velocity. Generally speaking, the search range of the ambiguity integer is limited, so the above process can compensate for the range migration with a reasonable computational complexity.

[0122] Step S6: Output the motion parameters of the target such as the range and velocity according to the result of the coherent accumulation of the two-dimensional matched filter.

[0123] In this embodiment, the performance of the moving target detection algorithm is verified through simulation experiments.

[0124] Simulation scenario

[0125] The parameters of the simulation system are as follows Figure 9 As shown, assuming the required detection speed range is [-1200 m / s, +1200 m / s], the fuzzy constant search range is [-10, 10].

[0126] In the simulation scenario, when discussing the results of coherent accumulation detection of multiple maneuvering targets, as shown Figure 10 are the parameters of Target 1 and Target 2 that conform to the third-order motion hypothesis.

[0127] The targets that actually need to be detected are generally non-cooperative targets with unknown motion patterns. Therefore, Target 3 with a complex motion model is added in this subsection. The initial position of this target is 6.80 Km, the amplitude is the same as that of Target 1, and the speed parameter v3 = 635 m / s. Its motion trajectory is as follows:

[0128] DR3(t m ) = -2.0sin(3pt m ) + v3t m

[0129] After pulse compression, the signal-to-noise ratio of the echo signal is 6 dB. Considering the complexity of the filtering algorithm and the filtering performance comprehensively, the algorithm in this embodiment takes L = 3, and the UKF is selected as the non-linear filtering algorithm. In the initialization stage of the filter, D = 48 is taken, the number of frequency points in SPICE is taken as I = 512, and the number of iterations is 6. In the experiment, it is assumed that the targets have the same process noise covariance, and the elements on its diagonal are [1e-4, 1e-9, 1e-9, 1e-9].

[0130] Analysis of Simulation Results

[0131] The numerical simulation results are as shown Figures 3 - 8 as follows. Figure 3 is the original echo after pulse compression. At this time, significant intersections appear in the trajectories of multiple targets. Figure 4 is the STFT time-frequency spectrum of the slow-time dimension time-frequency signal. At this time, the strong maneuverability of the targets causes many discontinuous instantaneous velocity ridge lines to appear in the time-frequency spectrum. This makes the instantaneous velocity estimation algorithm based on time-frequency distribution for trajectory association fail. Figure 5 is the instantaneous velocity estimation result obtained based on the STFT time-frequency ridge extraction method; Figure 6 is the instantaneous velocity estimation result obtained based on the present invention. Comparing Figure 5 and Figure 6 it can be seen that: Benefiting from the state space model, when the speed crosses the blind speed period / change trajectory intersection, the algorithm of the present invention can still obtain continuous instantaneous velocity estimation, that is to say, the estimated target motion trajectory is continuous. Figure 7The coherent accumulation detection result obtained by MDT, where the target energy concentration is very poor at this time. To plot the coherent accumulation distribution obtained by the method of the present invention, the present invention defines the following Doppler dimension vector:

[0132]

[0133] where, rem(·) and respectively represent the remainder-taking and integer-taking operations. Subsequently, after taking the outer product of u k with the range focusing distribution with the maximum response, the result as Figure 8 shown is obtained. It can be seen that: all the target energies can be well concentrated near the target point, and the initial velocity estimates are 1002.5 m / s, -969.5 m / s and 616.7 m / s respectively. These simulation experiment results show that for targets with multiple velocity ambiguities, even if their motion trajectories and velocity change curves intersect each other, the algorithm of the present invention can still give good detection results.

[0134] Function and effect of the embodiment

[0135] According to the range or Doppler migration compensation method based on Bayesian trajectory inference of the present invention, since the motion trajectory of a maneuvering target is inferred using Bayesian trajectory inference, and on this basis, a two-dimensional matched filter jointly in the fast-slow time dimension is constructed to compensate for the unknown range and / or Doppler migration brought by the high-speed / maneuvering motion of the target, providing a new method for the detection of maneuvering targets by Bayesian trajectory inference; the present invention realizes the range / Doppler migration calibration of maneuvering targets and coherent cumulative target detection in the way of Bayesian trajectory inference, without the need for parameter search in three dimensions and above with huge complexity, and has practical value; the algorithm of the present invention can also cope with targets with unknown motion forms and process various forms of radar systems, so it has practical application value in occasions such as detecting / identifying non-cooperative maneuvering targets with unknown motion forms.

[0136] To evaluate the performance of the moving target detection algorithm proposed by the present invention, simulation experiments were carried out in this embodiment. The above simulation experiment results show that for targets with multiple velocity ambiguities, even if their motion trajectories and velocity change curves intersect each other, the algorithm of the present invention can still give good detection results.

[0137] The above embodiments are only used to illustrate the specific implementation manners of the present invention, and the present invention is not limited to the description scope of the above embodiments.

Claims

1. A distance or Doppler migration compensation method based on Bayesian trajectory inference, characterized in that, It includes the following steps: Step S1: Obtain the range frequency of the echo signal of the radar after pulse compression. Step S2: Flip the range frequency of the echo signal after pulse compression, and extract the slow-time dimension time-frequency signal from the inverse Fourier transform of the multiplication of the unflipped and flipped echo signals. Step S3: Use each target motion trajectory in the slow-time dimension time-frequency signal as a state variable, and the slow-time dimension time-frequency signal as an observation input model, thereby constructing a state space model for multi-target motion trajectories. Step S4: Based on the state space model, infer the target motion trajectory through Bayesian filtering. Step S5: Based on the target motion trajectory, construct a two-dimensional matching filter for the joint fast-slow time dimension to compensate for the unknown range and / or Doppler migration caused by the high-speed / maneuvering motion of the target.

2. The range or Doppler migration compensation method based on Bayesian trajectory inference according to claim 1, characterized in that: Among them, In step S1, the echo signal is obtained by pulse compression within a coherent processing interval composed of M transmitted pulses by a pulse Doppler radar, and is expressed as: where r k (t m ) and are the radial distance and the amplitude after pulse compression of the k-th target respectively, t and t m are fast time and slow time respectively, f0 is the carrier frequency, and c is the speed of light in vacuum. In step S2, perform a Fourier transform on the echo signal to transform the echo signal into the range frequency-slow time domain, and is expressed as: where \(f\in[-f s / 2, -f s (N - 1) / 2N,\ldots,f s / 2]\) is the range frequency bin, \(f s is the sampling frequency, \(N\) represents the number of samplings in the fast time dimension, represents the amplitude of the \(k\)-th target in the frequency domain, Then, flip the echo signal up and down with 0 frequency as the center to obtain: Then, multiply the unflipped echo signal by the flipped echo signal and perform an inverse Fourier transform to obtain: where s self (τ, t m ) and s cross (τ, t m ) represent the auto-term and cross-term of the signal, respectively Finally, the extracted slow-time dimension time-frequency signal is expressed as: wherein, is the amplitude of the k-th target; is the phase factor of the target.

3. The range or Doppler migration compensation method based on Bayesian trajectory inference according to claim 1, characterized in that: Among them, In step S3, the expression of the space model is as follows: where η(t m ) is the measurement noise with a mean of 0.

4. The method for distance or Doppler migration compensation based on Bayesian trajectory inference according to claim 1, Characterized in that: Among them, step S5 includes the following sub-steps: Step S5-1: There is a phenomenon of velocity ambiguity in the target motion. Process the velocity ambiguity phenomenon by means of fuzzy integers to obtain the correct target motion trajectory. Step S5-2: Match the corresponding two-dimensional filter based on the target motion trajectory, and obtain the processed filtered signal through dot product calculation. Step S5-3: First transform the processed filtered signal into the fast time domain, and then perform a slow-time dimension Fourier transform to obtain the relevant parameters for compensating the unknown range and / or Doppler migration caused by the high-speed / maneuvering motion of the target.

5. The range or Doppler migration compensation method based on Bayesian trajectory inference according to claim 4, characterized in that: Among them, In step S5-1, for the Kth target, the trajectory corresponding to the fuzzy integer is:

6. The range or Doppler migration compensation method based on Bayesian trajectory inference according to claim 4, characterized in that: Among them, In step S5-2, the expression of the two-dimensional filter is as follows:

7. The range or Doppler migration compensation method based on Bayesian trajectory inference according to claim 4, characterized in that: Among them, In step S5-3, the relevant parameters include the residual remaining after compensating for range migration, the output range focusing distribution, and the instantaneous velocity. The expression of the slow-time dimension Fourier transform is as follows: In the formula, represents the residual remaining after the compensation distance migration, represents the output amplitude of the Kth target, The expression of the output distance focusing distribution is as follows: The expression of the instantaneous velocity is as follows: where v b = c / 2f0T r represents the blind speed; is the ambiguous speed.

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