Coherent detection method and system for maneuvering targets based on range-frequency axis inversion transform and second-order WVD

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 distance frequency axis inversion transform and second-order WVD, by pulse compressing radar echo signals, frequency inverting the pulse compressed signals along the distance frequency dimension, and gathering target echoes into the same distance unit; using second-order WVD to perform time-frequency transform on the echo signals in the distance unit, and estimating the target acceleration through Fourier transform processing; using a phase compensation function to construct the compensated distance frequency-slow time domain dimension signal that is the same as the uniform motion model, performing variable delay autocorrelation along the slow time dimension, and then performing Fourier transform on the slow time variable after decoupling through addition operation and scale Fourier transform to achieve coherent accumulation, and then estimating the actual speed and initial distance of the maneuvering target. 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 present invention belongs to the field of maneuvering target detection, and in particular relates to a maneuvering target coherent detection method and system based on range-frequency axis inversion transformation and second-order WVD. Background Art

[0002] With the development of science and technology, new stealth aircraft and small drones and other aerial targets have brought technical challenges to the detection capabilities of traditional radars due to their special design and small size, and have also put forward higher requirements for the estimation of the motion parameters of such targets. According to the basic theory of radar, increasing the transmit power, increasing the antenna aperture, and reducing the receiver noise coefficient in hardware can improve the signal-to-noise ratio (SNR) of the received signal. However, this change in hardware not only increases the cost of equipment development and use, but also increases the risk of radar exposure and destruction. In contrast, the use of signal processing algorithms such as coherent accumulation can not only achieve the above goals, but also has the advantages of flexibility and portability, becoming one of the most cost-effective means. However, the continuous movement of the target during the accumulation process can easily lead to complex range migration (RM) and Doppler frequency migration (DFM) phenomena in the echo signal, which seriously deteriorates the detection performance of the traditional moving target detection (MTD) algorithm.

[0003] To address these problems, other existing algorithms are used to solve them, such as Keystone Transform (KT) and Radon Fourier Transform (RFT) algorithms. KT achieves the decoupling of range frequency and slow time by scaling the slow time variables on each range frequency. However, KT generally needs to be implemented through the sinc interpolation method and cannot solve the problem of Doppler ambiguity. The Radon Fourier Transform (RFT) algorithm searches for the two-dimensional parameters of the target's initial range and radial velocity jointly. When the search parameters are equal to the target parameters, the energy accumulation reaches the maximum. However, the RFT algorithm will have the effect of blind velocity side lobes, and the search parameters require a lot of time and are not suitable for application in actual scenarios. These algorithms are all aimed at uniformly moving targets, and the target has a constant acceleration when it is in an accelerated dive or maneuvering evasion state. Compared with the uniform motion model, uniformly accelerated motion turns the slow time dimension signal into a non-stationary linear frequency modulated (LFM) signal. Therefore, it is quite different from the uniform motion algorithm in theory and method. In actual application scenarios, in order to quickly detect aerial targets, the radar coherent integration time must not be too long. Although the existing algorithms have good anti-noise performance, the high computational complexity causes the accumulation time to be as long as several minutes. When the computational complexity is low, the anti-noise performance is slightly insufficient. Summary of the invention

[0004] To this end, the present invention provides a coherent detection method and system for maneuvering targets based on range-frequency axis inversion transform and second-order WVD, which solves the problems of range migration and Doppler migration of aerial moving targets during long-term coherent accumulation. While reducing the calculation complexity, it can ensure the 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 range-frequency axis inversion transform and second-order WVD is provided, which includes the following contents:

[0006] Pulse compression is performed on the radar echo signal, and the pulse compressed signal is frequency-inverted along the range-frequency dimension to eliminate range migration and gather the target echo into the same range unit;

[0007] The second-order WVD is used to perform time-frequency transformation on the echo signal in the range unit, and the target acceleration is estimated by Fourier transforming the signal after time-frequency transformation.

[0008] A phase compensation function is constructed using the estimated target acceleration, and the phase compensation function is used to construct a compensated range frequency-slow time domain dimensional signal identical to the uniform motion model;

[0009] For the compensated distance frequency-slow time domain signal, variable delay autocorrelation is performed along the slow time dimension. After decoupling through addition operation and scale Fourier transform, the slow time variable is transformed to achieve coherent accumulation. The actual speed and initial distance of the maneuvering target are estimated by the peak value and the predetermined threshold in the Fourier transform process.

[0010] As a coherent detection method for maneuvering targets based on range-frequency axis inversion transform and second-order WVD of the present invention, further, for the linear frequency modulation signal emitted by the coherent radar during the detection process, the target echo signal after down-conversion by the receiver is obtained according to the target motion process model.

[0011] As a coherent detection method for maneuvering targets based on range-frequency axis inversion transform and second-order WVD of the present invention, further, the pulse compression process of the echo signal of the k-th target is expressed as: in, Indicates fast time, 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, c is the electromagnetic wave speed, f c Indicates carrier frequency, A c,k is the amplitude, R 0,k 、v k and a k They represent the initial distance, velocity and acceleration of the kth target echo signal respectively.

[0012] As a coherent detection method for maneuvering targets based on the range-frequency axis inversion transform and the second-order WVD of the present invention, further, in order to eliminate the range migration, a range-frequency axis is set, the signal is inverted along the range-frequency axis, and the signals before and after the inversion are multiplied, and the range migration in the range-slow time domain is corrected by performing Fourier transform on the range frequency corresponding to the fast time in the multiplied signal.

[0013] As a coherent detection method for maneuvering targets based on range-frequency axis inversion transform and second-order WVD of the present invention, further, for the signal after eliminating the range migration, the two-dimensional data is converted into one-dimensional data by selecting the slow time dimension to eliminate the influence of fast time, and the target echo is gathered into the same distance unit; and the maximum unambiguous speed, fuzzy factor and fuzzy speed of the coherent system radar are used to mark the true speed of the target.

[0014] As a coherent detection method of a maneuvering target based on range-frequency axis inversion transformation and second-order WVD of the present invention, further, the time-frequency transformation process of the SoWVD algorithm using the second-order WVD is expressed as:

[0015] Among them, τ0 is the constant delay, τ is the delay variable, and v 0,k is the blur speed.

[0016] As a coherent detection method for maneuvering targets based on range-frequency axis inversion transform and second-order WVD of the present invention, further, for the signal after time-frequency transform, the time delay variable and the slow time variable are respectively subjected to Fourier transform, according to the signal peak position, and using To estimate the target acceleration in, express The maximum value of .

[0017] As a coherent detection method for maneuvering targets based on range-frequency axis inversion transform and second-order WVD of the present invention, further, the range-frequency-slow-time domain dimensional signal of the k-th target after compensation is expressed as:

[0018] Among them, A 1,k is the corresponding amplitude, f r It's fast time The corresponding distance frequency, B is the transmission signal bandwidth.

[0019] As a coherent detection method for maneuvering targets based on distance-frequency axis inversion transform and second-order WVD of the present invention, further, for the case of coherent detection of multiple maneuvering targets, each maneuvering target is traversed in turn, and for each maneuvering target, the target acceleration, initial distance and speed are estimated by distance-frequency axis inversion transform and second-order WVD time-frequency transform until all maneuvering targets complete coherent detection.

[0020] Furthermore, the present invention also provides a coherent detection method for maneuvering targets based on range-frequency axis inversion transformation and second-order WVD, comprising: an inversion transformation module, a time-frequency transformation module, a phase compensation module and a coherent detection module, wherein:

[0021] The inversion transformation module is used to perform pulse compression on the radar echo signal, perform frequency inversion on the pulse compressed signal along the range frequency dimension, eliminate range migration, and gather the target echo into the same range unit;

[0022] The time-frequency transformation module is used to perform time-frequency transformation on the echo signal in the range unit by using the second-order WVD, and estimate the target acceleration by performing Fourier transformation on the signal after the time-frequency transformation;

[0023] A phase compensation module, used to construct a phase compensation function using the estimated target acceleration, and to construct a compensated distance frequency-slow time domain dimension signal identical to the uniform motion model using the phase compensation function;

[0024] The coherent detection module is used to perform variable delay autocorrelation along the slow time dimension for the compensated distance frequency-slow time domain signal, and then perform Fourier transform on the slow time variable after decoupling through addition operation and scale Fourier transform to achieve coherent accumulation. The actual speed and initial distance of the maneuvering target are estimated through the peak value and predetermined threshold in the Fourier transform process.

[0025] Beneficial effects of the present invention:

[0026] The present invention aims at the problems of range migration and Doppler migration of aerial moving targets during long-term coherent accumulation. The range migration is eliminated by reversing the range frequency axis, and the target echoes are gathered into the same range unit. The target acceleration is estimated by the second-order SoWVD algorithm for the echoes in this range unit, and the target acceleration is realized by two FFTs to avoid the use of scale Fourier transform to reduce the operation speed. The acceleration compensation term is used to transform the uniform acceleration model into a uniform speed model, and the coherent accumulation of non-parameter search is realized to estimate the speed and initial distance. It is further proved in combination with experimental data that the scheme of this case can effectively reduce the computational complexity, and has good parameter estimation performance and detection performance, and achieves a compromise coherent accumulation result, which can meet the needs of actual application scenarios and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the coherent detection process of maneuvering targets based on range-frequency axis inversion transformation and second-order WVD in the embodiment;

[0028] Figure 2 This is a schematic diagram of the radar observation scene in the embodiment;

[0029] Figure 3 This is a schematic diagram of the algorithm implementation process of this case in the embodiment;

[0030] Figure 4 The following is a comparison of the computational complexity of different algorithms in the embodiments;

[0031] Figure 5 It is a schematic diagram of the coherent accumulation simulation of the uniformly accelerated target by the MTD and SCIFT algorithms in the embodiment;

[0032] Figure 6 It is a comparison diagram of the coherent accumulation performance in the embodiment;

[0033] Figure 7 This is a schematic diagram of the coherent accumulation process of two targets in the embodiment;

[0034] Figure 8 This is a comparison of the detection performance of different algorithms in the embodiment;

[0035] Fig. 9 It is an illustration of RMSE of speed estimation in the embodiment;

[0036] Fig.10 is the acceleration estimation RMSE in the embodiment;

[0037] Fig.11 It is a schematic diagram of the coherent accumulation results of the measured data in the embodiment. DETAILED DESCRIPTION

[0038] 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.

[0039] The present invention provides a method for detecting maneuvering targets based on range-frequency axis inversion transform and second-order WVD. Figure 1 As shown, it contains the following contents:

[0040] S101, pulse compressing the radar echo signal, performing frequency inversion on the pulse compressed signal along the range frequency dimension, eliminating range migration, and gathering the target echoes into the same range unit;

[0041] S102, using a second-order WVD to perform time-frequency transformation on the echo signal in the distance unit, and estimating the target acceleration by performing Fourier transformation on the signal after the time-frequency transformation;

[0042] S103, constructing a phase compensation function using the estimated target acceleration, and using the phase compensation function to construct a compensated distance frequency-slow time domain dimension signal identical to the uniform motion model;

[0043] S104. For the compensated distance frequency-slow time domain signal, variable delay autocorrelation is performed along the slow time dimension, and then after decoupling through addition operation and scale Fourier transform, Fourier transform is performed on the slow time variable to achieve coherent accumulation, and the actual speed and initial distance of the maneuvering target are estimated through the peak value and the predetermined threshold in the Fourier transform process.

[0044] To solve the range migration and Doppler migration of aerial moving targets during long-term coherent integration, the range migration is eliminated by inverting the range-frequency axis and the target echoes are gathered into the same range unit. The second-order SoWVD algorithm is used to estimate the target acceleration for the echoes in this range unit, and the acceleration compensation term is used to transform the uniform acceleration model into a uniform speed model, so as to realize the coherent accumulation of non-parameter search to estimate the velocity and initial distance, which can improve the parameter estimation effect while reducing the computational complexity.

[0045] Furthermore, for the linear frequency modulation signal emitted by the coherent radar during the detection process, the target echo signal after down-conversion by the receiver is obtained according to the target motion process model.

[0046] The observation scene of the coherent radar on the aerial target is as follows: Figure 2 As shown, the radar is set to transmit a commonly used linear frequency modulation signal (LFM), which can be:

[0047]

[0048] in,

[0049]

[0050] 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 p represents 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 the Pulse Repetition Interval (PRI).

[0051] Assuming there are K targets in the observation scene, when the kth target moves with a constant acceleration, the distance between the radar and the target can be expressed as:

[0052]

[0053] Among them, R 0,k 、v k and a k are the initial distance, velocity and acceleration of the kth target respectively. Since the target motion process is similar to the "stop-go-stop" model, the motion of the target within a pulse can be ignored, that is:

[0054]

[0055] After down-conversion by the receiver, the echo signal of the kth target can be expressed as:

[0056]

[0057] Where c is the electromagnetic wave speed, A 0,k is the amplitude. After pulse compression, the echo signal can be expressed as:

[0058]

[0059] For formula (6) After Fourier transform, the corresponding distance frequency-slow time domain can be expressed as:

[0060]

[0061] Among them, f r yes The corresponding distance frequency, sinc function is the signal envelope.

[0062] It can be seen from formula (6) that when the change exceeds Δr = c / 2f s When the target has a large acceleration, the LRM effect will appear. Similarly, if the target has a large acceleration, the range envelope will bend, that is, the quadratic range migration (QRM) effect will also appear. The exponential term indicates the Doppler frequency of the linear migration of the target, that is:

[0063]

[0064] From equation (8), it can be seen that when the Doppler shift exceeds one frequency resolution unit, Doppler frequency migration (DFM) will occur, causing the target energy to be defocused when accumulated in the Doppler domain. In addition, due to the high speed of the target and the low PRF of the radar, the Doppler ambiguity problem may still exist. Compared with the case where the target moves at a constant speed, the maneuvering target has additional QRM and DFM effects. Only by effectively eliminating the above unfavorable factors can a good coherent accumulation be achieved.

[0065] In eliminating range migration, the signal can be reversed along the range frequency axis by setting the range frequency axis, and the signals before and after the inversion can be multiplied, and the range migration in the range-slow time domain can be corrected by Fourier transforming the range frequency corresponding to the fast time in the multiplied signal. Furthermore, for the signal after eliminating range migration, the influence of fast time can be eliminated by converting the two-dimensional data into one-dimensional data by selecting the slow time dimension, and the target echo can be gathered into the same range unit; and the maximum unambiguous speed, ambiguity factor and ambiguity speed of the coherent radar can be used to mark the true speed of the target.

[0066] By using slow time dimension inversion, the parameters of odd-order terms in the pulse signal echo can be eliminated and the signal power can be reduced. In this embodiment, the distance frequency axis is inverted and multiplied with the original signal so that the signal after the product eliminates the distance frequency f r The influence of the slow time dimension tm Therefore, the purpose of correcting the range migration is achieved. The range frequency inversion is defined as:

[0067] By performing frequency inversion on equation (6) along the distance frequency dimension, we can obtain

[0068]

[0069] in, Indicates the inversion of the distance-frequency axis. With the original signal S c,k (f r ,t m ) and we get:

[0070]

[0071] Among them, A 2,k is the amplitude. From formula (10), it can be seen that the distance frequency axis inversion multiplication eliminates f r , so that formula (10) and f r At the same time, f r With t m The coupling term of f is eliminated. r Perform inverse Fourier transform and get:

[0072]

[0073] Formula (11) completes the range migration correction in the range-slow time domain.

[0074] As shown in formula (11), There are two-dimensional variables in and t m However, the signal energy is It is irrelevant, so the slow time dimension after distance migration correction is selected to eliminate The impact of

[0075]

[0076] in, Indicates along Dimension selection, A 3,k represents the gain. At this point, the two-dimensional data is converted into one-dimensional data, eliminating f r The influence of this method reduces the computational complexity of the following constant-delay conjugate multiplication, making the algorithm faster.

[0077] Considering that the target speed will exceed the maximum unambiguous speed of the radar, the target speed can be recorded as:

[0078] vk =n T,k v b +v 0,k

[0079] Among them, v k is the true speed, n T,k is the fuzziness factor, v b is the maximum unambiguous velocity, v 0,k is the blur speed.

[0080] So we rewrite equation (12) as:

[0081]

[0082] Among them, using exp(-j2πf c n T,k v b t m / c)=1 for simplified processing.

[0083] It can be seen from formula (13) that the expression conforms to the form of a linear frequency modulation signal in the slow time dimension. In this embodiment, the SoWVD algorithm can be used to estimate the acceleration parameters. The specific process of the SoWVD algorithm can be described as follows:

[0084]

[0085] Among them, τ and τ1 are two time delay variables.

[0086] Substituting formula (13) into formula (14) yields:

[0087]

[0088] From formula (14), we can see that when τ and τ1 have a fixed delay difference, t m The coupling between τ and τ1 is eliminated, that is:

[0089] 2τ0=τ1-τ (16)

[0090] Where τ0 is a constant delay. Substituting equation (16) into equation (15) yields:

[0091]

[0092] As shown in formula (17), R SoWVD (t m ,τ,τ1) has a three-dimensional variable t m , τ and τ1. However, after introducing the constant time delay τ0, the three-dimensional variable is reduced to two dimensions (t m and τ). At the same time, the coupling between the variables is eliminated. Then, t mFourier transform of and τ can be obtained:

[0093]

[0094] From formula (18), we can see that R SoWVD (tm,τ;τ0) at f τ =0 and A peak value will be generated at the point where the target acceleration a can be estimated based on the peak position. k for:

[0095]

[0096] in, express The maximum value of .

[0097] From equation (19), we can see that the selection of τ0 plays an important role in the acceleration estimation in this case. A larger τ0 value will improve the accuracy of parameter estimation, but too large a value will cause spectrum aliasing. The selection of τ0 requires a trade-off between parameter estimation accuracy and spectrum aliasing. In this embodiment, τ0 < T CI / 4, where T CI The time for coherence accumulation.

[0098] When using SoWVD to estimate the target acceleration, there is no coupling between variables during the calculation process due to the constant time delay difference. Therefore, the overall calculation can be quickly calculated by two-dimensional FFT, which is faster and easier to implement. It avoids the need to introduce a scale factor to decouple and use scale Fourier transform. SoWVD is more conducive to actual application.

[0099] After estimating the target acceleration, the acceleration compensation function can be constructed to eliminate the influence of the acceleration in equation (7) and transform it into a uniform motion model. Then, the SCIFT algorithm is used to quickly estimate the true speed and realize coherent accumulation.

[0100] Using the estimated target acceleration, the following phase compensation function can be constructed to compensate the uniformly accelerated motion model to a uniform motion model:

[0101]

[0102] Multiplying equation (20) with equation (7), the compensated range frequency-slow time dimension signal is:

[0103]

[0104] From formula (21), we can see that after compensation, Q k (f r ,t m) is the same as the model of uniform motion. In this embodiment, the SCIFT algorithm can be used for coherent accumulation and estimation of the true speed. The SCIFT algorithm directly estimates the true speed of the target by using the distance frequency inverse Fourier transform, avoiding the process of searching for speed parameters, so the algorithm runs faster. Therefore, considering reducing the complexity of coherent accumulation, SCIFT can be used to coherently accumulate the signal, and the specific process can be designed as follows:

[0105] Use WVD transformation to check equation (21) along the slow time dimension t m Perform variable-delay autocorrelation:

[0106]

[0107] Among them, τ m is the time delay. From formula (22), we can see that after autocorrelation, R m (f r ,t m ,τ m ) and t m Therefore, t can be eliminated by adding the equation (22) m ,Right now:

[0108]

[0109] Among them, G1 is the cumulative gain, Indicates that along t m From formula (23), we can see that f r and τ m There are coupling terms The SIFT (Scaled Inverse Fourier Transform) is used to decouple the τ m Perform FFT to achieve coherent accumulation, that is:

[0110]

[0111] Among them, A T For gain, is the equivalent fast time after SIFT, is τ m The frequency, f dk =2v k / λ.

[0112] At the point There is a single peak at The estimate of is the true speed. Then, using the estimated To compensate for the line offset in equation (21), the signal energy can be accumulated through IFFT and FFT operations.

[0113]

[0114] The signal energy is accumulated in equation (25). Therefore, target detection and initial distance estimation can be achieved by comparing the peak value with a predetermined threshold, which can be determined by CFAR detection.

[0115] Furthermore, for the case of coherent detection of multiple maneuvering targets, each maneuvering target is traversed in turn, and for each maneuvering target, the target acceleration, initial distance and velocity are estimated through the range-frequency axis inversion transform and the second-order WVD time-frequency transform until all maneuvering targets have completed coherent detection.

[0116] Based on the above method, an embodiment of the present invention further provides a coherent detection method for maneuvering targets based on range-frequency axis inversion transform and second-order WVD, comprising: an inversion transform module, a time-frequency transform module, a phase compensation module and a coherent detection module, wherein:

[0117] The inversion transformation module is used to perform pulse compression on the radar echo signal, perform frequency inversion on the pulse compressed signal along the range frequency dimension, eliminate range migration, and gather the target echo into the same range unit;

[0118] The time-frequency transformation module is used to perform time-frequency transformation on the echo signal in the range unit by using the second-order WVD, and estimate the target acceleration by performing Fourier transformation on the signal after the time-frequency transformation;

[0119] A phase compensation module, used to construct a phase compensation function using the estimated target acceleration, and to construct a compensated distance frequency-slow time domain dimension signal identical to the uniform motion model using the phase compensation function;

[0120] The coherent detection module is used to perform variable delay autocorrelation along the slow time dimension for the compensated distance frequency-slow time domain signal, and then perform Fourier transform on the slow time variable after decoupling through addition operation and scale Fourier transform to achieve coherent accumulation. The actual speed and initial distance of the maneuvering target are estimated through the peak value and predetermined threshold in the Fourier transform process.

[0121] In order to verify the effectiveness of this solution, the following is a further explanation based on the test data:

[0122] 1) Computational complexity analysis

[0123] The implementation algorithm of this case can be as follows Figure 3 As shown, the existing relatively mature SCIFT, TDST, ACCF-LVD and RFT-KT algorithms are selected for comparison.

[0124] Define the number of fast time units as N r, the number of pulses is M. For the SCIFT algorithm, the computational complexity is O(4MNrlog2(NrM)).

[0125] For the TDST algorithm, the amount of calculation of the symmetric instantaneous autocorrelation function is O(M 2 N r ), in order to eliminate the three-dimensional coupling, a two-step SFT is used, with the calculation amount of O(3M 2 Nrlog2(M)) and O(3M 2 Nrlog2(N r )). Therefore, the total computational complexity of the TDST algorithm is O(N r M 2 (3log2N r M+1)).

[0126] For the ACCF-LVD algorithm, the computational complexity of the ACCF operation is O(2MN r log2(N r )), the computational complexity of the LVD algorithm based on CZT is O(3M 2 log2(M)). Therefore, its total computational complexity is O(2MN r log2N r +3M 2 log2M).

[0127] For the RFT-KT algorithm, the main steps include the computational complexity of So-KT, which is O(4MN r log2(M)), the computational complexity of the acceleration estimation based on de-skewing is O(MN r N a log2(M)), where N a is the amount of search acceleration, and the amount of LRM correction calculation based on RFT is O(MN r N v log2(N r )), where N v is the number of search speeds. Therefore, the computational complexity of the RFT-KT algorithm is approximately O(MN r (N a log2M+N v log2N r )).

[0128] The algorithm of this case solution mainly includes the delayed autocorrelation operation, which is about O(MN r ), the computational complexity of the two-dimensional FFT is The computational complexity of SCIFT is O(4MN r log2(N r M)). Therefore, the computational complexity of the algorithm in this case is approximately

[0129] Table 1 Comparison of computational complexity of different algorithms

[0130]

[0131] Assume M = N r =N a =N v ,The computational complexity of each algorithm is listed in Table 1. Figure 4 The computational complexity of the above algorithms is given intuitively. Obviously, the computational complexity of TDST and RFT-KT algorithms is relatively large, and the calculation takes a long time, which makes it difficult to use them for real-time processing. In contrast, SCIFT, ACCF-LVD and the algorithms in this case show a great advantage in computational complexity. Taking the number of pulses as 1000 as the benchmark, the computational complexity is reduced by about 10 compared with TDST and RFT-KT algorithms. 2 The algorithm operation time is greatly reduced. In addition, the computational complexity of the algorithm in this case is slightly higher than that of SCIFT and ACCF-LVD, and much lower than that of TDST and RFT-KT. Therefore, it can be said that the algorithm in this case requires a relatively moderate computational time, which is conducive to practical application.

[0132] 2) Single target coherent accumulation

[0133] The parameters in Table 2 are used to simulate the coherent accumulation process of LFM radar for a single weak target in the air. Five algorithms, MTD, SCIFT, ACCF-LVD, TDST, and RFT-KT, are selected as algorithms for comparison. The simulation target parameters are R0 = 100 km, v = 120 m / s, a = 10 m / s 2 .

[0134] Table 2 LFM radar simulation parameters

[0135]

[0136] During the experiment, Gaussian complex noise was added to the radar echo, and the signal-to-noise ratio after pulse compression was 2dB. Figure 5 In the figure, (a) is the distance-slow time result after pulse compression, and (b) is the traditional MTD accumulation result. MTD does not compensate for the LRM, QRM and DFM caused by the speed and acceleration of the target movement, and cannot achieve the coherent accumulation of the target energy. The speed estimation and coherent accumulation results of the SCIFT algorithm are shown in Figure 2. Figure 5 As shown in (c) and (d) in the figure, SCIFT is only applicable to the model of uniform motion and cannot estimate the target acceleration, resulting in the inability to construct the acceleration compensation term, so the target cannot be accumulated.

[0137] Figure 6(a), (b), (c), and (d) are the range motion correction, acceleration estimation, velocity estimation, and coherent accumulation results of the algorithm in this case. Different from the parameter search method, the algorithm in this case avoids the search for acceleration and velocity. The acceleration estimation can be quickly calculated through FFT and IFFT, which greatly reduces the computational complexity of the algorithm. For velocity estimation, the SCIFT algorithm with a faster computing speed is used in this case, which can directly estimate the target velocity without being affected by Doppler ambiguity. Figure 6 In the figure, (a) is the result of inverting the range-frequency axis and multiplying it with IFFT. The range migration is corrected and the target energy is concentrated into one range unit. (b) is the result of estimating the acceleration using SoWVD. The signal energy is accumulated into a peak value and the position is estimated from it. The difference with the real acceleration is small. After constructing the acceleration compensation term according to formula (19) and multiplying it with the original data, the uniform acceleration model is transformed into a uniform speed model. The SCIFT algorithm can be used to quickly estimate the speed and complete the coherent accumulation. (d) is the speed estimation result of the SCIFT algorithm. The peak position estimates the speed. The true speed is accurately estimated, and the final coherent accumulation result is shown in (d); (e) gives the coherent accumulation of the ACCF-LVD algorithm. Due to the incorrect parameter estimation of the ACCF-LVD algorithm under the current signal-to-noise ratio, the energy cannot be gathered into a peak and the coherent accumulation cannot be achieved; (f) is the coherent accumulation result after the RFT-KT algorithm searches for parameters. The RFT-KT algorithm does not search for the correct parameters under the current signal-to-noise ratio and cannot detect the target under this signal-to-noise ratio; (g) and (h) are the parameter estimation and coherent accumulation results of the TDST algorithm. (g) It can be found that the parameter estimation performance of the algorithm is better. When the influence of noise on the estimation is not obvious under the signal-to-noise ratio, the acceleration and speed of the target can be accurately estimated. Both TDST and the algorithm in this case can accurately estimate the motion parameters and complete the coherent accumulation. Among them, the parameter estimation of the TDST algorithm has a stronger anti-noise performance, but it takes a long time, which is not conducive to the rapid detection of targets in actual scenes. The algorithm in this case has the advantages of low computational complexity and short algorithm time consumption, and has obvious advantages in real-time detection of targets.

[0138] 3) Multi-target coherent accumulation

[0139] For multi-objective scenarios, unlike single-objective scenarios, the multiplication in formula (14) will inevitably introduce the influence of cross-terms of multiple objectives, thereby affecting the performance of parameter estimation and coherent accumulation.

[0140] Assuming there are multiple targets in the scene, equation (7) can be rewritten as:

[0141]

[0142] So formula (10) can be rewritten as:

[0143]

[0144] Among them, R auto (f r ,t m ) represents the autocorrelation term, R cross (f r ,t m ) represents the cross-correlation term, which is specifically expressed as:

[0145]

[0146] After IFFT of equation (27), the autocorrelation term range migration is corrected, but the cross-correlation term contains coupling terms that cannot correct the range migration. Therefore, the autocorrelation term is selected for the next operation, so equation (11) can be changed to:

[0147]

[0148] Among them, A 2,k is the amplitude after IFT. After obtaining equation (29), the SoWVD algorithm is used to estimate the acceleration. After substituting the constant delay conjugate correlation, equation (17) for a single target becomes:

[0149]

[0150] Among them, R auto (t m ,τ) and R cross (t m ,τ) are the multiplied autocorrelation terms and cross terms. The specific expression of the autocorrelation term is:

[0151]

[0152] Performing a two-dimensional Fourier transform on equation (31) yields:

[0153]

[0154] From formula (32), we can see that SoWVD auto The acceleration of the target can be estimated in . However, the influence of the cross term cannot be ignored. Without loss of generality, in this embodiment, the number of targets is set to two, and the influence of the cross term in equation (30) is analyzed.

[0155] When there are two targets, the cross terms contain 14 polynomials, two of which affect parameter estimation, and the remaining 12 are ignored, resulting in:

[0156]

[0157] After performing two-dimensional Fourier transform on equation (33), we get:

[0158]

[0159] Among them, So1, So2, So3 and So4 are the four items after transformation:

[0160]

[0161]

[0162]

[0163]

[0164] From equations (35) and (36), we can see that the accelerations of the two targets can be estimated at the corresponding peaks, but equations (37) and (38) will also estimate the parameters at the peaks, and the values ​​are the averages of the accelerations of the two targets. This means that there are four peak coordinate points in the parameter estimation after the two-dimensional Fourier transform, which are and Among them, P1 and P2 are the acceleration estimation points of the two targets, and P3 and P4 are about f τ =0 axisymmetric false estimation point, the estimated acceleration is It is not the acceleration of the real target. Therefore, false estimated parameters need to be excluded during phase compensation to accurately achieve coherent accumulation.

[0165] Table 3 Target parameters

[0166]

[0167] The simulated radar uses the algorithm in this case to coherently accumulate two targets. The target parameters are shown in Table 3, the radar parameters are shown in Table 2, and the simulation results are shown in Figure 7 As shown in the figure, (a) is the result after the pulse compression of the two targets. Because the speed of the two targets exceeds the maximum unambiguous speed, the range migration phenomenon occurs; (b) is the result after the range migration correction of the algorithm in this case. It can be found that there are three straight lines in the figure. The left and right sides are the cross terms of the two targets, and the middle straight line is the autocorrelation term of the range migration correction. According to the analysis, the cross term contains f r and t m Therefore, only the autocorrelation term after the range migration correction is used to perform the next step of the algorithm operation. Figure 7 (c) is the result of acceleration estimation. There are four peaks in the figure, and the estimated acceleration values ​​are According to the analysis, among the estimated values, only and The estimate is correct, and the estimated value is not much different from the true value. and is the false estimate introduced by the cross term. If the false estimate is used to construct the compensation term, the result of coherent accumulation is as follows Figure 7 As shown in (d), the two targets do not accumulate spikes, and the existence of the targets cannot be detected during CFAR detection. Figure 7 In the figure, (e) and (f) are the correct velocity estimation and coherent accumulation results of target 1. The estimated velocity of (e) is The same as the true value, (f) the accumulated result focuses on a peak at 100 km; similarly, (g) and (h) are the velocity estimation and coherent accumulation results of target 2. (g) The estimated velocity (h) The accumulated results focus on a peak at 98 km. The coherent accumulation results of target 1 and target 2 can be detected by CFAR. Therefore, the experiment verifies that the algorithm in this case can accurately estimate the true value of the velocity and complete the coherent accumulation after eliminating the erroneous acceleration estimation value under the multi-target situation.

[0168] 4) Detection performance evaluation

[0169] The detection performance of the above six algorithms is evaluated using an average unit CFAR detector. The signal-to-noise ratio after pulse compression is set to change from -20dB to 20dB at 1dB intervals, and 200 Monte Carlo simulations are performed under each signal-to-noise ratio condition. fa =10 -6 When , the detection probability of each algorithm changes with the signal-to-noise ratio as shown in Figure 8 As shown. It can be analyzed from the figure that all algorithms are based on the detection probability Pd = 0.9, and MTD and SCIFT are algorithms for estimating uniform target models, so when estimating uniform acceleration motion, the detection performance of the two is the worst. ACCF-LVD adopts a constant delay form, and loses more energy during the accumulation process, so the anti-noise performance is poor. The RFT-KT algorithm uses the search method to estimate the target parameters, which improves the signal-to-noise ratio more than the ACCF-LVD algorithm, but loses about 10dB of signal-to-noise ratio compared to TDST. The algorithm in this case scheme estimates acceleration by using variable delay correlation and constant delay difference, which loses about 8dB of signal-to-noise ratio compared to TDST, and is better than the 2dB signal-to-noise ratio of the RFT-KT algorithm. The algorithm in this case scheme has a significant reduction in computational complexity compared to the TDST and RFT-KT algorithms. Considering the detection performance and computational complexity, the algorithm in this case scheme achieves a good compromise.

[0170] 5) Parameter estimation performance

[0171] The ACCF-LVD, TDST and RFT-KT algorithms that can estimate the target velocity and acceleration are selected for comparison. The target parameters are consistent with the single target parameters. The signal-to-noise ratio is set to -20dB and changes from 1dB to 20dB. 200 Monte Carlo experiments are performed independently under each signal-to-noise ratio condition. The experimental data are compared with the simulation values, and RMSE is selected as the error estimation standard. The results are shown in Figures (9) and (10). It can be analyzed from the figure that the parameter estimation performance of the TDST algorithm is the best among the four algorithms, but the computational complexity of the TDST algorithm is too large, resulting in an increase in time consumption. Taking RMSE = 1 as the standard, the algorithm parameter estimation in this case scheme improves the detection performance by about 7dB compared with the ACCF-LVD algorithm, and by about 1-2dB compared with the RFT-KT algorithm, but there is a loss of about 6-7dB compared with the TDST algorithm. Considering the computational complexity and parameter estimation performance, the algorithm in this case scheme achieves a good compromise and has certain value for practical applications.

[0172] The effectiveness of the proposed algorithm is verified by using publicly available narrowband linear frequency modulation radar data. In this data set, the radar detects fixed-wing UAV targets under ground background conditions and obtains pulse compression echo data. The radar parameters are shown in Table 4.

[0173] Table 4 Basic parameters of Ka-band radar

[0174]

[0175] Select data4 from the public data set 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, the 1st to 1,600th pulses of the data segment can be selected for the measured data experiment. The radar pulse compression results are shown in Figure 1. Fig.11 As shown in (a) in the figure. Since the echoes in this data set have serious ground clutter, Fig.11 (b) in the figure shows the target display result after two pulses are cancelled. At this time, the clutter is effectively suppressed. The result after pulse cancellation is used to perform range frequency inversion multiplication to eliminate range migration, such as Fig.11 As shown in (c) in the figure. The acceleration is estimated by SoWVD algorithm, as shown in Fig.11 As shown in (d) in the figure, the acceleration of the target can be estimated from the peak position. After phase compensation, the target is effectively accumulated into a significant peak spectrum through the SCIFT algorithm coherent accumulation, such as Fig.11 As shown in (e) in the figure, the initial distance of the target is estimated based on the peak position: Speed ​​is about Compared with the target motion data R0=1.554km calculated by GPS, It is proved that the algorithm proposed in this case can effectively realize target coherent accumulation and complete the estimation of moving target parameters.

[0176] 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.

[0177] 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 range-frequency axis inversion transform and second-order WVD, characterized in that: Contains the following: The radar echo signal is pulse compressed, and the pulse compressed signal is frequency-inverted along the range-frequency dimension to eliminate range migration and gather the target echoes into the same range unit. The pulse compression process of the echo signal of the kth target is expressed as: Indicates fast time, 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, c is the electromagnetic wave speed, f c Indicates carrier frequency, A c,k is the amplitude, R 0,k 、v k and a k They represent the initial distance, velocity and acceleration of the kth target echo signal respectively; the echo signal in the distance unit is transformed into time-frequency by the second-order WVD, and the target acceleration is estimated by Fourier transforming the signal after the time-frequency transformation; the time-frequency transformation process of the SoWVD algorithm using the second-order WVD is expressed as: τ0 is a constant delay, τ is a variable delay, v 0,k is the fuzzy speed; for the signal after time-frequency transformation, the delay variable and the slow time variable are Fourier transformed respectively, according to the signal peak position, and using To estimate the target acceleration in, express The maximum value of A phase compensation function is constructed using the estimated target acceleration, and the phase compensation function is used to construct a compensated range frequency-slow time domain dimensional signal identical to the uniform motion model; For the compensated distance frequency-slow time domain signal, variable delay autocorrelation is performed along the slow time dimension. After decoupling through addition operation and scale Fourier transform, the slow time variable is transformed to achieve coherent accumulation. The actual speed and initial distance of the maneuvering target are estimated by the peak value and the predetermined threshold in the Fourier transform process.

2. The method for coherently detecting maneuvering targets based on range-frequency axis inversion transform and second-order WVD according to claim 1 is characterized in that: In the detection process, according to the linear frequency modulation signal emitted by the coherent radar, the target echo signal after down-conversion by the receiver is obtained based on the target motion process model.

3. The method for coherently detecting maneuvering targets based on range-frequency axis inversion transform and second-order WVD according to claim 1, characterized in that: In eliminating range migration, a range-frequency axis is set, the signal is inverted along the range-frequency axis, and the signals before and after the inversion are multiplied. The range migration in the range-slow time domain is corrected by Fourier transforming the range frequency corresponding to the fast time in the multiplied signal.

4. The method for coherently detecting maneuvering targets based on range-frequency axis inversion transform and second-order WVD according to claim 1 or 3, characterized in that: For the signal after eliminating the range migration, the two-dimensional data is converted into one-dimensional data by selecting the slow time dimension to eliminate the influence of fast time and gather the target echo into the same distance unit; The maximum unambiguous speed, fuzzy factor and fuzzy speed of the coherent radar are used to mark the real speed of the target.

5. The method for coherently detecting maneuvering targets based on range-frequency axis inversion transform and second-order WVD according to claim 1, characterized in that: The distance frequency-slow time domain signal of the kth target after compensation is expressed as: Among them, A 1,k is the corresponding amplitude, f r It's fast time The corresponding distance frequency, f c represents the carrier frequency, t m represents the slow time variable, B is the transmission signal bandwidth, c is the electromagnetic wave speed, R 0,k and v k They represent the initial distance and speed of the kth target echo signal respectively.

6. The method for coherently detecting maneuvering targets based on range-frequency axis inversion transform and second-order WVD according to claim 1, characterized in that: In the case of coherent detection of multiple maneuvering targets, each maneuvering target is traversed in turn, and for each maneuvering target, the target acceleration, initial distance and velocity are estimated through range-frequency axis inversion transform and second-order WVD time-frequency transform until all maneuvering targets have completed coherent detection.

7. A coherent detection system for maneuvering targets based on range-frequency axis inversion transform and second-order WVD, characterized in that: The method according to claim 1 is implemented, comprising: an inverse transformation module, a time-frequency transformation module, a phase compensation module and a coherent detection module, wherein: The inversion transformation module is used to perform pulse compression on the radar echo signal, perform frequency inversion on the pulse compressed signal along the range frequency dimension, eliminate range migration, and gather the target echo into the same range unit; The time-frequency transformation module is used to perform time-frequency transformation on the echo signal in the range unit by using the second-order WVD, and estimate the target acceleration by performing Fourier transformation on the signal after the time-frequency transformation; A phase compensation module, used to construct a phase compensation function using the estimated target acceleration, and to construct a compensated distance frequency-slow time domain dimension signal identical to the uniform motion model using the phase compensation function; The coherent detection module is used to perform variable delay autocorrelation along the slow time dimension for the compensated distance frequency-slow time domain signal, and then perform Fourier transform on the slow time variable after decoupling through addition operation and scale Fourier transform to achieve coherent accumulation. The actual speed and initial distance of the maneuvering target are estimated through the peak value and predetermined threshold in the Fourier transform process.

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