A radar weak target multi-mode motion parameter estimation and coherent accumulation method

Abstract

The application discloses a radar weak target multi-mode motion parameter estimation and coherent accumulation method, which comprises the following steps: S1, performing pulse compression on the radar echo of a maneuvering target along the distance direction to obtain an echo signal; S2, dividing the echo signal in a CPI based on a short-time window to obtain a sub-CPI signal; S3, correcting the range migration of the signal in the sub-CPI by using a short-time Keystone transformation, and extracting a range signal in the azimuth direction; S4, performing a short-time fractional Fourier transformation on the range signal in the azimuth direction, estimating the instantaneous motion parameters in the sub-CPI, estimating the motion mode conversion time based on the instantaneous motion parameters in the sub-CPI, and obtaining the number of motion modes and the motion parameters in each mode; and S5, constructing a phase compensation function according to the motion parameter estimation, compensating the range migration and Doppler migration in the original echo, and realizing long-time coherent accumulation. The application avoids high-dimensional search of parameters, has low calculation complexity, high calculation efficiency, and good engineering application prospect.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and more specifically, to a method for estimating and coherently accumulating multimodal motion parameters of weak radar targets. Background Technology

[0002] Coherent accumulation can effectively improve the signal-to-noise ratio (SNR) of echoes from weak targets, thereby enhancing radar's ability to detect them. Most existing coherent accumulation algorithms are based on the single-motion-mode assumption, meaning the observed target experiences only one motion mode (e.g., uniform velocity, uniform acceleration, variable acceleration, etc.) within the coherent processing interval (CPI). However, with the rapid development of aerospace technology, the maneuverability of real-world threats is becoming increasingly sophisticated. Therefore, within the CPI, the observed target may experience multiple motion modes. This multi-modal motion renders traditional single-motion-mode signal models inapplicable, leading to a significant performance degradation in existing coherent accumulation algorithms. Furthermore, real-world threats often appear as multiple targets in combat, placing high demands on simultaneous multi-target detection.

[0003] Currently, existing methods for estimating and coherently accumulating multimodal motion parameters of weak radar targets mainly fall into two categories: The first category is still based on a single-mode motion model, approximating the multimodal motion trajectory by increasing the order of the motion model polynomial. However, as the complexity of the motion model continues to increase, the processing difficulty of this type of method increases rapidly, and the processing effect is unsatisfactory. The second category is based on a multimodal motion model, using high-dimensional parameter search methods to achieve range migration correction and Doppler migration correction, ultimately realizing multimodal motion parameter estimation and coherent accumulation. However, due to the use of high-dimensional parameter search principles, this type of method has low computational efficiency and poor engineering practicality. Therefore, it is indeed necessary to develop a new method for estimating and coherently accumulating multimodal motion parameters of weak radar targets. Summary of the Invention

[0004] The purpose of this invention is to provide a method for estimating and coherently accumulating multimodal motion parameters of weak radar targets, so as to overcome the defects of the existing technology.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for estimating and coherently accumulating multimodal motion parameters of weak radar targets includes the following steps:

[0007] S1. The radar echo of a moving target is pulse-compressed along the range direction to obtain the echo signal;

[0008] S2. Divide the echo signal within the CPI based on the short time window to obtain the sub-CPI signal;

[0009] S3. Use short-time Keystone transform to correct the range migration of the signal within the sub-CPI and extract the azimuth echo signal;

[0010] S4. Perform a short-time fractional Fourier transform on the azimuth signal to estimate the instantaneous motion parameters within the sub-CPI, and estimate the motion mode transition time based on the instantaneous motion parameters within the sub-CPI to obtain the number of motion modes and the motion parameters within each mode.

[0011] S5. Construct a phase compensation function based on the motion parameter estimation to compensate for the distance migration and Doppler migration in the original echo, thereby achieving long-term coherent accumulation.

[0012] Furthermore, step S1 specifically involves: detecting radar echoes s from highly maneuverable targets. R (t m ,τ r The echo signal s is obtained by pulse compression along the distance direction. c,n (t m ,τ r Its expression is:

[0013]

[0014] Further, step S2 specifically includes:

[0015] Assume the number of sub-CPIs is Q and the time span of the sub-CPIs is T. sc Then the start and end times of the qth sub-CPI are T and T, respectively. sc,q-1 = (q-1)·T sc and T sc,q =q·T sc Assuming the duration of the sub-CPI is less than the duration of any motion mode, then:

[0016] Case 1: Assuming the q-th sub-CPI is located within the n-th motion mode, the target echo of the q-th sub-CPI is represented as:

[0017]

[0018] in,

[0019] The second case: Assuming the q-th sub-CPI spans two motion modes, the target echo of the q-th sub-CPI is represented as:

[0020]

[0021] in,

[0022] Further, step S3 specifically involves: performing a Keystone transform on the sub-CPI to correct the distance migration and obtain s. c,q,KT (t n ,τ r Extracting from the location From the range unit signal, the azimuth signal s is obtained. c,q,ext (t p Based on the two scenarios in step S2, there are also two possible results after Keystone transform correction:

[0023] First scenario:

[0024]

[0025] Among them, D l For signal amplitude, v s,l,n After compensating for the ambiguity velocity, the remaining velocity is used to extract the azimuth signal, which is then expressed as follows:

[0026]

[0027] The second scenario:

[0028]

[0029] The expression for the extracted azimuth signal is:

[0030]

[0031] Furthermore, the specific steps in step S4 to compensate for range migration and Doppler migration in the original echo to achieve long-term coherent accumulation are as follows:

[0032] S41. Perform a Fast Fourier Transform on the echo along the range direction to obtain s. c,n (t m ,f);

[0033] S42, Based on constructing a phase compensation function for s c,n (t m Compensation is performed on f), and the compensation result for the l-th segment of the signal is s. c,l,n (t m ,f);

[0034] S43, regarding s c,l,n (t m f) Perform an inverse fast Fourier transform along the distance direction to obtain s c,l,n (t m ,τ r );

[0035] S44, against s c,l,n (t m ,τr A fast Fourier transform along the azimuth direction is performed to obtain the long-term coherent accumulation result of the l-th segment.

[0036] Compared with the prior art, the advantages of this invention are as follows: This invention uses short-time Keystone transform (ST-KT) to correct the range migration of echo signals within sub-CPI, and then uses short-time fractional Fourier transform (ST-FRFT) to estimate the target motion parameters and mode transition time, avoiding high-dimensional search of parameters, resulting in low computational complexity and high computational efficiency; This invention can realize long-term coherent accumulation of multi-modal motion and multi-target, and has good engineering application prospects. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of the radar weak target multimodal motion parameter estimation and coherent accumulation method of the present invention.

[0039] Figure 2 These are two partitioning scenarios to consider when dividing the observed target into sub-CPIs.

[0040] Figure 3 This is the simulation result of the present invention in a multimodal single-objective scenario.

[0041] Figure 4 These are the simulation results of this invention in a multimodal, multi-objective scenario.

[0042] Figure 5 This is a comparison of the coherent accumulation results of the present invention and existing methods in a single-target scenario. Detailed Implementation

[0043] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0044] The purpose of this embodiment is to provide a method for estimating multimodal motion parameters and coherent accumulation of radar targets with weak signals. First, the echo signal within the current phase-in-phase (CPI) is divided into sub-CPI signals based on a short time window. Then, the range migration of the signal within the sub-CPI is corrected using a short-time Keystone transform (ST-KT), allowing the extraction of the azimuth echo. Performing a short-time fractional Fourier transform (ST-FRFT) on this azimuth signal enables motion parameter estimation and mode transition timing estimation. Furthermore, a phase compensation function is constructed based on the motion parameter estimation results to compensate for range migration and Doppler migration in the original echo, ultimately achieving long-term coherent accumulation. This method does not require high-dimensional parameter search, has low computational complexity, and high parameter estimation accuracy, significantly improving upon the shortcomings of existing technologies.

[0045] Suppose a pulse radar transmits a linear frequency modulated (LFM) signal waveform, and its transmitted signal expression is:

[0046]

[0047] Among them, f c Represents the carrier frequency, t = t m +τ r t represents time. m =mT r ,m=1,2,...,M represents slow time, i.e., azimuth time, τ r T represents fast time. r T represents the pulse repetition time, M represents the number of coherently accumulated pulses, and T represents the pulse repetition time. p Indicates the pulse width, and k represents the modulation frequency of the LFM waveform. Represents the window function.

[0048] Assuming there are multiple moving targets within the observation area, and these targets have different scattering intensities and distances from the radar, the echo signal in a multi-target scenario can be modeled as follows:

[0049]

[0050] Where L is the number of targets within the observation area, l = 1, 2, ..., L is the l-th target, σ l Let τ be the scattering intensity of the l-th target. l =2R l (t m ) / c represents the time delay corresponding to the target, R l (t m ) represents the distance, λ c =c / f c λ is the wavelength, and c is the speed of light.

[0051] Further assume that the l-th maneuvering target experiences N times within CPI. l If there are 3 motion modes, then R l (t m This can be represented as:

[0052]

[0053] Where n = 1, 2, ..., N l T l,n-1 and T l,n These represent the start and end times of the nth motion mode, respectively. Specifically, T... l,0 =0 and These represent the start and end times of the entire CPI, respectively.

[0054] Without loss of generality, for each stage of motion, considering only the acceleration term, then R l,n (t m This can be represented as:

[0055]

[0056] Among them, R 0,l,n v l,n and a l,n Let represent the initial distance, initial velocity, and acceleration of the nth motion mode, respectively. Therefore, the motion parameters between adjacent motion modes satisfy the following relationship:

[0057]

[0058] Where, ΔT l,n-1 =T l,n-1 -T l,n-2 , n≥2.

[0059] like Figure 1 As shown, the technical solution adopted in this embodiment is as follows: A method for estimating and coherently accumulating multimodal motion parameters of weak radar targets, comprising the following steps:

[0060] Step S1: Radar echo s of the moving target R (t m ,τ r The echo signal s is obtained by pulse compression along the distance direction. c,n (t m ,τ r Its expression is:

[0061]

[0062] Among them, A l Let x be the magnitude of the l-th target, sinc(x) = sin(πx) / πx be the sinc function, and B = k·Tp Let T be the signal bandwidth. From the above equation, it can be seen that the echo of a multimodal moving target will exhibit range migration and Doppler frequency migration. The range migration consists of range travel caused by velocity and range curvature caused by acceleration. The magnitude of the range migration is related to the unknown parameter T. l,n v l,n a l,n Relevant. To correct for range migration and Doppler frequency migration and achieve long-term coherent accumulation, accurate estimation of these unknown parameters is necessary.

[0063] Step S2: Divide the echo signal within the CPI based on the short time window to obtain the sub-CPI signal.

[0064] Specifically, to facilitate distance migration correction, the entire CPI needs to be divided into multiple sub-CPIs based on a short time window. Assume the number of sub-CPIs is Q, and the time width of each sub-CPI is T. sc Then the start and end times of the qth sub-CPI are T and T, respectively. sc,q-1 = (q-1)·T sc and T sc,q =q·T sc Without loss of generality, we further assume that the duration of the sub-CPI is less than the duration of any motion mode. Under this assumption, such as Figure 2 As shown, there are two situations that need to be considered:

[0065] S21. In the first case, assume that the q-th sub-CPI is located within the n-th motion mode, i.e., T sc,q-1 ≥T l,n-1 and T sc,q <T l,n In this case, the target echo of the q-th sub-CPI can be expressed as:

[0066]

[0067] in,

[0068] S22. In the second case, assume that the q-th sub-CPI spans two motion modes, i.e., T l,n-1 <T sc,q-1 <T l,n and T l,n <T sc,q <T l,n+1 In this case, the target echo of the q-th sub-CPI can be expressed as:

[0069]

[0070] in,

[0071] Step S3: Use short-time Keystone transform to correct the range migration of the signal within the sub-CPI and extract the azimuth echo signal.

[0072] Specifically, assuming that the time width of each sub-CPI is short enough, the distance curvature caused by acceleration can be ignored, and only the linear distance movement caused by velocity needs to be considered, then the Keystone transform can be used for distance migration correction (RMC). As mentioned above, two cases need to be discussed.

[0073] S31. In the first case, transforming the echo of the q-th sub-CPI to the range frequency domain can be expressed as:

[0074]

[0075] Considering the velocity fuzziness problem, the velocity in the above equation can be rewritten as:

[0076] v l,n =N l,a ·v a +v s,l,n

[0077] Among them, v a =λ c • PRF / 2 is the blur rate, N l,a Let |v| be the Doppler ambiguity number. s,l,n |<v a / 2 represents the remaining velocity component after fuzzy velocity compensation. Then s c,q (t m f) can be further expressed as:

[0078]

[0079] Among them, R 0,l,q =R 0,l,n -v l,n T l,n-1 In s c,q (t m In f, there exist f and t m The coupling between them is due to the influence of linear distance migration due to velocity. For high-altitude targets, the influence of Doppler ambiguity needs to be addressed. For the ambiguity number N... l,a Accurate estimation of fuzzy numbers can be achieved through parameter search. Assuming that the influence of fuzzy velocity can be effectively eliminated through fuzzy number search and compensation, then s c,q (t m The second exponential term in f) This can be ignored. According to the principles of the Keystone transformation, let:

[0080]

[0081] After decoupling, the echo of the q-th sub-CPI can be written as:

[0082]

[0083] For narrowband radar systems, since f << f c ,but Therefore s c,q (t m f) can be approximated as:

[0084]

[0085] In the above formula s c,q (t n From the expression f, it can be seen that t n The coupling between s and f has been decoupled. c,q (t n Performing an inverse Fourier transform (IFT) along f yields:

[0086]

[0087] Among them, D l This represents the amplitude of the two-dimensional time-domain signal after KT correction. From s c,q,KT (t n ,τ r As can be seen from the data, after KT correction, the energy of the echo signal is concentrated within the same range cell. It can be seen that, for the first case, range migration correction can be achieved using the Keystone transform.

[0088] S32. In the second case, the sub-CPI spans two motion modes, making the situation relatively complex.

[0089] Based on the relationship between the motion parameters of adjacent modes, s of S22 c,q (t m ,τ r The envelope distribution of the second motion mode in the equation can be written as:

[0090]

[0091] Based on the envelope distribution relationship in the above formula, according to a l,n The magnitude of the parameter value can be divided into two cases.

[0092] S321. In the first case, assume a l,n If it is very small, then R 0,l,n+1 +v l,n+1 (t m -Tl,n The last two terms in the expression can be ignored, therefore the s of S22 c,q (t m ,τ r This can be rewritten as:

[0093]

[0094] Under this assumption, linear distance migration constitutes the majority of the distance migration within the sub-CPI, therefore, KT correction can be used to eliminate this linear distance migration component. After KT correction, the two-dimensional time-domain echo signal can be written as...

[0095]

[0096] From s c,q,KT (t n ,τ r As can be seen from the expression, despite including two motion modes, the echo energy is still concentrated in the same range cell after KT correction.

[0097] S322. In the second case, assume that a l,n If the resulting range migration cannot be ignored, then the range migration of the sub-CPI contains higher-order components. According to the properties of the Keystone transform, the performance of range migration correction will degrade, and the energy of the echo will still be distributed in different range cells.

[0098] As can be seen from the expression, when the envelope is located At that time, s c,q,KT (t m ,τ r The amplitude of the CPI signal will produce local peaks, but the signal-to-noise ratio in the sub-CPI echo will still be very low. In practical applications, the distance between the target and the radar is usually unknown. Therefore, in order to extract a specific azimuth signal after the Keystone transform, it is usually necessary to traverse all range cells.

[0099] Step S4: Perform a short-time fractional Fourier transform on the azimuth signal to estimate the instantaneous motion parameters within the sub-CPI, and estimate the motion mode transition time based on the instantaneous motion parameters within the sub-CPI to obtain the number of motion modes and the motion parameters within each mode.

[0100] Specifically, for instantaneous motion parameter estimation, the echo signal of the q-th sub-CPI that completes RMC can be extracted by traversing the search to find the position located at τ. r =2R 0,l,qThe target azimuth echo is shown in the image. Based on the previous derivation, it can be seen that the extracted signal is a mixed signal composed of multiple linear frequency modulated signals superimposed. The instantaneous motion parameters contained within this signal are estimated using the Short Time Fractional Fourier Transform (STFRFT), and we will still discuss two cases.

[0101] S41. In case one, the extracted target azimuth echo can be represented as:

[0102]

[0103] Among them, t p =t n -τ l,q , τ l,q =(T sc,q-1 +T sc,q ) / 2, therefore -T w / 2≤t p <T w / 2,T w =T sc,q -T sc,q-1 , φ 0,l,q For a fixed phase and with t p Irrelevant. In the above formula, the LFM parameter can be expressed as:

[0104]

[0105]

[0106] Furthermore, according to the definition of ST-FRFT, performing an ST-FRFT transform on the extracted signal yields:

[0107]

[0108] in:

[0109]

[0110]

[0111] S p The matching transformation order of STFRFT in (0,u) is:

[0112]

[0113] Regarding the order of this matching transform, we can further obtain:

[0114]

[0115] Therefore, the location of the peak value in the ST-FRFT transform result can be obtained as follows:

[0116] u opt,l,q =2πf l,q sinα opt,l,q

[0117] Finally, based on the previously defined LFM parameters, the instantaneous motion parameters can be obtained as follows:

[0118]

[0119]

[0120] However, due to the motion mode transition time T l,n-1 The value of is not yet known, so the true value of instantaneous velocity cannot be obtained at this time.

[0121] S42. In case two, according to a l,n The value can be divided into two cases, specifically:

[0122] S421. In the first case, a l,n The value is very small, affecting the signal along the sub-CPI. By proposing this, we can obtain:

[0123]

[0124] Among them, when -T w / 2≤t p When <T′, w q,1 (t p )=1;T′≤t p <T w / 2 hours, w q,2 (t p ) = 1. T′ = T l,n -τ l,q φ 0,l,q,1 and φ 0,l,q,2 It is independent of τ. The parameters of LFM are:

[0125]

[0126]

[0127] The extracted signal is a superposition of multiple chirp signal components. Performing an STF-rFT on the extracted signal yields:

[0128]

[0129] As can be seen, there is no single matching transform order at this time, so it is impossible to obtain a well-focused STFRFT transform result, nor can its peak position be used to estimate instantaneous motion parameters.

[0130] S422, In the second case, a l,n The value of is not negligible, range migration cannot be fully corrected, and target energy is dispersed across different range cells. Therefore, the azimuth signal extracted from the sub-CPI is more complex, and its analytical expression cannot be derived. In this case, instantaneous motion parameters cannot be estimated using the ST-FRFT transform.

[0131] Specifically, the estimation of motion mode transition time based on instantaneous motion parameters within a sub-CPI is divided into two steps: coarse estimation and fine estimation.

[0132] For coarse estimation: According to the definition of multimodal motion, the target's acceleration value will change abruptly at the moment of motion mode transition. This can be used to coarsely estimate the number of motion modes and the transition time. Based on the acceleration value obtained from STFRFT estimation, the acceleration change value of adjacent sub-CPIs can be defined as:

[0133]

[0134] Where q = 1, 2, ..., Q-1. Therefore, the detector for the MTP can be given as:

[0135]

[0136] Where δ is the detection threshold, and the binary hypotheses are as follows:

[0137] H1: An MTP exists in the (q+1)th sub-CPI;

[0138] H0: There is no MTP in the (q+1)th sub-CPI.

[0139] Using the above formula, the number of motion modes and MTP can be estimated. However, due to... The sampling interval is only equal to the time width of the sub-CPI, so the accuracy of the MTP obtained by this estimation is poor, which is called coarse estimation.

[0140] For the fine estimation: Based on the coarse estimation, the precise estimate of MTP and the initial velocity estimate of the target in each motion mode are further obtained. For the nth motion mode, we can obtain:

[0141]

[0142]

[0143] Here, Mean(·) calculates the mean. Therefore, the time at which the above mean is calculated can be expressed as:

[0144]

[0145] Therefore, the instantaneous velocities of the nth and (n+1)th motion modes can be expressed as:

[0146]

[0147]

[0148] Furthermore, based on the definition of multimodal, the precise estimate of MTP can be obtained as follows:

[0149]

[0150] Finally, the initial velocities for each motion mode can be obtained as follows:

[0151]

[0152] Step S5: Construct a phase compensation function based on the motion parameter estimation to compensate for the distance migration and Doppler migration in the original echo, thereby achieving long-term coherent accumulation.

[0153] Specifically, after estimating the motion mode transition time and motion parameters, long-term coherent accumulation can be completed through piecewise motion compensation, ultimately yielding an accumulation result with a high signal-to-noise ratio.

[0154] Transforming the target echo pulse compression signal to the range frequency domain yields:

[0155]

[0156] in:

[0157]

[0158] Based on the estimated motion parameters, the phase compensation function can be constructed as follows:

[0159]

[0160] in:

[0161]

[0162]

[0163] Therefore, motion compensation can be achieved through phase multiplication. Assuming the estimated motion parameters are sufficiently accurate, the compensated result is:

[0164]

[0165] It can be seen that after motion compensation, distance migration and Doppler migration are completely eliminated. Furthermore, transforming the above equation to the two-dimensional time domain, we obtain:

[0166]

[0167] Finally, performing a Fourier transform along the azimuth direction on the above equation allows for coherent accumulation:

[0168]

[0169] Among them, T M =M·PRI is the duration of CPI, f a This represents the Doppler frequency. It can be seen that after coherent accumulation, the amplitude of the target echo signal increases by a factor of M, meaning the signal-to-noise ratio improves by a factor of M.

[0170] The invention will be further illustrated below through experimental simulation.

[0171] The system parameters are shown in Table 1 below:

[0172] Table 1. Simulation System Parameters for This Example

[0173]

[0174] Experiment 1: Single-target scenario

[0175] Assume a single target exhibits three modes during the observation time: the first mode is uniformly accelerated motion with an initial distance of 100 km, a velocity of -200 m / s, an acceleration of -50 m / s², and a duration of 0–0.86 s; the second mode is uniform motion with a velocity of -243 m / s and zero acceleration, lasting from 0.86 s to 1.32 s; and the third mode is uniformly accelerated motion with a velocity of -243 m / s and an acceleration of 50 m / s², lasting from 1.32 s to 2 s. The signal-to-noise ratio (SNR) after pulse compression is used as the input SNR, set to 0 dB, and the duration of the sub-CPI is 0.1 s. Simulation results are as follows: Figure 3 As shown.

[0176] exist Figure 3 (a) is a two-dimensional time-domain plot after pulse compression. The input signal-to-noise ratio is low, and the target trajectory is almost submerged in noise. Figure 3 (b) shows the SK-KT-FRFT accumulation result for a certain sub-CPI, which contains a peak with a high signal-to-noise ratio. Based on the location of this peak, the instantaneous motion parameters within the sub-CPI can be estimated. The estimation results for instantaneous velocity and acceleration are as follows: Figure 3 (c) and Figure 3 As shown in (d). In this simulation experiment, the fuzzy velocity v a =100m / s, Doppler ambiguity number N l,a =-2. (This is incomplete and requires further context.) Figure 3 (d) The difference between adjacent accelerations is calculated, and the result is as follows: Figure 3 As shown by the blue line in (e). Figure 3 The red line in (e) represents the threshold of the MTP detector (δ = 10 m / s). 2 ).from Figure 3 As can be seen in (e), the target has three motion modes within the CPI. According to Figure 3 The coarse estimation result in (e) is used again to refine the signal. The comparison between the refined parameter estimation results and the true values ​​is shown in Table 2. Based on the parameter estimation results, a phase compensation function is constructed to compensate for the echo, and then long-term coherent accumulation is implemented. The accumulation results are shown in Table 2. Figure 3 As shown in (f).

[0177] Table 2 Comparison of Actual Values ​​and Estimated Values

[0178]

[0179]

[0180] Experiment 2: Multi-object scenario

[0181] Through the derivation of the specific implementation scheme, it can be seen that the algorithm can also achieve motion parameter estimation and long-term coherent accumulation for multimodal and multi-moving targets. The effectiveness of the algorithm is verified through three different sets of multimodal and multi-target experiments. The radar system parameter settings are shown in Table 1, and the motion parameters of the multiple targets are shown in Table 3. With the input signal-to-noise ratio set to 0 dB, the simulation results obtained using this algorithm are as follows: Figure 4 As shown.

[0182] Table 3. Motion parameter settings for multimodal and multi-target applications.

[0183]

[0184] In the first set of experiments, both target 1 and target 2 experienced uniformly accelerated motion in the first mode and uniform velocity motion in the second mode, but their motion parameters differed, as shown in the first row of Table 3. Furthermore, the initial velocities of target 1 and target 2 were 100 km / h and 100.1 km / h, respectively. Therefore, the trajectories of these two targets did not intersect within the CPI, as shown below. Figure 4 As shown in (a). In this set of experiments, the estimated instantaneous maneuver parameters are as follows: Figure 4 (b) and Figure 4 As shown in (c). Furthermore, by combining the parameter estimation and MTP estimation results, a compensation function can be constructed to compensate for the echo. The coherent accumulation results are shown below. Figure 4 (d) and Figure 4 As shown in (e). In Figure 4 (d) and Figure 4 In (e), there is a spurious peak, which is because the motion parameters of the two targets, especially the acceleration, are similar in value.

[0185] In the second set of experiments, targets 3 and 4 had the same initial distance and MTP, as shown in the second row of Table 3, but their velocities and accelerations were different. Therefore, the trajectories of the two targets overlapped in the initial CPI phase and then gradually separated, as shown in the second row of Table 3. Figure 4 As shown in (f). The instantaneous parameter estimation results for these two targets are as follows. Figure 4 (g) and Figure 4 As shown in (h), the results of long-term coherent accumulation are as follows: Figure 4 (i) and Figure 4 As shown in (j). In Figure 4 (i) and Figure 4 In (j), both objectives 3 and 4 achieved good energy accumulation, proving that the algorithm is effective.

[0186] In the third set of experiments, within the first mode, target 5 moved slowly at a constant speed, while target 6 moved rapidly with uniform acceleration. Although the initial distances between the two targets were 100km and 100.05km respectively, their trajectories overlapped within the 8th sub-CPI, as shown below. Figure 4 As shown in (k). From Figure 4 (l) and Figure 4 The estimation results for (m) are consistent with the theoretical values ​​in Table 3. Finally, the accumulation results for objectives 5 and 6 are as follows: Figure 4 (n) and Figure 4 As shown in (o).

[0187] These three sets of simulation experiments demonstrate that the present invention can effectively achieve long-term coherent accumulation of multimodal and multi-objective systems.

[0188] Experiment 3: Algorithm Performance Comparison

[0189] To further verify the performance of this invention, different long-term coherent accumulation algorithms were compared. The comparison algorithms selected were GRFT and STGRFT. GRFT is based on a single-mode motion model, while STGRFT is based on a multi-mode motion model. In this experiment, only single-target multi-mode motion was considered, and the radar system parameters were set as in Table 1, with the input signal-to-noise ratio reduced to -3dB. The long-term coherent accumulation results of the three algorithms are as follows: Figure 5 As shown.

[0190] Because the input signal-to-noise ratio is lower Figure 5 The target trajectory in (a) is submerged in noise and becomes even more blurred. Figure 5 (b) and Figure 5 (c) shows the coherent accumulation results of GRFT and STGRFT, respectively. Figure 5(d) shows the coherent accumulation results of the algorithm used in this invention. The comparison shows that this invention exhibits the best accumulation performance. Furthermore, this invention has the best computational efficiency. In this experiment, the STGRFT algorithm took 501.5 seconds, while this invention only took 33.4 seconds. Therefore, compared to existing methods, the method presented in this invention has better computational accuracy and engineering practicality.

[0191] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, the patent owner may make various modifications or alterations within the scope of the appended claims, as long as they do not exceed the protection scope described in the claims of the present invention, they shall be within the protection scope of the present invention.

Claims

1. A method for estimating and coherently accumulating multimodal motion parameters of weak radar targets, characterized in that, Includes the following steps: S1. The radar echo of a moving target is pulse-compressed along the range direction to obtain the echo signal; S2. Divide the echo signal within the CPI based on the short time window to obtain the sub-CPI signal; S3. Use short-time Keystone transform to correct the range migration of the signal within the sub-CPI and extract the azimuth echo signal; S4. Perform a short-time fractional Fourier transform on the azimuth signal to estimate the instantaneous motion parameters within the sub-CPI, and estimate the motion mode transition time based on the instantaneous motion parameters within the sub-CPI to obtain the number of motion modes and the motion parameters within each mode. S5. Construct a phase compensation function based on the motion parameter estimation to compensate for the range migration and Doppler migration in the original echo, thereby achieving long-term coherent accumulation; Step S1 specifically involves: detecting radar echoes from highly maneuverable targets. Echo signal is obtained by pulse compression along the distance direction. Its expression is: ； This indicates slow time, specifically location time. It represents fast time. For the first The magnitude of each target, B For signal bandwidth; Step S2 specifically involves: Assume the number of sub-CPIs is The time width of the sub-CPI is Then the first The start and end times of each CPI component are respectively and Assuming the duration of the sub-CPI is less than the duration of any motion mode, then: First scenario: Assume the... If each sub-CPI is within the nth motion mode, then the nth CPI is within the nth motion mode. The target echo of individual CPI is represented as follows: in, ; The second scenario: Assume the... If a CPI sub-index spans two motion modes, then the first sub-index... The target echo of individual CPI is represented as follows: in, , ; For the first The initial distance of each motion mode, For the first The initial velocity of each motion mode; Step S3 specifically involves: performing Keystone transformation on the sub-CPI to correct distance migration and obtain... Extraction located at From the range unit signal, the azimuth signal is obtained. Based on the two scenarios in step S2, there are also two possible results after Keystone transform correction: First scenario: in, For signal amplitude, After compensating for the ambiguity velocity, the remaining velocity is then expressed as follows: ； The second scenario: The expression for the extracted azimuth signal is: 。 2. The method for estimating and coherently accumulating multimodal motion parameters of weak radar targets according to claim 1, characterized in that, The specific steps for compensating for range migration and Doppler migration in the original echo in step S4 to achieve long-term coherent accumulation are as follows: S41. Perform a Fast Fourier Transform on the echo along the range direction to obtain... ; S42, Based on constructing a phase compensation function As compensation, the first The compensation result of the segment signal is ; S43, to Inverse Fast Fourier Transform along the distance direction is obtained ; S44, to Performing a Fast Fourier Transform along the azimuth direction yields the first... The result of long-term coherent accumulation of segments.

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