Coherent detection method and system for maneuvering targets based on improved coordinate rotation and Lu distribution

Abstract

The present invention belongs to the field of maneuvering target detection, and particularly relates to a maneuvering target coherent detection method and system based on improved coordinate rotation and Lu distribution, which performs pulse compression and two-dimensional discrete form transformation on radar echo signals, sets a rotation search angle range, rotates the echo trajectory to the same distance unit through rotation coordinate transformation to determine the optimal rotation search angle, and estimates the target speed and initial distance according to the optimal rotation search angle; extracts the signal in the same distance unit according to the initial distance, and estimates the target acceleration and jerk parameters using the improved Lu distribution algorithm; compensates the target acceleration and jerk parameters using a phase function to correct the linear Doppler frequency shift caused by acceleration and the quadratic Doppler frequency shift caused by jerk, and realizes coherent accumulation through Fourier transform. The present invention can ensure parameter estimation performance and effect while reducing computational complexity, and is convenient for application in actual scenarios.

Description

Technical Field

[0001] The invention belongs to the field of maneuvering target detection, and in particular relates to a maneuvering target coherent detection method and system based on improved coordinate rotation and Lu distribution. Background Art

[0002] With the development of high-speed, high-acceleration and high-jerk aerial maneuvering targets such as hypersonic aircraft and ultra-high-speed unmanned aerial vehicles, the detection and motion parameter estimation of such targets by ground and air radars have attracted more and more attention. Due to the characteristics of high-speed maneuvering targets such as high speed, many motion parameters and low radar cross-section (RCS), the detection performance of the moving target detection (MTD) method is seriously reduced. Therefore, in order to improve the detection performance of radar, a long-term coherent accumulation solution is proposed. However, in the accumulation process, there will be range migration (RM) caused by speed, linear Doppler frequency migration (LDFM) caused by acceleration and quadratic Doppler frequency migration (QDFM) caused by jerk, resulting in a decrease in accumulation performance. .

[0003] According to the order of the target motion model, the existing research methods can be divided into the following three categories: (a) the coherent accumulation algorithm for uniform motion targets, which is mainly aimed at the case where the radial velocity remains unchanged when the target is flying steadily under normal conditions; (b) the coherent accumulation algorithm for uniformly accelerated motion targets, which is mainly aimed at the case where the target has a constant acceleration; (c) the coherent accumulation algorithm for variable acceleration targets, which is mainly aimed at the case where the target has a complex motion state with additive elements. Among them, the purpose of the coherent accumulation algorithm for uniform motion targets is to eliminate RM. The specific methods can be divided into: parameter search type and non-search type. The search type algorithm can effectively accumulate under low SNR conditions, but the computational complexity is high. Although the non-search type algorithm can remove the coupling of range frequency and slow time, it cannot solve the problem of velocity ambiguity caused by high-speed targets. The coherent accumulation algorithm for uniformly accelerated motion targets mainly eliminates the LDFM effect. Although it can obtain the optimal detection performance under low signal-to-noise ratio, its huge amount of calculation seriously limits its practical application. The coherent accumulation algorithm for variable acceleration moving targets mainly includes the first two types of motion, and also eliminates the QDFM caused by acceleration. However, if the signal has nonlinear migration, the accumulation performance will deteriorate. In addition, due to the use of curve fitting to estimate motion parameters, the accuracy of parameter estimation will decrease at low SNR, resulting in a certain performance loss. Although some schemes have good anti-noise performance, the RFT search operation is large and the calculation speed is slow. Summary of the invention

[0004] To this end, the present invention provides a method and system for coherent detection of maneuvering targets based on improved coordinate rotation and Lu distribution, which solves problems such as range migration and Doppler migration caused by long-term coherent accumulation of high-speed targets. While reducing the calculation complexity, it can ensure parameter estimation performance and effect, which is convenient for application in actual scenarios.

[0005] According to the design scheme provided by the present invention, a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution is provided, which includes the following contents:

[0006] The radar echo signal is pulse compressed and transformed into a two-dimensional discrete form, and the rotation search angle range is set. The echo trajectory is rotated to the same distance unit through the rotation coordinate transformation to determine the optimal rotation search angle, and the target speed and initial distance are estimated according to the optimal rotation search angle;

[0007] The signals in the same distance unit are extracted according to the initial distance, and the target acceleration and jerk parameters are estimated by using the improved Lu distribution algorithm;

[0008] The target acceleration and jerk parameters are compensated by using phase function to correct the linear Doppler frequency shift caused by acceleration and the quadratic Doppler frequency shift caused by jerk, and coherent accumulation is achieved through Fourier transform.

[0009] As a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution, the present invention further uses a high-order polynomial model to characterize the target motion for the linear frequency modulation signal emitted by the radar during the detection process, and performs pulse compression on the reflected echo signal received by the receiver.

[0010] As the coherent detection method of maneuvering targets based on improved coordinate rotation and Lu distribution of the present invention, further, the pulse compression process of the echo signal of the kth target is expressed as: in, Indicates fast time, T p is the pulse duration, k r =B / T p is the LFM signal modulation frequency, B is the transmission signal bandwidth, f c represents the carrier frequency, t m =m / f p represents the slow time variable, m=0,1,…,M-1 is the pulse index, M is the total number of accumulated pulses, f p =1 / T r is the radar pulse repetition frequency, T r represents the pulse repetition interval, c is the electromagnetic wave speed, A c,k is the amplitude, R 0,k、v k 、a k and g k They represent the initial distance, velocity, acceleration and jerk of the kth target echo signal respectively.

[0011] As the coherent detection method of maneuvering targets based on improved coordinate rotation and Lu distribution of the present invention, further, the rotation search angle range is determined according to radar parameters and the target range-target tilt angle in the Doppler frequency domain.

[0012] As the coherent detection method of maneuvering target based on improved coordinate rotation and Lu distribution of the present invention, further, using The signal after two-dimensional discrete form transformation is rotated, and the energy of the rotated signal is integrated along the slow time dimension. The optimal rotation search angle is obtained according to the maximum value after integration, where (m,n) and (m′,n′) are the coordinates before and after the signal rotation, respectively. Search angle for rotation.

[0013] As a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution of the present invention, further, a cost function is constructed to estimate and obtain the optimal rotation search angle, wherein the cost function is expressed as: Among them, (m′,n′) are the coordinates of the signal after rotation, is the rotation search angle; by solving the cost function, The rotation angle corresponding to the maximum value is used as the optimal rotation search angle required to be obtained.

[0014] As a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution of the present invention, further, for the optimal rotation search angle, the formula is used To estimate the target speed and initial distance in, is the optimal rotation search angle, μ is the oversampling rate, ρ represents the distance sampling unit, Δr represents the distance resolution unit, T r is the pulse interval time, n max Indicates the maximum discretization index value of the target distance.

[0015] As a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution of the present invention, further, for the estimated initial distance of the target, the target slow time dimension signal is extracted along the slow time dimension, and the parameter symmetric autocorrelation function in the improved Lu distribution algorithm is used to extract the oversampling rate and distance variables in the signal for calculating the target acceleration and jerk, wherein, for the parameter symmetric autocorrelation function extraction process, the signal is first decoupled by the scale Fourier transform, and then the two-dimensional Fourier transform is used to obtain the slow time variable and the frequency corresponding to the variable delay, and the oversampling rate and distance variables are obtained by the peak coordinates gathered by the two-dimensional Fourier transform in the plane composed of the frequency.

[0016] As a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution of the present invention, further, for the case of coherent detection of multiple maneuvering targets, each maneuvering target is traversed in turn, and estimated in turn through rotating coordinate transformation and improved Lu distribution algorithm until all maneuvering targets complete coherent detection.

[0017] Furthermore, the present invention also provides a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution, comprising: a coordinate rotation estimation module, a Lu distribution estimation module and a coherent accumulation module, wherein:

[0018] The coordinate rotation estimation module is used to perform pulse compression and two-dimensional discrete form transformation on the radar echo signal, and set the rotation search angle range. The optimal rotation search angle is determined by rotating the echo trajectory to the same distance unit through the rotation coordinate transformation, and the target speed and initial distance are estimated according to the optimal rotation search angle.

[0019] The Lv distribution estimation module is used to extract the signal in the same distance unit according to the initial distance, and estimate the target acceleration and jerk parameters by using the improved Lv distribution algorithm;

[0020] The coherent accumulation module is used to compensate the target acceleration and jerk parameters by using the phase function to correct the linear Doppler frequency shift caused by acceleration and the quadratic Doppler frequency shift caused by jerk, and realize the coherent accumulation by Fourier transform.

[0021] Beneficial effects of the present invention:

[0022] The present invention aims at the problems of range migration (RM) and Doppler migration generated during long-term coherent accumulation of high-speed targets. By searching for the best rotation angle of the coordinate axis within a certain range, the coordinate axis is rotated by the coordinate rotation transformation MLRT algorithm to eliminate the RM effect, and the target speed and initial distance are calculated according to the rotation angle; further, the signal in the same distance unit after eliminating the RM effect is extracted along the slow time dimension, the QFM signal is processed by the MLVD algorithm to estimate the target acceleration and jerk, and the phase terms of the acceleration and jerk in the original signal are compensated and coherent accumulation is achieved by FFT, which has lower computational complexity and higher detection performance and parameter estimation performance. The actual measured data of unmanned aerial vehicles detected by Ka-band radar is further used for verification. The scheme of this case has good coherent accumulation capability, can meet the needs of actual application scenarios, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the coherent detection process of a maneuvering target based on improved coordinate rotation and Lu distribution in the embodiment;

[0024] Figure 2 It is a schematic diagram of the coordinate rotation transformation principle in the embodiment;

[0025] Figure 3 This is a schematic diagram of the implementation process of the MLRT-MLVD algorithm in the embodiment;

[0026] Figure 4 It is a schematic diagram of the computational complexity comparison of different algorithms in the embodiments;

[0027] Figure 5 This is a schematic diagram of the single target coherent accumulation result of the MLRT-MLVD algorithm in this embodiment;

[0028] Figure 6 Schematic diagram of the comparison of coherent accumulation results of different algorithms when SNR=-5dB in the embodiment;

[0029] Figure 7 This is a schematic diagram of the multi-objective coherent accumulation results of the MLRT-MLVD algorithm in this embodiment;

[0030] Figure 8 Schematic diagram of the comparison of detection probabilities of different algorithms in the embodiment;

[0031] Fig. 9 Schematic diagram of the comparison of speed, acceleration and jerk parameter estimation errors of different algorithms in the embodiment;

[0032] Fig.10 It is a schematic diagram of the accumulation results of the measured data in the embodiment. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention is further described in detail below in conjunction with the accompanying drawings and technical solutions.

[0034] The present invention provides a method for coherently detecting a maneuvering target based on improved coordinate rotation and Lu distribution, see Figure 1 As shown, it contains the following contents:

[0035] S101, performing pulse compression and two-dimensional discrete form transformation on the radar echo signal, and setting a rotation search angle range, rotating the echo trajectory to the same distance unit by rotating coordinate transformation to determine the optimal rotation search angle, and estimating the target speed and initial distance according to the optimal rotation search angle;

[0036] S102, extracting signals within the same distance unit according to the initial distance, and estimating target acceleration and jerk parameters using an improved Lu distribution algorithm;

[0037] S103, using a phase function to compensate for the target acceleration and jerk parameters to correct the linear Doppler frequency shift caused by the acceleration and the quadratic Doppler frequency shift caused by the jerk, and realizing coherent accumulation through Fourier transform.

[0038] For the third-order motion model, the target motion parameters are estimated based on coordinate rotation and Lu distribution to achieve coherent integration and target positioning detection, and solve problems such as range migration and Doppler migration caused by long-term coherent accumulation of high-speed targets. It has low computational complexity and high detection performance and parameter estimation performance, which is convenient for application in practical scenarios.

[0039] Furthermore, for the linear frequency modulation signal emitted by the radar during the detection process, a high-order polynomial model is used to characterize the target motion, and the reflected echo signal received by the receiver is pulse compressed.

[0040] Assume that the radar transmits the commonly used linear frequency modulation (LFM) signal, that is:

[0041]

[0042] in,

[0043]

[0044] In formula (1) Indicates fast time, T p is the pulse duration; k r =B / T p is the LFM signal modulation frequency, B is the transmission signal bandwidth, f c Indicates carrier frequency; t m =m / f prepresents the slow time variable, which is used to measure the propagation time of the signal between pulses; m = 0, 1, L, M-1 is the pulse index, M is the total number of accumulated pulses, f p =1 / T r is the radar pulse repetition frequency (PRF), T r Indicates Pulse Repetition Interval (PRI).

[0045] In the actual radar detection process, the target's motion mode is not simply limited to constant acceleration. Especially for long-term coherent accumulation, complex maneuvers are inevitable, such as sudden changes in the flight state of fighter jets and drones, and terminal maneuver penetration of cruise missiles. Therefore, it is more appropriate to use a high-order polynomial model to characterize the target motion, which can be expressed as:

[0046]

[0047] Among them, R 0,k 、v k 、a k and g k are the initial distance, velocity, acceleration and jerk of the kth target respectively.

[0048] After the receiver receives the reflected echo, the echo signal of the kth target can be expressed as:

[0049]

[0050] Where c is the electromagnetic wave speed, A 0,k is the amplitude. After pulse compression, the echo signal can be expressed as:

[0051]

[0052] For formula (6) After Fourier transform, the corresponding distance frequency-slow time domain can be expressed as:

[0053]

[0054] Among them, f r yes The corresponding distance frequency, sinc function is the signal envelope.

[0055] It can be seen from formula (5) that when the change exceeds Δr = c / 2f sWhen the target is moving, the range migration (RM) effect will appear. Due to the complexity of the target motion, the signal is highly nonlinear in the slow time dimension. The exponential term of formula (7) indicates the Doppler frequency of the linear migration of the target, that is:

[0056]

[0057] At this time, we must not only consider the migration phenomenon of the signal envelope, but also the complex changes in the Doppler frequency, including both linear Doppler frequency migration and secondary Doppler frequency migration.

[0058] Assuming that a complex maneuvering target in the air is maneuvering rapidly with a third-order motion model, the pulse compression signal of the radar receiving echo is shown in equation (5), which is expressed again as follows:

[0059]

[0060] The bandwidth of a narrowband radar system is much smaller than the carrier frequency, that is, B = f c At this point, it can be assumed that the distance migration caused by the target acceleration and jerk in the coherent integration time does not exceed one distance sampling unit, and the migration term corresponding to the acceleration and jerk in the envelope can be ignored. Therefore, equation (8) is simplified to:

[0061]

[0062] The two-dimensional discrete form of formula (9) can be expressed as:

[0063]

[0064] in, represents the distance resolution unit, f s =μB is the signal sampling rate, μ is the oversampling rate. Therefore, the distance variable is r=nρ, and the target distance is R 0,k =n R,k ρ, ρ=c / 2f s represents the distance sampling unit, n and n R,k are the discretization indexes of r and R0 respectively. m is the discretization index of slow time, T r is the pulse interval time.

[0065] In order to eliminate the RM effect caused by the target speed, the MLRT algorithm can be designed to perform a rotation transformation on the coordinates. Figure 2 A schematic diagram of the MLRT algorithm is given, (a) target RM effect, (b) MLRT result (c) MLRT results The MLRT algorithm is defined as follows:

[0066]

[0067] Among them, (m,n) and (m′,n′) represent the coordinates before and after the rotation, respectively. is the rotation angle. Specifically, the coordinates before and after the rotation satisfy the relationship:

[0068]

[0069] Substituting formula (12) into formula (10) yields:

[0070]

[0071] when When , formula (13) becomes:

[0072]

[0073] It can be seen from formula (14) that the RM caused by the target speed is corrected. Since the target energy is concentrated in the same distance unit, in this embodiment, the energy can be integrated along the slow time dimension to estimate the rotation angle. Therefore, the following cost function can be constructed to achieve angle estimation, and the discrete value can be achieved by adding and summing:

[0074]

[0075] when When the maximum value is reached, the RM effect of the target is corrected. First estimate The rotation angle corresponding to the maximum value, and then the target real speed and initial distance are estimated in turn:

[0076]

[0077] Furthermore, for the estimated initial distance of the target, the target slow time dimension signal is extracted along the slow time dimension, and the parameter symmetric autocorrelation function in the improved Lu distribution algorithm is used to extract the oversampling rate and distance variables in the signal for calculating the target acceleration and jerk. Among them, for the parameter symmetric autocorrelation function extraction process, the signal is first decoupled by the scale Fourier transform, and then the two-dimensional Fourier transform is used to obtain the slow time variable and the frequency corresponding to the variable delay. The oversampling rate and distance variables are obtained by the peak coordinates gathered by the two-dimensional Fourier transform in the plane composed of the frequency.

[0078] The target's true speed and initial distance can be estimated by the MLRT algorithm, and the target's high-order parameters, such as acceleration and jerk, can be estimated by the improved Lu distribution MLVD algorithm. Using the estimated initial distance, the target slow-time dimension signal can be extracted from equation (14):

[0079]

[0080] Among them, t′ m = m′T r is the slow time variable after the coordinate rotation transformation. The signal at this time is a one-dimensional signal and is only related to the slow time variable. From formula (17), it can be seen that the one-dimensional signal conforms to the expression form of the QFM signal, so formula (17) can be rewritten as:

[0081]

[0082] in,

[0083] The LVD algorithm can estimate the carrier frequency and frequency modulation slope of the LFM signal, but because the QFM signal contains cubic terms, the LVD cannot accurately estimate the cubic coefficient of the signal, that is, the quadratic frequency modulation rate. Therefore, for the time-frequency analysis of the QFM signal, the MLVD algorithm is used in this embodiment to estimate the acceleration and jerk of formula (17). The principle is introduced below:

[0084] The parametric symmetric self-correlation function (PSSF) of the MLVD algorithm is defined as:

[0085]

[0086] Where τ is the variable delay, τ0 and α are the fixed delay redundancies. τ0 can be set to 0.178M, M is the length of the slow time, and α is set to 1. Substituting equation (18) into equation (19) yields:

[0087]

[0088] From equation (19), we can see that PSSF reduces the order of QFM signal, and the result after multiplication can extract the target μ and γ. m There are coupling terms between and τ, which need to be decoupled using the scale-defined Fourier transform SFT:

[0089]

[0090] Among them, h is a constant and affects the estimated range of γ, t n is the slow time after transformation. Substituting formula (21) into formula (20) yields:

[0091]

[0092] From formula (22), we can see that t′ m The coupling terms of and τ have been eliminated. To estimate the two parameters μ and γ, a two-dimensional Fourier transform can be performed on equation (22), namely:

[0093]

[0094] where f n With f τ They are t n The frequency corresponding to τ after FFT.

[0095] From formula (23), we can see that at f n With f τ In the plane formed by n ,f τ ) gather into a peak value. By extracting the positive ordinate corresponding to the peak value, the corresponding μ and γ values ​​can be estimated, which can be converted into the acceleration and jerk of the target and expressed as:

[0096]

[0097] Among them, f n,max and f τ,max is L(f n ,f τ ) The coordinates corresponding to the peak.

[0098] After estimating the motion parameters of the target, the following phase function can be constructed to correct the LDFM and QDFM effects, namely:

[0099]

[0100] Multiply equation (25) and equation (14) and calculate the slow time dimension t′ m Perform FFT to achieve coherent accumulation:

[0101]

[0102] Furthermore, for the case of coherent detection of multiple maneuvering targets, each maneuvering target is traversed in turn, and estimated in turn through rotating coordinate transformation and improved Lu distribution algorithm until all maneuvering targets complete coherent detection.

[0103] Assuming there are K targets, equation (11) can be rewritten as follows in the case of multiple targets:

[0104]

[0105] Where k = 1, 2, LK. Substituting equation (12) into (27) yields:

[0106]

[0107] Similarly, the i-th search angle satisfy When , formula (28) becomes:

[0108]

[0109] From formula (29), it can be seen that after the rotation angle, the RM of the i-th target is corrected, while the remaining K-1 targets still have the RM effect. In the RD domain, the echo of the i-th target after pulse compression is in the same distance unit, while the remaining K-1 targets are not corrected to the same distance unit.

[0110] According to formula (16), the true speed and initial distance of the i-th target can be estimated. The slow time dimension signal corresponding to the initial distance is extracted:

[0111]

[0112] Where, is the initial distance of the i-th target Then, the MLVD algorithm is used to estimate the parameters of the one-dimensional slow-time signal to obtain the acceleration and jerk.

[0113]

[0114] in, Finally, the compensation terms of acceleration and jerk are constructed to complete the coherent accumulation.

[0115] It can be seen from formula (29) that after the coordinate axis is rotated, the signal in the same distance unit can be extracted. The extracted signal is a one-dimensional signal, and when the MLVD algorithm is used, the signal is not affected by the cross term, which improves the anti-noise performance of the algorithm.

[0116] Based on the above content, the implementation algorithm of this case can be as follows Figure 3 As shown, the specific steps can be designed as follows:

[0117] Step 1: Pulse compress the radar echo to obtain equation (10);

[0118] Step 2: Based on the specific parameters of the radar and the estimated target range-Doppler image target tilt angle, predetermine the rotation angle search range [θ min ,θ max ];

[0119] Step 3: Use the MLRT algorithm to implement angle rotation for equation (11) and perform energy integration on the rotated signal. The optimal search angle is obtained based on the maximum value after integration. Substitute into equation (13) to eliminate distance migration and estimate Calculate the true speed and initial distance

[0120] Step 4: According to Extract the corrected one-dimensional signal along the slow time dimension from equation (14);

[0121] Step 5: Use the MLVD algorithm to estimate the parameters of the one-dimensional signal formula (17) and obtain the target acceleration and jerk

[0122] Step 6: Construct the compensation terms of acceleration and jerk and multiply them with equation (14), then perform FFT on the slow time dimension signal to achieve coherent accumulation.

[0123] Step 7: Determine whether all targets have been traversed. If all targets have been accumulated, perform CFAR detection, otherwise return to step 3 and repeat steps 3 to 7 for the next target.

[0124] Further, based on the above method, an embodiment of the present invention also provides a coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution, comprising: a coordinate rotation estimation module, a Lu distribution estimation module and a coherent accumulation module, wherein:

[0125] The coordinate rotation estimation module is used to perform pulse compression and two-dimensional discrete form transformation on the radar echo signal, and set the rotation search angle range. The optimal rotation search angle is determined by rotating the echo trajectory to the same distance unit through the rotation coordinate transformation, and the target speed and initial distance are estimated according to the optimal rotation search angle.

[0126] The Lv distribution estimation module is used to extract the signal in the same distance unit according to the initial distance, and estimate the target acceleration and jerk parameters by using the improved Lv distribution algorithm;

[0127] The coherent accumulation module is used to compensate the target acceleration and jerk parameters by using the phase function to correct the linear Doppler frequency shift caused by acceleration and the quadratic Doppler frequency shift caused by jerk, and realize the coherent accumulation by Fourier transform.

[0128] In order to verify the effectiveness of this solution, the following is a further explanation based on the test data:

[0129] 1) Algorithm complexity

[0130] GRFT, KT-GDP, KT-CPF, KT-PGA, and PSICPF algorithms are selected for comparison. Assume that N a 、N g 、N v Represents the number of searches for acceleration, jerk, and speed, respectively. N F 、N p They are the number of angle searches, the number of folding factor searches, and the number of PGA iterations. The number of fast time units is Nr , the number of pulses is M.

[0131] The main steps and complexity of the MLRT-MLVD algorithm in this case solution include: MLRT operation and MLVD operation, with computational complexity of O(MN r N θ ) and O(M 2 log2M). Therefore, the complexity of the MLRT-MLVD algorithm is

[0132] The GRFT algorithm performs phase compensation through multi-dimensional parameter search to achieve coherent accumulation, and the calculation complexity is about O(MN r N v N a N g ).

[0133] The KT-GDP algorithm mainly uses the KT transform (Keystone Transform, KT) to correct distance migration, and the computational complexity is about As well as the parameter search for acceleration and jerk, the computational complexity is about O(N a N g MN r log2N r ). Therefore, the total complexity of the KT-GDP algorithm is approximately O[N r MN a N g log2N r +N F (Mlog2M)].

[0134] The KT-CPF algorithm mainly includes the speed folding factor search, which requires N F KT transformations. Therefore, the total complexity of the algorithm is about O(3N F N r Mlog2M).

[0135] The KT-PGA algorithm mainly includes coarse accumulation and fine accumulation. Coarse accumulation includes the search of folding factors, and fine accumulation includes PGA iterative operations. Therefore, the computational complexity is about O(N F N p N r Mlog2M).

[0136] The PSICPF algorithm mainly includes bilinear autocorrelation operations, and the computational complexity is O(M 2 ), Scaled Nonuniform Fast Fourier Transform (SNUFFT) and IFT operations, the computational complexity is O(2M2 log2M) and O(M 2 log2M). Compared with the slow-time Scaled Fourier Transform (SFT) and FT, the computational complexity of integrating the signal is approximately O(3M 2 log2M) and O(M 2 log2M). The computational complexity of KT and folding factor search is O(4MN respectively. r log2M) and O(N F N r Mlog2N r M). Therefore, the total computational complexity of the algorithm is O(7N r M 2 log2M+N F MN r log2MN r ).

[0137] Table 1 Comparison of computational complexity of different algorithms

[0138]

[0139] The computational complexity of the above algorithm is given in Table 1. Assume N p =10, N F =20. Figure 4 The computational complexity of the above methods is intuitively demonstrated. The computational complexity of GRFT is obviously much higher than that of other algorithms, that is, it takes the longest time and does not meet the actual needs of efficient and fast detection. Compared with GRFT, KT-GDP and PSICPF, MLRT-MLVD only searches for the rotation angle, and the MLVD operation is performed after the angle search, so the computational complexity is relatively low. In addition, the computational complexity of the MLRT-MLVD algorithm is lower than that of the KT-PGA and KT-CPF algorithms before 400 pulses, and the computational complexity is between the KT-PGA and KT-CPF algorithms after 400 pulses, and the difference is only about one order of magnitude. Therefore, the KT-CPF algorithm is faster than MLRT-MLVD in calculation speed, but the detection performance of the MLRT-MLVD algorithm under low SNR conditions is inferior to that of KT-CPF.

[0140] 2) Algorithm performance evaluation

[0141] The effectiveness of the MLRT-MLVD algorithm in this case is demonstrated through single-objective and multi-objective simulation experiments. The simulation parameters are shown in Table 2.

[0142] Table 2 Radar simulation parameters

[0143]

[0144] The coherent accumulation result of a single target is as follows: Figure 5 As shown, the target motion parameters are: R0 = 100km, v = 250m / s, a = 15m / s 2 , g = 9 m / s 3 , the signal-to-noise ratio after pulse compression is 5dB. (a) is the trajectory of the target after pulse compression. It can be clearly seen that the range migration occurs due to the high-speed movement of the target. (b) is the search result of the coordinate axis rotation angle. Within the preset search range, the optimal rotation angle is The target speed and initial distance are calculated based on the rotation angle, which are v = 250m / s and R0 = 100km respectively: (c) is the result after the coordinate rotation and the distance migration correction, at which time the target trajectory is corrected to the same distance unit. Then, the slow time dimension signal in the distance unit is extracted, and the acceleration and jerk are estimated using the MLVD algorithm; (d) is the result of the MLVD algorithm parameter estimation, and its peak position can be used to estimate the target motion parameter as a = 15m / s 2 , g = 9 m / s 3 Finally, after constructing the compensation terms of acceleration and jerk, LDFM and QDFM are eliminated to achieve coherent accumulation, and the result is shown in (e).

[0145] In order to compare the performance of MLRT-MLVD, KT-GDP, KT-CPF, GRFT, PSICPF and KT-PGA coherent accumulation under low SNR conditions, Figure 6 The coherent accumulation results of different algorithms are given when SNR = -5dB; specifically, Figure 6In the figure, (a) and (b) are the coherent accumulation results of MLRT-MLVD and KT-GDP, respectively. It can be seen that both have good coherent accumulation performance, but the computational complexity of MLRT-MLVD is much lower than that of KT-GDP, and it can be processed in real time more quickly; (c) is the coherent accumulation result of KT-CPF. It can be found that the algorithm cannot achieve accumulation. Since the CPF algorithm only uses the energy ridge in the time-modulation frequency distribution to construct the least squares, and does not use coherent accumulation, the accumulation performance is poor; (d) is the coherent accumulation result of GRFT. Although the anti-noise performance of GRFT is better than other algorithms, the high computational complexity of four-dimensional search and the influence of blind speed sidelobes bring difficulties to the real-time and accuracy of target detection; (e) is the coherent accumulation result of PSICPF. It can be seen that the algorithm cannot achieve coherent accumulation due to the slice product estimation parameter of each range frequency; (f) is the coherent accumulation result of KT-PGA. It can be seen that the position of the target energy focus is somewhat different from the actual target position. This is because the algorithm only uses the phase information of the signal, and the parameter fitting error is large during curve fitting, resulting in failure to fully compensate for the LDFM and QDFM effects.

[0146] The coherent accumulation results for weak multi-targets are as follows: Figure 7 As shown in Table 3, the motion parameters of the two targets are given.

[0147] Table 3 Target motion parameters

[0148]

[0149] Figure 7 In the figure, (a) is the result of pulse compression of the two target signals. Obviously, both targets have RM effect. (b) is the result of searching for rotation angle. The optimal rotation angles of the two targets are and The speed and initial distance of the two targets are calculated as v1 = 150 m / s, R 1,0 =100.001km and v2 = -100m / s, R 2,0 =99.497km, the estimated parameters are slightly different from the set parameters; (c) and (d) are the results of eliminating the RM effect for target 1 and target 2, respectively. The two target signals gathered in the same distance unit are extracted respectively, and the MLVD algorithm is used to estimate their respective motion parameters. The results are shown in (e) and (f). The estimated parameters are a1=15m / s 2 , g1=9m / s 3 and a2=-20.25m / s 2 , g2=-15m / s 3; (g) and (h) are the results of the coherent accumulation of the two targets, respectively. It can be clearly seen that the two targets show good coherent accumulation effect, indicating that the algorithm in this case can perform effective coherent accumulation and parameter estimation for multiple targets.

[0150] 3) Noise immunity evaluation

[0151] like Figure 8 shown.

[0152] 4) Parameter estimation performance evaluation

[0153] The root mean square error RMSE is used as the evaluation standard, and the parameter estimation curves of each algorithm are as follows: Fig. 9 As shown, (a) velocity parameter RMSE, (b) acceleration parameter RMSE, (c) jerk parameter RMSE. Similar to the target detection curve, the parameter estimation curve basically maintains the same signal-to-noise ratio threshold. It can be seen from the error estimation curves of the three parameters that the GRFT algorithm has the best parameter estimation performance. When the signal-to-noise ratio is higher than -5dB, the MLRT-MLVD algorithm in this case has similar estimation performance to the KT-GDP algorithm. Compared with the KT-CPF, KT-PGA and PSICPF algorithms, the parameter estimation performance has obvious advantages. Considering the detection performance, parameter estimation performance and computational complexity, the algorithm proposed in this case achieves a better compromise than other algorithms.

[0154] 5) Accumulated performance of measured data

[0155] The algorithm in this case is tested using real data. The real data uses ground objects as the noise background and uses Ka-band radar to detect fixed-wing UAV targets to obtain pulse compression echo data. The radar parameters are shown in Table 4.

[0156] Table 4 Basic parameters of Ka-band radar

[0157]

[0158] Data 4 from the public dataset is selected for processing. This data contains 64,000 pulses. Since the data is labeled at a rate of 50 ms, that is, one result is output every 1,600 pulses. Pulses 1 to 1,600 are selected for the measured data experiment. The radar pulse compression results are shown in Figure 2. Fig.10 As shown in (a) in the figure, there is serious ground clutter in the echo of this data set. Fig.10 (b) shows the result of two-pulse target cancellation, and the clutter is effectively suppressed. After searching the rotation angle, the best angle is obtained. like Fig.10 As shown in (c). According to formula (16), the target speed and initial distance are calculated as follows: Then, the MLRT operation eliminates the RM effect, such as Fig.10 As shown in (d) in . Fig.10 (e) is the target motion parameter estimated by the MLVD algorithm. From the peak position of the focus, the acceleration and jerk of the target can be estimated as It can be seen that the drone is in a uniform flight state. After phase compensation, coherent accumulation is performed, and the target position is gathered into a significant peak, such as Fig.10 As shown in (f) in the figure. It is known that the GPS positioning data of this data is R0 = 1.554 km, The difference between the initial distance and speed estimated by the algorithm in this case is small. Therefore, it can be proved that the algorithm proposed in this case can effectively realize the target coherent accumulation and complete the moving target parameter estimation.

[0159] The above data proves that compared with the existing GRFT, KT-GDP, KT-CPF, KT-PGA, and PSICPF algorithms, the algorithm proposed in this case has lower computational complexity and higher detection performance and parameter estimation performance, and achieves a good compromise between computational complexity and noise resistance and parameter estimation performance; it is verified using actual measured data of UAVs detected by Ka-band radar, and the results show that the algorithm proposed in this case has good accumulation capabilities and can meet the needs of actual application scenarios.

[0160] Unless otherwise specifically stated, the relative steps, numerical expressions and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present invention.

[0161] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution, characterized in that: Contains the following: The radar echo signal is pulse compressed and transformed into a two-dimensional discrete form, and the rotation search angle range is set. The echo trajectory is rotated to the same distance unit by rotating the coordinate transformation to determine the optimal rotation search angle, and the target speed and initial distance are estimated according to the optimal rotation search angle; wherein, the pulse compression process of the echo signal of the kth target is expressed as: Indicates fast time, T p is the pulse duration, k r =B / T p is the LFM signal modulation frequency, B is the transmission signal bandwidth, f c represents the carrier frequency, t m =m / f p represents the slow time variable, m=0,1,…,M-1 is the pulse index, M is the total number of accumulated pulses, f p =1 / T r is the radar pulse repetition frequency, T r represents the pulse repetition interval, c is the electromagnetic wave speed, A c,k is the amplitude, R 0,k 、v k 、a k and g k Respectively represent the initial distance, velocity, acceleration and jerk of the kth target echo signal; using The signal after two-dimensional discrete form transformation is rotated, and the energy of the rotated signal is integrated along the slow time dimension. The optimal rotation search angle is obtained according to the maximum value after integration. (m,n) and (m′,n′) are the coordinates before and after the signal rotation, respectively. is the rotation search angle; the optimal rotation search angle is estimated and obtained by constructing a cost function, and the cost function is expressed as: By solving the cost function, The rotation angle corresponding to the maximum value is taken as the optimal rotation search angle required to be obtained; for the optimal rotation search angle, use the formula To estimate the target speed and initial distance is the optimal rotation search angle, μ is the oversampling rate, ρ represents the distance sampling unit, Δr represents the distance resolution unit, T r is the pulse interval time, n max Indicates the maximum value of the maximum discretization index of the target distance; The signal in the same distance unit is extracted according to the initial distance, and the target acceleration and jerk parameters are estimated by using the improved Lu distribution algorithm; wherein, for the estimated target initial distance, the target slow time dimension signal is extracted along the slow time dimension, and the parameter symmetric autocorrelation function in the improved Lu distribution algorithm is used to extract the oversampling rate and distance variables used to calculate the target acceleration and jerk in the signal, and for the parameter symmetric autocorrelation function extraction process, the signal is first decoupled by the scale Fourier transform, and then the two-dimensional Fourier transform is used to obtain the slow time variable and the frequency corresponding to the variable delay, and the oversampling rate and distance variables are obtained by the peak coordinates gathered by the two-dimensional Fourier transform in the plane composed of the frequency; The target acceleration and jerk parameters are compensated by using the phase function to correct the linear Doppler frequency shift caused by acceleration and the quadratic Doppler frequency shift caused by jerk, and the phase coherent accumulation is realized by Fourier transform. For the case of coherent detection of multiple maneuvering targets, each maneuvering target is traversed in turn, and estimated in turn through rotating coordinate transformation and improved Lu distribution algorithm until all maneuvering targets have completed coherent detection.

2. The method for coherent detection of maneuvering targets based on improved coordinate rotation and Lu distribution according to claim 1, characterized in that: In the detection process, a high-order polynomial model is used to characterize the target motion according to the linear frequency modulation signal emitted by the radar, and the pulse compression is performed on the reflected echo signal received by the receiver.

3. The method for coherently detecting maneuvering targets based on improved coordinate rotation and Lu distribution according to claim 1, characterized in that: The rotation search angle range is determined based on radar parameters and the target range-Doppler frequency domain target inclination angle.

4. A coherent detection method for maneuvering targets based on improved coordinate rotation and Lu distribution, characterized in that: The method according to claim 1 is implemented, comprising: a coordinate rotation estimation module, a phase distribution estimation module and a coherent accumulation module, wherein: The coordinate rotation estimation module is used to perform pulse compression and two-dimensional discrete form transformation on the radar echo signal, and set the rotation search angle range. The optimal rotation search angle is determined by rotating the echo trajectory to the same distance unit through the rotation coordinate transformation, and the target speed and initial distance are estimated according to the optimal rotation search angle. The Lv distribution estimation module is used to extract the signal in the same distance unit according to the initial distance, and estimate the target acceleration and jerk parameters by using the improved Lv distribution algorithm; The coherent accumulation module is used to compensate the target acceleration and jerk parameters by using the phase function to correct the linear Doppler frequency shift caused by acceleration and the quadratic Doppler frequency shift caused by jerk, and realize the coherent accumulation by Fourier transform.

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