A radar maneuvering target parameter estimation method under unknown time information

Abstract

The present application relates to a kind of radar maneuvering target parameter estimation methods under unknown time information, the echo signal of the maneuvering target of unknown time information is obtained by radar system, pulse compression is carried out to echo signal;Keystone transformation and RCM compensation function are constructed to carry out distance unit drift correction;The signal of the distance unit where maneuvering target is located is extracted and modeled as polynomial phase signal;Phase tracking is carried out to model based on extended Kalman filter, and tracking phase is intercepted using sliding time window, and the polynomial coefficient is inverted to reconstruct a new polynomial phase using the tracking phase of interception, and the similarity of tracking phase and reconstructed phase is compared to estimate time information;According to the time information obtained, the effective signal containing maneuvering target information is extracted, and phase tracking and inversion are carried out again to estimate motion parameters.The method is aimed at the motion parameter estimation of maneuvering target under unknown time information, and has outstanding advantages in calculation complexity and precision.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a method for estimating parameters of a radar maneuvering target when time information is unknown. Background Art

[0002] Radar can detect targets around the clock and in all weather conditions. It transmits electromagnetic waves and extracts target information from the received reflected echoes, leveraging the target's reflection characteristics. This allows for target detection and ranging, parameter estimation, trajectory tracking, imaging, and recognition. In recent years, driven by the urgent needs of radar in areas such as counter-stealth, anti-low-altitude penetration, and long-range early warning, maneuvering target detection and motion parameter estimation have received increasing attention and in-depth research.

[0003] Before performing high-resolution radar imaging, it is necessary to accurately estimate the motion parameters of a maneuvering target. For parameter estimation of maneuvering targets with simple motion, generally, only the estimation and compensation of low-order motion parameters (second-order and below) are required to achieve good imaging results. However, with the rapid development of aerospace technology and the increasing demand for practical applications, the motion characteristics of maneuvering targets are becoming increasingly complex, resulting in more complex range unit migration (RCM) and Doppler frequency migration (DFM). The phase errors caused by the high-order motion parameters of the target due to complex maneuvers cannot be ignored, otherwise the imaging results will be defocused. Therefore, conventional low-order motion models are no longer sufficient. It is necessary to model the maneuvering target as a high-order motion model, including motion parameters such as first-order velocity, second-order acceleration, third-order acceleration, linear range movement, second-order range curvature, third-order range curvature, and even higher-order acceleration. Currently, the study of high-order motion models has become a major topic in the field of radar detection.

[0004] Among existing methods, Xu Jia et al. proposed in the non-patent publication "Radar maneuvering target motion estimation based on generalized radon-fourier transform" (IEEE Transactions on Signal Processing, vol. 60, no. 12, pp. 6190–6201, 2012) that coherent accumulation can be used to search for parameter information of any high-order motion model. While this method achieves good results under low signal-to-noise ratio (SNR) conditions, the ergodic search results in an increased computational complexity as the order of the motion model increases. Furthermore, PPS parameter estimation based on a higher-order ambiguity function (HAF) is also an effective research method for maneuvering target detection. HAF utilizes local autocorrelation to recursively reduce the PPS order to obtain a single-frequency signal, known as phase differentiation (PD). While HAF and HAF-based methods are effective, they still suffer from the following drawbacks: First, low SNRs may result in a certain performance loss due to the high-order nonlinear transformation and PD operation; second, estimation errors propagate from higher-order coefficients to lower-order coefficients, increasing parameter estimation errors. Wu Siliang et al. proposed in the non-patent document A novel parameter estimation for polynomial phase signals using the spectrum phase, IEEE Signal Processing Letters, vol. 27, pp. 1919–1923, 2020 that a method based on time-frequency representation (TFR) and spectral phase unwrapping (SPU) can give the most advanced estimation results under low signal-to-noise ratio, but this method is computationally intensive and requires a strict convex polynomial phase. More importantly, the amplitude spectrum threshold (AST) is a critical and unknown parameter that will directly affect the estimation performance of the method.

[0005] The above methods not only have many defects, but also require known target time parameter information, that is, the area where the target signal is located is considered to be identifiable. However, in the actual application of radar detection, the time when maneuvering targets, especially non-cooperative targets, enter and leave the radar coverage area is unknown, which further increases the difficulty of target parameter estimation.

[0006] In summary, the existing technologies for estimating parameters of maneuvering targets with unknown time information have the following main problems:

[0007] 1. The lack of time information will cause the performance of existing parameter estimation methods to degrade or even fail, and there is currently no effective solution;

[0008] 2. Low-order motion models are not compatible with complex maneuvering targets, resulting in large parameter estimation errors;

[0009] 3. When using incoherent accumulation for parameter estimation, the signal-to-noise ratio will be lost, which cannot meet the high signal-to-noise ratio requirements;

[0010] 4. The search-based parameter estimation method has a huge computational load. When searching for high-order model parameters, the computational load increases with the order.

[0011] 5. When using high-order fuzzy functions for parameter estimation, the high-order parameter errors will be transferred to the low-order estimation results, resulting in low accuracy of the final parameter estimation. Summary of the Invention

[0012] The purpose of the present invention is to provide a radar maneuvering target parameter estimation method under unknown time information to solve the above-mentioned problems of high computational cost, low parameter estimation accuracy, unsuitability for complex maneuvering targets and heavy reliance on target time parameter information.

[0013] To achieve the above object, the present invention provides a method for estimating radar maneuvering target parameters when time information is unknown, comprising the following steps:

[0014] S1. Acquire the echo signal of a maneuvering target with unknown time information through the radar system and perform pulse compression on the echo signal;

[0015] S2, using Keystone transform and constructing RCM compensation function to perform range unit migration correction, concentrating the signal energy of the maneuvering target in one range unit;

[0016] S3, extracting the signal of the range unit where the maneuvering target is located and modeling it as a polynomial phase signal;

[0017] S4. Performing phase tracking on the polynomial phase signal model based on an extended Kalman filter, intercepting the tracking phase using a sliding time window, inverting the polynomial coefficients using the intercepted tracking phase to reconstruct a new polynomial phase, and comparing the similarity between the tracking phase and the reconstructed phase to estimate time information;

[0018] S5. Extract the polynomial phase signal containing the maneuvering target information based on the obtained time information, and continue to solve to estimate the motion parameters.

[0019] Preferably, the step S1 includes:

[0020] The radar system obtains the echo signal of a maneuvering target with unknown time information, and the expression is as follows:

[0021]

[0022] Where: j represents the imaginary unit, δ s represents the reflection coefficient of the maneuvering target, t r Indicates the distance to fast time, t a Indicates the azimuth slow time, w r (·) represents the rectangular window function in the distance direction, w a (·) represents the rectangular window function in the azimuth direction, R(t a ) represents the instantaneous distance between the maneuvering target and the radar in azimuth, K r represents the chirp rate of the signal, f c represents the carrier frequency, c represents the speed of light, λ represents the wavelength and

[0023] R(t a ) is as follows:

[0024]

[0025] Where: α i (i=0,1,2……L) represents the motion parameters, L represents the highest order of motion, α0, α1, α2 and α3 represent the initial distance, velocity, acceleration and acceleration rate respectively;

[0026] Combining equations (1) and (2), the expression of the two-dimensional time domain echo signal after pulse compression is as follows:

[0027]

[0028] Where: sinc(·) represents the Sigmoid function and is defined as B r Indicates the signal bandwidth.

[0029] Preferably, the step S2 includes:

[0030] 1) Perform Keystone transform on the echo signal after pulse compression to correct the main component of range unit migration

[0031] The Keystone transformation formula is as follows:

[0032] (f c +f r )t a =f c η (4)

[0033] Where: η represents the new azimuth slow time after transformation, f r Indicates the distance to the fast time t r Frequency range;

[0034] After performing the range Fourier transform on equation (3), the expressions of the echo signals of the maneuvering target in the range-frequency domain and the azimuth-time domain are as follows:

[0035]

[0036] Where: W r (·) represents the range frequency envelope;

[0037] Substitute equation (4) into equation (5), and combine f c / (f c +f r )≈1-f r / f c , we get the expression of the two-dimensional signal after Keystone transformation:

[0038]

[0039] 2) Construct RCM compensation function to correct distance bending

[0040] The expression of the RCM compensation function is as follows:

[0041]

[0042] Where: and Respectively represent the estimated values ​​of the second-order α2 and the third-order α3;

[0043] Multiplying equation (7) with equation (6) and performing inverse fast Fourier transform along the range direction, we can obtain the pulse compression signal after range unit migration correction, which is expressed as follows:

[0044]

[0045] 3) Accumulate the maximum peak gain along the azimuth direction

[0046] For equation (8), we use the two-dimensional search maximum value to obtain and The expression for two-dimensional search is as follows:

[0047]

[0048] Where: represents the distance IFFT matrix, Indicates slow time accumulation operation along the azimuth direction;

[0049] Based on the above search results, the expression of the two-dimensional time domain echo signal is obtained by simplifying Equation (8):

[0050]

[0051] Where: A(η) = δ s w a (η) represents the echo amplitude.

[0052] Preferably, the step S3 includes:

[0053] 1) Considering noise and discrete time sampling, the expression of the PPS model is as follows:

[0054]

[0055] Where: v(k) represents the variance δ 2 A(k) represents the amplitude function, φ(k) represents the polynomial phase function and Indicates the pulse sample index, N a Indicates the number of azimuth pulses, T r represents the pulse repetition time and T r =1 / PRF, PRF represents the pulse repetition frequency;

[0056] 2) For the radar echo signal with unknown time information, a pseudo-PPS model is constructed, which is expressed as:

[0057]

[0058] Where: k s Indicates the starting sampling index of the PPS component, k e Indicates the stop sampling index of the end of the PPS component, defined as N e =k e -k s +1, N e Indicates the number of valid sampling points containing PPS components.

[0059] Preferably, the process of performing phase tracking on the polynomial phase signal model based on the extended Kalman filter in step S4 includes:

[0060] 1) Constructing a phase tracking EKF model

[0061] Based on the smoothness assumption of phase and amplitude, the binary state space equation is constructed as follows, which consists of two linear state equations and one nonlinear observation equation:

[0062]

[0063] Where: represents the phase state vector, which consists of three consecutive phase samples and p k represents the amplitude state vector, p k=[A(k-1),A(k),A(k+1)] T , B represents the constant matrix of the smoothing assumption, B = [0,1,0; 0,0,1; 0,-1,2], y k represents three consecutive measurement signal samples, y k =[real(x k ),imag(x k )] T And x k =[x p (k-1),x p (k),x p (k+1)] T ,ω k-1 The process noise vector representing the phase state equation, v k-1 The process noise vector representing the amplitude state equation, n k represents the observation noise vector, It is determined by the phase state vector and the amplitude state vector and is expressed as:

[0064]

[0065] Where: ⊙ represents the Hadamard product operation, h1(p k )=[p k ,p k ] T ,

[0066] Using EKF to solve equation (13), we get the phase state vector Estimated value of Combined with the expression of the theoretical phase φ(k), we get the expression for estimating the polynomial coefficient vector representing the motion parameters:

[0067]

[0068] Where: represents the estimated motion parameters, represents the tracked phase state vector, Ψ represents the polynomial phase fundamental matrix and is expressed as follows:

[0069]

[0070] Preferably, the process of intercepting the tracking phase using the sliding time window in step S4 and inverting the polynomial coefficients using the intercepted tracking phase to reconstruct a new polynomial phase includes:

[0071] 2) Initial phase tracking

[0072] APAI-EKF is used to process the pseudo PPSx in equation (12) p (k), we get the expression of the initial phase φ1:

[0073]

[0074] 3) PPS coefficient inversion

[0075] A sliding time window is applied on the initial phase φ1, and the sampling index of the sliding time window is from k s w to k e w , and the tracking phase and its polynomial coefficient vector captured within the sliding time window are denoted as φ2 and α w , then:

[0076]

[0077] Where: The length of the sliding time window is And L w ≤N e ;

[0078] from arrive Apply sliding time windows to φ1 in turn, and then obtain the intercept phase φ2 and polynomial coefficient vector α corresponding to each sliding time window w ;

[0079] The φ2 and α under different sliding time windows are w Represented as a data set, the expression is as follows:

[0080]

[0081] Where: N w =N a -L w +1 indicates the number of sliding time windows, l indicates the sliding time window index, and l is from 1 to N w ,φ 2l and The expression is as follows:

[0082]

[0083] Where: represents the i-th order phase coefficient estimation result of the l-th sliding time window, The calculation formula and ψ wl The expression is as follows:

[0084]

[0085] 4) Phase reconstruction

[0086] After obtaining the coefficients of the intercept phase under different sliding time windows, the estimated coefficients are used Reconstruct a new polynomial phase, the expression is as follows:

[0087]

[0088] Where: represents the reconstructed phase of the lth sliding time window;

[0089] For all sliding time windows, the reconstructed phase is represented as the following dataset:

[0090]

[0091] Where:

[0092] When all sampling points in the lth sliding time window contain the target signal component, that is, When the reconstructed phase is equal to the intercepted tracking phase φ 2l Similar, expressed as:

[0093]

[0094] Preferably, the process of comparing the similarity between the tracking phase and the reconstructed phase to estimate the time information in step S4 includes:

[0095] 5) Calculate phase variance

[0096] Record different sliding time windows With φ 2l The difference:

[0097]

[0098] Where:

[0099] Describing Δφ based on the variance of the phase difference l Whether the elements in are continuously stable is expressed as follows:

[0100]

[0101] Where: var(·) represents the operation of calculating variance;

[0102] 6) Calculate entry / exit time

[0103] By observing the minimum value at Δφ var The target’s entry / exit time can be obtained by looking at the position in:

[0104] ① When Lw =N e hour

[0105] There is only one sliding time window that meets the requirement that all sampling points contain PPS components. Let the sliding time window index be l m , then Δφ var The minimum value in The time when the target enters and leaves the radar coverage area and Calculated by the following formula:

[0106]

[0107] ②L w <N e

[0108] There is N e -L w +1 sliding time window meets the requirements, in Δφ var There are N e -L w +1 smaller value, set the sliding time window index from m to n, n = m + N e -L w , the time when the target enters and leaves the radar coverage area and Calculated by the following formula:

[0109]

[0110] Where: and are the estimated time for the maneuvering target to enter and leave the radar coverage area, which gives the k in formula (12): s and k e The estimated value of and

[0111] Preferably, step S5 includes:

[0112] Will and Substitute into formula (12) to extract the effective signal x containing the target information e (k), the expression is as follows:

[0113]

[0114] The target motion parameters are estimated by solving equation (32) using APAI-EKF.

[0115] Preferably, the process of estimating the target motion parameters by solving equation (32) using APAI-EKF includes:

[0116] First, x e (k) Phase tracking is performed to obtain an estimated value of the tracking phase, and then the estimated motion parameters are inverted using the least squares estimation method of formula (15). Considering that the estimation is relatively rough, finally, in order to further improve the estimation performance and achieve the Cramer-Rao lower bound, the O'Shea refinement strategy is used to refine the rough estimate.

[0117] The present invention has at least the following beneficial effects:

[0118] 1. The present invention proposes a parameter estimation method for radar maneuvering targets with unknown time information. First, the KT transform and two-dimensional search are used to implement RCMC of the pulse compression signal. Then, an EKF tracking model consisting of two state equations and one observation equation is established. Phase tracking and a sliding time window are used to estimate the target's entry and exit times. Finally, the effective signal is extracted based on the time information to estimate the motion parameters. The method as a whole is based on the phase tracking EKF to obtain the time information and motion parameters of the maneuvering target, rather than using existing parameter search, time-frequency analysis, or high-order fuzzy function methods to achieve parameter estimation. To a certain extent, this method improves the problems of poor computational efficiency, error propagation, and low parameter estimation accuracy.

[0119] 2. The method provided by the present invention uses an improved EKF designed specifically for tracking Doppler phase. It is independent of the target motion sequence, making the method of the present invention well suited for the problem of estimating high-order parameters of complex maneuvering targets and achieving true and effective estimation of the motion parameters of high-order maneuvering targets.

[0120] 3. The method provided by the present invention reduces the computational cost while ensuring high accuracy of parameter estimation, converts high-dimensional search problems into two-dimensional search and one-dimensional search problems, avoids multi-dimensional search of the parameter space, and has obvious advantages in computational efficiency and computational complexity.

[0121] It should be understood that the contents described in this section are not intended to identify the key or important features of the embodiments of the present disclosure, nor are they intended to limit the scope of the present disclosure. Other features of the present disclosure will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] The above and other features, advantages and aspects of the embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements.

[0123] Figure 1 A flow chart of a radar maneuvering target parameter estimation method under unknown time information according to embodiment 1 of the present invention is shown;

[0124] Figure 2 The pseudo-PPS signal phase tracking result of simulation 1 in embodiment 2 of the present invention is shown;

[0125] Figure 3 A comparison chart of computational complexity curves of three different parameter estimation methods for simulation 2 in embodiment 2 of the present invention under different pulse numbers is shown;

[0126] Figure 4 The target signal processing results of simulation 3 in embodiment 2 of the present invention are shown, wherein Figure 4 (a) is the echo signal diagram after pulse compression, Figure 4 (b) is the two-dimensional search result diagram of signal acceleration and acceleration rate. Figure 4 (c) is the target signal diagram after RCMC;

[0127] Figure 5 The initial phase tracking results of simulation 4 in embodiment 2 of the present invention are shown. Figure 5 (a) is a comparison diagram of the initial phase and the theoretical phase. Figure 5 (b) is a schematic diagram showing the change of the difference between the initial phase and the theoretical phase;

[0128] Figure 6 The phase reconstruction results of different sliding time windows of simulation 5 in embodiment 2 of the present invention are shown. Figure 6 (a) is the phase reconstruction comparison diagram under the condition of window length 2000 (0-1s), Figure 6 (b) is the phase reconstruction comparison diagram under the condition of window length 3000 (0.5-2s), Figure 6 (c) is the phase reconstruction comparison diagram when the window length is 4000 (1-3s). Figure 6 (d) is the phase reconstruction comparison diagram when the window length is 2000 (1.5-2.5s);

[0129] Figure 7 Schematic diagram showing the change of the sliding time window phase variance of simulation 6 in embodiment 2 of the present invention;

[0130] Figure 8 The root mean square error results of two different parameter estimation methods in simulation 7 in embodiment 2 of the present invention are shown, where Figure 8 (a) is a comparative diagram of the root mean square error of the target entry time. Figure 8 (b) is a comparative diagram of the root mean square error of the target departure time;

[0131] Figure 9 The mean square error results of motion parameter estimation using three different parameter estimation methods in simulation 8 in embodiment 2 of the present invention at different signal-to-noise ratios are shown. Figure 9(a) is a comparison diagram of the mean square error of the velocity parameters. Figure 9 (b) is a comparison diagram of the mean square error of acceleration parameters. Figure 9 (c) is a comparative diagram of the mean square error of the acceleration rate parameters. DETAILED DESCRIPTION

[0132] The following description of exemplary embodiments of the present disclosure is made in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding. These details should be considered as merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0133] Example 1

[0134] The idea of ​​the technical solution of the present invention is as follows Figure 1 As shown in the figure, the radar system acquires the echo signal of a maneuvering target with unknown time information, and performs pulse compression on the echo signal; the Keystone transform is used and the RCM compensation function is constructed to perform range unit migration correction on the maneuvering target signal; the signal of the range unit where the maneuvering target is located is extracted and modeled as a polynomial phase signal; the polynomial phase signal model is phase tracked based on the extended Kalman filter, the tracking phase is intercepted using a sliding time window, the polynomial coefficients are inverted using the intercepted tracking phase to reconstruct a new polynomial phase, and the similarity between the tracking phase and the reconstructed phase is compared to estimate the time information; the polynomial phase signal containing the maneuvering target information is extracted based on the obtained time information, and the solution is continued to estimate the motion parameters.

[0135] The technical details of the present invention will be described in more detail below with reference to derivations and formulas.

[0136] 1. Assuming that the radar transmits a linear frequency modulation signal, the echo of the maneuvering target after removing the carrier frequency can be expressed as:

[0137]

[0138] Where: j represents the imaginary unit, δ s represents the reflection coefficient of the maneuvering target, t r Indicates the distance to fast time, t a Indicates the azimuth slow time, w r (·) represents the rectangular window function in the distance direction, w a (·) represents the rectangular window function in the azimuth direction, R(t a ) represents the instantaneous distance between the maneuvering target and the radar in azimuth, K r represents the chirp rate of the signal, f crepresents the carrier frequency, c represents the speed of light, and The wavelength λ can be calculated.

[0139] Considering that the maneuvering target has characteristics such as speed, acceleration, acceleration rate, and even high-order acceleration, the instantaneous distance R(t a ) can be expressed as t based on Taylor series expansion a A high-order polynomial of :

[0140]

[0141] Where: α i (i = 0, 1, 2, ..., L) represents the motion parameter, i.e., the coefficient of the i-th order polynomial after the instantaneous slant range is expanded. L represents the highest order of motion, i.e., the highest order of expansion. α0, α1, α2, and α3 represent the initial distance, velocity, acceleration, and acceleration rate, respectively.

[0142] Combining equations (1) and (2), the two-dimensional time domain echo signal after pulse compression can be expressed as:

[0143]

[0144] Where: sinc(·) represents the Sigmoid function and is defined as B r Indicates the signal bandwidth.

[0145] It can be seen that the effects of range cell migration (RCM) and Doppler frequency migration (DFM) of a maneuvering target occur simultaneously during the observation period. Since DFM has a more significant impact on target detection and imaging than RCM, and RCM correction generally considers at most third-order motion (i ≤ 3), while DFM compensation requires consideration of higher-order motion (i > 3), range cell migration correction (RCMC) is performed on the echo signal after pulse compression to estimate unknown time information and motion parameters.

[0146] 2. The steps of performing range unit migration correction on the echo signal after pulse compression include:

[0147] 1) Perform Keystone transform on the echo signal after pulse compression to correct the main component of range unit migration

[0148] The Keystone transformation formula is as follows:

[0149] (f c +f r )t a =f c η (4)

[0150] Where: η represents the new azimuth slow time after transformation, f r Indicates the distance to the fast time t r Frequency range;

[0151] After performing the range Fourier transform on equation (3), the expressions of the echo signals of the maneuvering target in the range-frequency domain and the azimuth-time domain are as follows:

[0152]

[0153] Where: W r (·) represents the range frequency envelope;

[0154] Substitute equation (4) into equation (5), and consider f c / (f c +f r )≈1-f r / f c , we can get the expression of the two-dimensional signal after Keystone transformation:

[0155]

[0156] At this time, with f r The related exponential term containing α1 does not exist, that is, the first-order RCM has been corrected, and f r and η 2 、f r and η 3 The coupling between them still exists, so further correction is required for the range bending caused by the second-order (α2) and third-order (α3) motions.

[0157] 2) Construct RCM compensation function to correct distance bending

[0158] The expression of the RCM compensation function is as follows:

[0159]

[0160] Where: and Represent the estimated values ​​of α2 and α3 respectively;

[0161] Multiplying equation (7) with equation (6) and performing inverse fast Fourier transform (IFFT) along the distance direction, we can obtain the pulse compression signal after RCMC, which is expressed as follows:

[0162]

[0163] 3) Accumulate the maximum peak gain along the azimuth direction

[0164] For equation (8), we use the two-dimensional search maximum value to obtain and The expression for two-dimensional search is as follows:

[0165]

[0166] Where: represents the distance IFFT matrix, Indicates slow time accumulation operation along the azimuth direction;

[0167] When the search results meet and When the remaining part of the RCM is corrected, the target signal can be concentrated in the same range unit.

[0168] In addition, when 2α3(N a T r / 2) 3 <c / 4B r When the distance unit curvature caused by the third-order (α3) motion can be ignored, the two-dimensional search degenerates into a one-dimensional search. In this conditional judgment formula, N a Indicates the number of azimuth pulses, T r represents the pulse repetition time and T r =1 / PRF, PRF represents the pulse repetition frequency.

[0169] Substituting the above search results into equation (8), the simplified expression of the two-dimensional time domain echo signal is as follows:

[0170]

[0171] Where: A(η) = δ s w a (η) represents the echo amplitude.

[0172] After completing the range unit migration correction, the signal energy of the maneuvering target is concentrated in a range unit. The signal in this range unit can be modeled as a polynomial phase signal (PPS). Since the phase of the PPS model contains the relevant motion parameters, the motion parameters can be estimated by solving the PPS model.

[0173] The PPS model assumes that all samples contain target signal components, that is, the time information of the target entering and leaving the radar coverage area is known. In the case of high signal-to-noise ratio, the PPS model is applicable because the entry / exit time of the maneuvering target can be easily observed; however, in the case of low signal-to-noise ratio, the signal is significantly affected by noise, making it difficult to directly obtain the time information (i.e., k s and k e ), at this time the PPS model does not fully conform to the actual situation.

[0174] We call the PPS model under the condition of unknown time information a pseudo-PPS model. Since the pseudo-PPS model contains PPS components that are consistent with the actual situation, before solving the pseudo-PPS model, it is necessary to estimate the time information related to the PPS components. For the PPS components, the phase tracking and parameter inversion method based on the extended Kalman filter (EKF) can be used to obtain k s and k e , based on which an effective signal containing target information can be obtained.

[0175] If you do not get k s and k e In this case, if EKF is used directly for phase tracking, the presence of pure noise units will cause the tracked phase to deviate from the theoretical phase. This deviation will reduce the estimation accuracy of the motion parameters. Therefore, the time information must be estimated first.

[0176] 3. Extract the corrected maneuvering target signal and model it as a polynomial phase signal

[0177] 1) Considering noise and discrete time sampling, the expression of the PPS model is as follows:

[0178]

[0179] Where: v(k) represents the variance δ 2 A(k) represents the amplitude function, φ(k) represents the polynomial phase function and Represents the pulse sample index; It is worth noting that the change of amplitude is slower than that of phase. In the field of radar detection, the signal amplitude changes slowly and is related to the antenna direction. Figure 1 To.

[0180] 2) For the radar echo signal with unknown time information, a pseudo-PPS model is constructed, which is expressed as follows:

[0181]

[0182] Where: k s Indicates the starting sampling index of the PPS component, k e Indicates the stop sampling index of the end of the PPS component, defined as N e =k e -k s +1, N e Indicates the number of valid sampling points containing PPS components.

[0183] From Equation (12), we can see that the phase of the noise unit fluctuates randomly, while the phase of the signal unit is mainly determined by the target motion information and follows specific rules. Therefore, we can solve the polynomial coefficient vector α=[α0,α1,...,α L ] T to estimate motion parameters.

[0184] 4. The steps for estimating time information based on EKF phase tracking and parameter inversion include:

[0185] 1) Constructing a phase tracking EKF model

[0186] Based on the smoothness assumption of phase and amplitude, the binary state space equation is constructed as follows, which consists of two linear state equations and one nonlinear observation equation:

[0187]

[0188] Where: represents the phase state vector, which consists of three consecutive phase samples and p k represents the amplitude state vector, p k =[A(k-1),A(k),A(k+1)] T , B represents the constant matrix of the smoothing assumption, B = [0,1,0; 0,0,1; 0,-1,2], y k represents three consecutive measurement signal samples, y k =[real(x k ),imag(x k )] T And x k =[x p (k-1),x p (k),x p (k+1)] T ,ω k-1 The process noise vector representing the phase state equation, v k-1 The process noise vector representing the amplitude state equation, n k represents the observation noise vector, It is determined by the phase state vector and the amplitude state vector and is expressed as:

[0189]

[0190] Where: ⊙ represents the Hadamard product operation, h1(p k )=[p k ,p k ] T ,

[0191] Using EKF to solve equation (13), we can get the phase state vector Estimated value of Combined with the expression of the theoretical phase φ(k), we get the expression for estimating the polynomial coefficient vector representing the motion parameters:

[0192]

[0193] Where: represents the estimated motion parameters, represents the tracked phase state vector, Ψ represents the polynomial phase fundamental matrix and is expressed as follows:

[0194]

[0195] Considering that the tracking phase of the signal cell is a translation of the theoretical phase and is smooth, which is a feature that the tracking phase of the noise cell does not have, the time information can be estimated by identifying the difference in the phase tracking results of the noise cell and the signal cell.

[0196] 2) Initial phase tracking

[0197] The extended Kalman filter algorithm with amplitude-phase alternating iteration (APAI-EKF) is used to process the pseudo PPSx in equation (12). p (k) The initial phase φ1 is obtained, which is expressed as:

[0198]

[0199] definition Obviously, is the initial phase before the PPS component appears, is the initial phase after the PPS component ends, and is the tracking phase of the noise unit. If the polynomial coefficients of the pseudo-PPS model are directly extracted using formula (15), the result cannot represent the theoretical value α. This inaccurate estimate is recorded as α′, and α′=[α0′,α1′,…,α L ′] T .

[0200] According to formula (11), the expansion relationship between φ1 and the polynomial coefficient vector α′ is:

[0201]

[0202] 3) PPS coefficient inversion

[0203] The key to estimating the target entry / exit time is to evaluate the convergence trend of the initial phase. In this step, a sliding time window is mainly used to intercept the initial phase and calculate the coefficients of the PPS component.

[0204] First, a sliding time window is imposed on the initial phase φ1, and the sampling index of the sliding time window is from k s w to k e w At this time, if the phase intercepted in the sliding time window is still regarded as a polynomial phase, the intercepted tracking phase and its polynomial coefficient vector are recorded as φ2 and α respectively. w , then:

[0205]

[0206] Where: The length of the sliding time window is And L w ≤N e .

[0207] Finally, from arrive Apply sliding time windows to φ1 in turn, and then obtain the intercept phase φ2 and polynomial coefficient vector α corresponding to each sliding time window w .

[0208] The φ2 and α under different sliding time windows are w Represented as a data set, the expression is as follows:

[0209]

[0210] Where: N w =N a -L w +1 indicates the number of sliding time windows, l indicates the sliding time window index, and l is from 1 to N w ,φ 2l and The expression is as follows:

[0211]

[0212] Where: represents the i-th order phase coefficient estimation result of the l-th sliding time window, The calculation formula and ψ wl The expression is as follows:

[0213]

[0214] 4) Phase reconstruction

[0215] After obtaining the coefficients of the intercept phase under different sliding time windows, the estimated coefficients are used Reconstruct a new polynomial phase, the expression is as follows:

[0216]

[0217] Where: represents the reconstructed phase of the lth sliding time window.

[0218] For all sliding time windows, the reconstructed phase is represented as the following dataset:

[0219]

[0220] Where:

[0221] It can be understood that when all sampling points in the lth sliding time window contain the target signal component, that is, When the reconstructed phase is equal to the intercepted tracking phase φ 2l Similar, expressed as:

[0222]

[0223] 5) Calculate phase variance

[0224] From formula (27), we can see that when all sampling points in the lth sliding time window contain PPS components, the reconstructed phase vector Almost the same as the intercepted tracking phase vector φ 2l Equal; on the contrary, when φ 2l Phase of noise cell hour, With φ 2l Therefore, the challenge of estimating entry / exit time becomes identifying and φ 2l The similarities between them.

[0225] Record different sliding time windows With φ 2l The difference:

[0226]

[0227] Where:

[0228] Since the variance indicates the degree to which a random variable deviates from its mathematical expectation, the variance of the phase difference can be used to describe Δφ. l Whether the elements in are continuously stable is expressed as follows:

[0229]

[0230] Where var(·) represents the operation of calculating variance.

[0231] 6) Calculate entry / exit time

[0232] By observing the minimum value at Δφ var Specifically, according to the window length (L w ), we need to discuss two situations:

[0233] The first case: L w =N e

[0234] It can be seen that only one sliding time window can meet the requirement that all sampling points contain PPS components. Assume that the sliding time window index is l m , then Δφ var The minimum value in Other values ​​are large and fluctuate. The time when the target enters and leaves the radar coverage area is calculated by the following formula:

[0235]

[0236] The second case: L w <N e

[0237] This situation is more common. As the sliding time window slides, there are N e -L w +1 window meets the requirements, in Δφ var There are N e -L w +1 smaller value, the other values ​​are larger and fluctuate. For these continuously stable phase variances, assume that the time window index is from m to n, n = m + N e -L w , the time when the target enters and leaves the radar coverage area is calculated by the following formula:

[0238]

[0239] Where: and are the estimated time for the maneuvering target to enter and leave the radar coverage area, which gives the k in formula (12): s and k e The estimated value of and

[0240] 5. Estimating motion parameters

[0241] according to and Use formula (12) to extract the effective signal x containing the target information e (k), the expression is as follows:

[0242]

[0243] By solving equation (32) through APAI-EKF, the target motion parameters can be estimated.

[0244] Specifically, first, e (k) Phase tracking is performed to obtain an estimated value of the tracking phase, and then the estimated motion parameters are inverted using the least squares estimation method of formula (15). Considering that the estimation is relatively rough, finally, in order to further improve the estimation performance and achieve the Cramer-Rao lower bound, the O'Shea refinement strategy is used to refine the rough estimate.

[0245] Example 2

[0246] According to Example 1, the present invention uses the proposed method to calculate the time when a maneuvering target enters / leaves the radar coverage area as follows:

[0247] Input: Target echo signal after RCMC, namely pseudo PPSx p (k), the highest motion order of the target is L, and the window length is L w .

[0248] The initial phase tracking is achieved through the APAI-EKF algorithm, and φ1 is obtained:

[0249] φ1=[φ1(1),…,φ1(k s ),…,φ1(k e ),…,φ1(N a )] T

[0250] =APAI-EKF Algorithm{x p (k)}

[0251] For l=1 to N w

[0252] By intercepting φ1 through the sliding time window, we can get φ 2l :φ 2l =[φ1(l),…,φ1(l+L w -1)] T

[0253] Calculate the fundamental matrix Ψ wl :

[0254] Calculating the PPS coefficient

[0255] Reconstruct phase

[0256] End For

[0257] Get φ2: where φ 2l = [φ1(l), φ1(l+1), …, φ1(l+L w -1)] T

[0258] Get φ r : where

[0259] Construct phase difference dataset Δφ:

[0260] Calculate phase variance Δφ var :

[0261] Determine sliding time window indices m and n according to Δφ var ;

[0262] If L w = N e

[0263] Calculate entry and exit times:

[0264] Else If L w <N e

[0265] Calculate entry and exit times:

[0266] End If

[0267] Output: estimates of entry / exit times, i.e. and

[0268] Example 3

[0269] The effectiveness of the method in Example 1 can be illustrated by simulation experiments. The radar parameters and maneuvering target parameters used in Simulations 3-8 are shown in Tables 1 and 2:

[0270] Table 1 Radar parameters

[0271] Parameter name Value Parameter name Value Carrier frequency 6 GHz PRF 2000 Hz Range bandwidth 10 MHz Pulse duration 10 μs Range sampling rate 20 MHz Observation time 0-4s

[0272] Table 2 Maneuvering target parameters

[0273] Parameter name Value Parameter name Value Initial range 5 Km Velocity 90 m / s Acceleration <![CDATA[26m / s 2 ]]> Acceleration rate <![CDATA[10m / s 3 ]]> Target entry time 1s Target exit time 3s

[0274] Simulation 1:

[0275] Assume that the target enters the radar coverage area at 0.5s and leaves after 1s. The phase tracking results of the pseudo PPS signal are as follows: Figure 2 shown.

[0276] from Figure 2 It can be seen that the tracking phase deviates from the theoretical phase and fluctuates significantly in the noise area. This is mainly because the phase of the noise unit no longer meets the phase smoothness assumption. The tracking phase at the noise unit fluctuates significantly and does not converge. On the contrary, the tracking phase It is smooth in the target signal area, and its phase convergence trend is consistent with the theoretical phase.

[0277] Simulation 2:

[0278] In order to facilitate the comparison of the computational complexity of different motion parameter estimation methods under unknown time information, Figure 3 The computational complexity curves of three different methods under different pulse numbers are given. Assume that the radial velocity, acceleration and jerk of the target are in the range of [-300m / s, 300m / s], [-30m / s 2 ,30m / s 2 ] and [-20m / s 3 ,20m / s 3 ], the number of range cells is 512, the radar carrier frequency is 6 GHz, the pulse repetition frequency (PRF) is 200 Hz, the observation time is 4 s, and the required computational effort is C m Note that the y-axis is lgC m .

[0279] As the motion order increases, the computational complexity of both WRFRFT and EGRFT-WFRFT methods will increase significantly. Compared with WRFRFT and EGRFT-WFRFT, the computational complexity of the method of the present invention is much lower, and the increase in L order has no obvious effect on the computational complexity.

[0280] Simulation 3:

[0281] The parameters in Table 1 and Table 2 are used to simulate and analyze the pulse compression and RCMC results of the target signal. Specifically, the compressed echo (SNR is 10dB) is as follows Figure 4 As shown in (a), it can be seen that the target's residence time only accounts for a part of the entire observation time. Figure 4 (b) shows the two-dimensional search results of acceleration and acceleration rate, indicating that the estimated values ​​are very close to the theoretical values. Next, RCMC is performed using the two-dimensional search results. The results are as follows: Figure 4(c) shows that the target signal is concentrated in the same range cell, which proves that the accuracy of the two-dimensional search result meets the requirements of RCMC.

[0282] Simulation 4:

[0283] In order to verify the effectiveness of the time information estimation method proposed in the present application, the initial phase tracking results are obtained by simulation, including the comparison diagram of the tracked initial phase and the theoretical phase, and the variation diagram of the difference value between the tracked initial phase and the theoretical phase, as shown in Figure 5 (a) and Figure 5 (b) respectively.

[0284] It can be seen that the phase difference value in the target signal region remains stable, which also shows that the initial phase is a translation of the theoretical phase, that is, the convergence trend in the target signal region is consistent with the theoretical phase, and no convergence is achieved in the noise region. Although the initial phase converges in the target signal region, the value is not the theoretical value. Therefore, directly using the initial stage for parameter estimation will inevitably lead to inaccurate results, which needs to be further processed.

[0285] Simulation 5:

[0286] The simulation applies different sliding time windows to the initial phase to reconstruct the phase, and the simulation results are shown in Figure 6 , specifically, Figure 6 (a) the length of the sliding time window is 2000 (0-1s) and the sliding time window is full of noise signals, Figure 6 (b) the length of the sliding time window is 3000 (0.5-2s) and the sliding time window is a mixture of noise signals and target signals, Figure 6 (c) the length of the sliding time window is 4000 (1-3s) and the length of the sliding time window is accurately matched with the duration of the target entering the radar coverage region, Figure 6 (d) the length of the sliding time window is 2000 (1.5-2.5s) and the sliding time window is only partially target signal without noise signal.

[0287] In addition, the difference value results of the initial phase and the reconstructed phase in the sliding time window are also given in the local enlarged images of each figure. It is obvious that only when all the sampling points in the sliding time window are target signals, the reconstructed phase is very close to the initial phase, and only has a very small difference value.

[0288] Simulation 6:

[0289] The entering / leaving time of the target is estimated by calculating the phase variance of all sliding time windows; in the simulation, the time window length L w is set to 600, the number of pulses N a is 8000, and therefore the number of time windows N wis 7401, and the variance results are as follows Figure 7 shown.

[0290] It is clear that as the sliding time window moves, the phase variance in the shaded area remains stable (the phase variance is always less than 0.5). This indicates that the initial phase is almost the same as the reconstructed phase, that is, all sampling points in these time windows contain the target signal component. Figure 7 The index of the sliding time window corresponding to the middle shaded area is from 2000 to 5398, so and The estimated values ​​are 2000 and 5998 (5398+L w ), the time information of the maneuvering target entering and leaving the radar coverage area can be calculated according to formula (31): Obviously, the estimated results are almost consistent with the actual values ​​in Table 2, which proves the feasibility of the proposed method.

[0291] Simulation 7:

[0292] To demonstrate the robustness of the proposed method, a simulation was conducted to analyze the impact of the signal-to-noise ratio (SNR) on the performance of entry / exit time estimation. The SNR was set to vary within the range of [-20:2:30] dB, and 200 Monte Carlo simulations were performed. The time information estimation results of the WRFRFT and proposed methods were presented. The root mean square error (RMSE) of the two methods on the target entry / exit time results was calculated and the RMSE curve was plotted. The results are shown in Figure 2. Figure 8 (a) and Figure 8 (b) shown.

[0293] As shown in the figure, when the signal-to-noise ratio is approximately -4dB, the proposed method achieves an RMSE of much less than 0.1s for estimating the target's entry / exit time. This indicates that the estimated entry / exit time has similar accuracy at a signal-to-noise ratio threshold of approximately -4dB. When the signal-to-noise ratio threshold is as low as -8dB, while the existing WRFRFT method also demonstrates excellent performance in estimating entry time, its accuracy for estimating the target's exit time is significantly reduced, with an RMSE of approximately 0.1s.

[0294] Simulation 8:

[0295] The echo component containing the target information is extracted from the entire echo signal by estimating the entry / exit time. Then, the motion parameters are estimated by performing phase tracking and parameter inversion again. The mean square error (MSE) is used to evaluate the estimation accuracy of the motion parameters. The calculation formula of MSE is:

[0296]

[0297] in: is α i Estimates, It is the Mthc The Monte Carlo test results are shown in Figure 2. Here, the number of Monte Carlo simulations Mon = 200.

[0298] The accuracy evaluation results of the estimated velocity, acceleration and acceleration rate are as follows: Figure 9 (a) Figure 9 (b) and Figure 9 (c) As shown in the figure, when the signal-to-noise ratio is around -4 dB, the MSE of our method can reach that of the CRLB method. Compared with the WRFRFT method, the signal-to-noise ratio loss is approximately 4 dB, but the computational efficiency is significantly improved. When the signal-to-noise ratio is greater than -4 dB, our method has good robustness for estimating the motion parameters of maneuvering targets with unknown temporal information. The proposed method strikes a more appropriate balance between estimation accuracy and computational efficiency, which is also a prominent advantage of our method.

[0299] While various embodiments of the present disclosure have been described above, the foregoing description is intended to be illustrative, non-exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technological improvements in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.

[0300] The above are merely optional embodiments of the present disclosure and are not intended to limit the present disclosure. Those skilled in the art will readily appreciate that the present disclosure may be modified and varied in various ways. Any modifications, equivalent substitutions, improvements, and the like made within the spirit and principles of the present disclosure shall be included within the scope of protection of the present disclosure.

Claims

1. A method for estimating radar maneuvering target parameters when time information is unknown, characterized in that: The following steps are involved: S1. Acquire the echo signal of a maneuvering target with unknown time information through the radar system and perform pulse compression on the echo signal; S2, using Keystone transform and constructing RCM compensation function to perform range unit migration correction, concentrating the signal energy of the maneuvering target in one range unit; S3, extracting the signal of the range unit where the maneuvering target is located and modeling it as a polynomial phase signal; S4. Performing phase tracking on the polynomial phase signal model based on an extended Kalman filter, intercepting the tracking phase using a sliding time window, inverting the polynomial coefficients using the intercepted tracking phase to reconstruct a new polynomial phase, and comparing the similarity between the tracking phase and the reconstructed phase to estimate time information; S5. extracting a polynomial phase signal containing information about the maneuvering target based on the acquired time information, and continuing to solve the signal to estimate motion parameters; The step S1 comprises: The radar system obtains the echo signal of a maneuvering target with unknown time information, and the expression is as follows: Where: j represents the imaginary unit, δ s represents the reflection coefficient of the maneuvering target, t r Indicates the distance to fast time, t a Indicates the azimuth slow time, w r (·) represents the rectangular window function in the distance direction, w a (·) represents the rectangular window function in the azimuth direction, R(t a ) represents the instantaneous distance between the maneuvering target and the radar in azimuth, K r represents the chirp rate of the signal, f c represents the carrier frequency, c represents the speed of light, λ represents the wavelength and R(t a ) is as follows: Where: α i (i=0,1,2……L) represents the motion parameters, L represents the highest order of motion, α0, α1, α2 and α3 represent the initial distance, velocity, acceleration and acceleration rate respectively; Combining equations (1) and (2), the expression of the two-dimensional time domain echo signal after pulse compression is as follows: Where: sinc(·) represents the Sigmoid function and is defined as B r Indicates the signal bandwidth; The step S2 comprises: 1) Perform Keystone transform on the echo signal after pulse compression to correct the main component of range unit migration The Keystone transformation formula is as follows: (f c +f r )t a =f c η(4) where: η represents the new azimuth slow time after transformation, f r Indicates the distance to the fast time t r Frequency range; After performing the range Fourier transform on equation (3), the expressions of the echo signals of the maneuvering target in the range-frequency domain and the azimuth-time domain are as follows: Where: W r (·) represents the range frequency envelope; Substitute equation (4) into equation (5), and combine f c / (f c +f r )≈1-f r / f c , we get the expression of the two-dimensional signal after Keystone transformation: 2) Construct RCM compensation function to correct distance bending The expression of the RCM compensation function is as follows: Where: and Respectively represent the estimated values ​​of the second-order α2 and the third-order α3; Multiplying equation (7) with equation (6) and performing inverse fast Fourier transform along the range direction, we can obtain the pulse compression signal after range unit migration correction, which is expressed as follows: 3) Accumulate the maximum peak gain along the azimuth direction For equation (8), we use the two-dimensional search maximum value to obtain and The expression for two-dimensional search is as follows: Where: represents the distance IFFT matrix, Indicates slow time accumulation operation along the azimuth direction; Based on the above search results, the expression of the two-dimensional time domain echo signal is obtained by simplifying Equation (8): Where: A(η) = δ s w a (η) represents the echo amplitude.

2. The radar maneuvering target parameter estimation method under unknown time information according to claim 1, characterized in that: The step S3 comprises: 1) Considering noise and discrete time sampling, the expression of the PPS model is as follows: Where: v(k) represents the variance δ 2 A(k) represents the amplitude function, φ(k) represents the polynomial phase function and Indicates the pulse sample index, N a Indicates the number of azimuth pulses, T r represents the pulse repetition time and T r =1 / PRF, PRF represents the pulse repetition frequency; 2) For the radar echo signal with unknown time information, a pseudo-PPS model is constructed, which is expressed as: Where: k s Indicates the starting sampling index of the PPS component, k e Indicates the stop sampling index of the end of the PPS component, defined as N e =k e -k s +1, N e Indicates the number of valid sampling points containing PPS components.

3. The radar maneuvering target parameter estimation method under unknown time information according to claim 2, characterized in that: The process of performing phase tracking on the polynomial phase signal model based on the extended Kalman filter in step S4 includes: 1) Constructing a phase tracking EKF model Based on the smoothness assumption of phase and amplitude, the binary state space equation is constructed as follows, which consists of two linear state equations and one nonlinear observation equation: Where: represents the phase state vector, which consists of three consecutive phase samples and p k represents the amplitude state vector, p k =[A(k-1),A(k),A(k+1)] T , B represents the constant matrix of the smoothing assumption, B = [0,1,0; 0,0,1; 0,-1,2], y k represents three consecutive measurement signal samples, y k =[real(x k ),imag(x k )] T And x k =[x p (k-1),x p (k),x p (k+1)] T ,ω k-1 The process noise vector representing the phase state equation, v k-1 The process noise vector representing the amplitude state equation, n k represents the observation noise vector, It is determined by the phase state vector and the amplitude state vector and is expressed as: Where: ⊙ represents the Hadamard product operation, h1(p k )=[p k ,p k ] T , Using EKF to solve equation (13), we get the phase state vector Estimated value of Combined with the expression of the theoretical phase φ(k), we get the expression for estimating the polynomial coefficient vector representing the motion parameters: Where: represents the estimated motion parameters, represents the tracked phase state vector, Ψ represents the polynomial phase fundamental matrix and is expressed as follows:

4. The radar maneuvering target parameter estimation method under unknown time information according to claim 3, characterized in that: The process of intercepting the tracking phase using the sliding time window in step S4 and inverting the polynomial coefficients using the intercepted tracking phase to reconstruct a new polynomial phase includes: 2) Initial phase tracking APAI-EKF is used to process the pseudo PPS x in equation (12) p (k), we get the expression of the initial phase φ1: 3) PPS coefficient inversion A sliding time window is applied on the initial phase φ1, and the sampling index of the sliding time window is from k s w to k e w , and the tracking phase and its polynomial coefficient vector captured within the sliding time window are denoted as φ2 and α w , then: Where: The length of the sliding time window is And L w ≤N e ; from arrive Apply sliding time windows to φ1 in turn, and then obtain the intercept phase φ2 and polynomial coefficient vector α corresponding to each sliding time window w ; The φ2 and α under different sliding time windows are w Represented as a data set, the expression is as follows: Where: N w =N a -L w +1 indicates the number of sliding time windows, l indicates the sliding time window index, and l is from 1 to N w ,φ 2l and The expression is as follows: Where: represents the i-th order phase coefficient estimation result of the l-th sliding time window, The calculation formula and ψ wl The expression is as follows: 4) Phase reconstruction After obtaining the coefficients of the intercept phase under different sliding time windows, the estimated coefficients are used Reconstruct a new polynomial phase, the expression is as follows: Where: represents the reconstructed phase of the lth sliding time window; For all sliding time windows, the reconstructed phase is represented as the following dataset: Where: When all sampling points in the lth sliding time window contain the target signal component, that is, When the reconstructed phase is equal to the intercepted tracking phase φ 2l Similar, expressed as:

5. The radar maneuvering target parameter estimation method under unknown time information according to claim 4, characterized in that: The process of comparing the similarity between the tracking phase and the reconstructed phase to estimate the time information in step S4 includes: 5) Calculate phase variance Record different sliding time windows With φ 2l The difference: Where: Describing Δφ based on the variance of the phase difference l Whether the elements in are continuously stable is expressed as follows: Where: var(·) represents the operation of calculating variance; 6) Calculate entry / exit time By observing the minimum value at Δφ var The target’s entry / exit time can be obtained by looking at the position in: ① When L w =N e hour There is only one sliding time window that meets the requirement that all sampling points contain PPS components. Let the sliding time window index be l m , then Δφ var The minimum value in The time when the target enters and leaves the radar coverage area and Calculated by the following formula: ②L w <N e There is N e -L w +1 sliding time window meets the requirements, in Δφ var There are N e -L w +1 smaller value, set the sliding time window index from m to n, n = m + N e -L w , the time when the target enters and leaves the radar coverage area and Calculated by the following formula: Where: and are the estimated time for the maneuvering target to enter and leave the radar coverage area, which gives the k in formula (12): s and k e The estimated value of and 6. The radar maneuvering target parameter estimation method under unknown time information according to claim 5, characterized in that: The step S5 comprises: Will and Substitute into formula (12) to extract the effective signal x containing the target information e (k), the expression is as follows: The target motion parameters are estimated by solving equation (32) using APAI-EKF.

7. The method for estimating radar maneuvering target parameters under unknown time information according to claim 6, characterized in that: The process of estimating the target motion parameters by solving equation (32) through APAI-EKF includes: First, x e (k) Phase tracking is performed to obtain an estimated value of the tracking phase, and then the estimated motion parameters are inverted using the least squares estimation method of formula (15). Considering that the estimation is relatively rough, finally, in order to further improve the estimation performance and achieve the Cramer-Rao lower bound, the O'Shea refinement strategy is used to refine the rough estimate.

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