High-speed multi-target distance and speed joint estimation method, device and program product

Abstract

The present invention discloses a high-speed multi-target distance and speed joint estimation method, device and program product, which relates to the field of radar signal processing and is used to obtain robust and reliable multi-target distance and speed joint estimation results. The present invention performs FRFT processing on the echo signal, extracts peak points from the amplitude matrix of the processing result and screens the effective peak points, extracts effective target energy lines based on the effective peak points of each row, performs smoothing filtering on the effective target energy lines, and finally estimates the distance and speed of the corresponding target based on the angle sampling value and u-axis projection value of the effective peak point with the largest amplitude on each effective target energy line. The present invention takes into account the influence of the target speed on the frequency modulation slope of the radar echo, and the estimation result is more accurate. In addition, the joint estimation of distance and speed is realized on a single-cycle echo, avoiding the averaging effect of multiple cycles.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing, and in particular to a high-speed multi-target distance and velocity joint estimation method based on FRFT. Background Art

[0002] Linear Frequency Modulation (LFM) pulse radar is a primary method for space target detection, parameter estimation, and tracking. However, parameter estimation for high-speed, multi-target space targets presents numerous challenges. For high-speed space targets, LFM pulse radar echoes exhibit significant range-velocity coupling, making joint range-velocity estimation from single-cycle echoes difficult to achieve using conventional methods.

[0003] Traditional methods use multi-cycle radar echoes, extract the target peak position after pulse compression, and then estimate the target range and velocity by building a target motion model. However, the positions and velocities of multiple targets are independent of each other, and there may be complex features such as overlapping target trajectories and dynamic motion changes. This can lead to increased errors in target range and velocity parameter estimation, or even failure.

[0004] Other researchers have proposed other methods to address the problem of joint target range and velocity estimation. Chinese patent publication CN112526474A proposes a "Method for Joint Range and Velocity Estimation of FMCW Radar Based on Full-Phase Fourier Transform," which utilizes full-phase Fourier transforms to achieve joint target range and velocity estimation. Chinese patent publication CN118011381A proposes a "Method, System, and Medium for Joint Range and Velocity Estimation Based on FMCW Radar," which achieves joint target range and velocity estimation through 2D-FFT transformation combined with the CZT algorithm. However, neither of these methods considers the variations in the radar echo frequency modulation slope caused by the varying speeds of multiple targets. This leads to theoretically unavoidable errors in the range and velocity estimation of high-speed or ultra-high-speed targets, compromising estimation accuracy. Furthermore, both methods require processing radar echoes over multiple cycles, which, due to the averaging effect, are not well adapted to complex characteristics such as target maneuvers. Summary of the Invention

[0005] The object of the present invention is to provide a high-speed multi-target distance and speed joint estimation method, device and program product to address all or part of the above-mentioned problems, so as to obtain robust and reliable multi-target distance and speed joint estimation results.

[0006] The technical solution adopted in the present invention is as follows:

[0007] A high-speed multi-target distance and velocity joint estimation method based on FRFT (fractional Fourier transform), comprising:

[0008] Perform down-conversion sampling on the radar echo signal to obtain a digital echo signal;

[0009] Performing FRFT processing on the digital echo signal to obtain a processing result;

[0010] Obtaining an amplitude matrix of the processing result, filtering the amplitude matrix according to a set threshold, and extracting peak points for each row;

[0011] According to the set target minimum spacing, the peak points of each row are screened to obtain the retained valid peak points;

[0012] Extracting effective target energy lines according to the effective peak points of each row, and performing smoothing filtering on the effective target energy lines;

[0013] The distance and speed of the corresponding target are estimated based on the angle sampling value and the u-axis projection value of the effective peak point with the maximum amplitude on each of the effective target energy lines.

[0014] The present application also provides a device comprising a processor and a storage medium, wherein the storage medium stores a computer program. When the processor runs the computer program in the storage medium, it executes the above-mentioned FRFT-based high-speed multi-target distance and speed joint estimation method.

[0015] The present application also provides a computer program product, including a computer program, which, when executed by a processor, executes the above-mentioned FRFT-based high-speed multi-target distance and speed joint estimation method.

[0016] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0017] The high-speed multi-target distance and velocity joint estimation method based on FRFT proposed in this application takes into account the influence of target velocity on the frequency modulation slope of radar echo, making the echo model more accurate. In addition, this application realizes the joint estimation of distance and velocity on a single-cycle echo, avoiding the averaging effect of multiple cycles, and can adapt well to complex characteristics such as target maneuverability, thereby obtaining a robust and reliable multi-target distance-velocity joint estimation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0019] Figure 1 This is a flow chart of a high-speed multi-target distance and speed joint estimation method based on FRFT provided in an embodiment of the present application.

[0020] Figure 2 This is a simulation diagram of the FRFT processing amplitude when searching for the first angle in an embodiment of the present application.

[0021] Figure 3 This is a simulation diagram of the FRFT processing amplitude for all search angles in the embodiment of the present application.

[0022] Figure 4 This is a simulation diagram of the relationship curve between the relative speed of all target energy line amplitudes in the embodiments of the present application. DETAILED DESCRIPTION

[0023] All features disclosed in this specification, or all steps in the disclosed methods or processes, except mutually exclusive features and / or steps, can be combined in any manner.

[0024] Any feature disclosed in this specification (including any appended claims and abstract), unless otherwise stated, may be replaced by other equivalent or similar features. That is, unless otherwise stated, each feature is only an example of a series of equivalent or similar features.

[0025] The conventional method of using multi-period radar echoes for target range and velocity joint estimation suffers from large estimation errors, as does the inevitable error caused by the change in radar echo frequency modulation slope due to the different speeds of multiple targets in the prior art. Furthermore, the prior art requires the use of multiple-period radar echoes to introduce an averaging effect. The present invention provides a high-speed multi-target range and velocity joint estimation method, apparatus, and program product, aiming to obtain robust and reliable multi-target range and velocity joint estimation results while avoiding the multi-period averaging effect.

[0026] Description of common knowledge that may be involved in this application:

[0027] 1) Linear frequency modulation signal.

[0028] The expression of linear frequency modulation signal s(t) is:

[0029] s(t)=G(t)exp(j(2πf b t+πkt 2 )), (1-1)

[0030] Where t is the time variable, exp(·) is the exponential function, j is the imaginary unit, and f b is the starting frequency of the linear FM signal, is the frequency modulation slope of the linear frequency modulation signal, B is the transmission signal bandwidth, P is the transmission signal pulse width, G(t) is the amplitude envelope window function, and G(t) can be taken as a rectangular window function. The expression is:

[0031]

[0032] 2)FRFT.

[0033] The definition of FRFT is:

[0034]

[0035] Among them, x(t) is the signal to be analyzed, α is the angle, and u is the displacement factor. α and u together form a two-dimensional transformation domain, K α (t,u) is the transformation kernel of FRFT, and its expression is:

[0036]

[0037] Where δ(t) represents a unit impulse signal, and q is an arbitrary integer. Note that in equations (1-4), the cases where α = 2qπ and α = (2q + 1)π are only to ensure the rigor of the fractional Fourier transform expression. In practical applications, the value range of α is usually set to: That is, α is in the first or fourth quadrant of the two-dimensional time-frequency domain. For the case where α is in the second or third quadrant of the time-frequency domain, it can be easily equivalent to the fourth or first quadrant, which will not be discussed in detail here.

[0038] In some embodiments of the present application, a high-speed multi-target distance and velocity joint estimation method based on FRFT includes the following process:

[0039] S1. Down-convert and sample the radar echo signal to obtain a digital echo signal.

[0040] At the radar receiving end, for each pulse period (PRI), the radar echo signal r(t) is received. As a feasible implementation method, the radar echo signal is down-converted and digitally sampled to obtain a digital echo signal r d (n), which is expressed as:

[0041] r d (n) = r(nT s ), (1-5)

[0042] Among them, T s is the sampling interval, and its reciprocal is the sampling rate f s =1 / T s , n is the index value of the discrete sequence, its value is: 0,1,2,...,N r -1, where N rFor r d (n) The total number of sampling points.

[0043] S2, digital echo signal r d (n) Perform FRFT processing to obtain a processing result.

[0044] As a feasible implementation method, the above-mentioned digital echo signal r d (n) performing FRFT processing, including:

[0045] S2.1, according to the target speed change interval [v d ,v u ] and the speed search step Δv, calculate the angle sampling value α required for FRFT processing i The calculation process includes:

[0046] According to the target speed change interval [v d ,v u ] and the speed search step Δv, and obtain the speed sampling value v i :

[0047] v i =v d +iΔv, (1-6)

[0048] Where i = 0, 1, 2, ..., M-1, where M is the total number of target speeds to be searched, and its value is taken as:

[0049]

[0050] Here, round(·) indicates rounding to the nearest integer.

[0051] According to the speed sampling value v i , calculate the corresponding speed proportional coefficient η i :

[0052]

[0053] Where c represents the speed of light, and its value can be taken as c = 3 × 10 8 m / s.

[0054] Then the angle sampling value α to be searched in the FRFT transform is i Calculate as follows:

[0055]

[0056] Wherein, arctan(·) is the inverse tangent function, k is the frequency modulation slope of the linear frequency modulation signal s(t) as mentioned above, and i=0, 1, 2, ..., M-1.

[0057] S2.2. Calculate the u-axis sampling interval u required for FRFT processing based on the set radial distance resolution interval Δl s .

[0058]

[0059] Among them, cos(·) is the cosine function, It means traversing i∈{0,1,2,...,M-1} and taking the minimum value among them.

[0060] S2.3, according to the above angle sampling value α i and u-axis sampling interval u s , for the digital echo signal r d (n) Perform FRFT processing.

[0061] Step S2.1 obtains M angle sampling values ​​α i , plus the u-axis sampling interval u obtained in step S2.2 s , for the digital echo signal r d (n) Perform FRFT processing to obtain the processing results The processing results are arranged in the form of discrete matrices.

[0062]

[0063] in, is the FRFT transform kernel function, and its value is calculated according to formula (1-4). p is the discretization index of the u-axis, and its value is: p = 0, 1, 2, ..., N-1, where N represents the total number of sampling points on the u-axis.

[0064] There are M rows and N columns in total, where the vertical row direction corresponds to the sampling value α of each angle i , i=0,1,2,...,M-1, the horizontal column direction corresponds to the u-axis projection value pu s , p=0,1,2,...,N-1.

[0065] S3. Get processing results The magnitude matrix According to the set threshold, the amplitude matrix Filter and extract the peak points for each row.

[0066] As a feasible implementation method, in step S3, the amplitude matrix is Filtering includes:

[0067] S3.1. Based on processing results The threshold is set by the average power of

[0068] Assume P noise express The average power of , ζ is the amplitude multiplication coefficient, and satisfies ζ≥1. In some optional implementations, the threshold Thi is selected as follows:

[0069]

[0070] S3.2, the amplitude matrix The amplitudes smaller than the threshold Thi are set to zero, and those larger than the threshold Thi are retained.

[0071] In addition, step S3 also includes:

[0072] S3.3, the amplitude matrix Each row of data is processed by peak point extraction, and the peak point extraction method can be used with existing technology. Record the extracted peak point corresponding to the amplitude matrix The angle sampling value α in i , u-axis projection value pu s and amplitude information.

[0073] S4, according to the set target minimum distance d min , filter the peak points of each row respectively to obtain the retained valid peak points.

[0074] As a feasible implementation, in step S4, the peak points of each row are screened according to the set target minimum spacing, including:

[0075] S4.1, according to the set target minimum distance d min , calculate the minimum projection spacing u projected onto the u axis min .

[0076] By the target minimum distance d min Convert the minimum projection distance u min The method is:

[0077]

[0078] S4.2. Minimum projection spacing u in each row min Only one peak point is retained within the range as a valid peak point.

[0079] In some embodiments, step S4.2 includes:

[0080] Based on the minimum projection distance u min Group the peak points of each row.

[0081] The peak point with the largest amplitude in each group is retained as the valid peak point.

[0082] The above grouping process can be as follows: judge each peak point of each row in turn, if the distance between the current peak point and the previous peak point on the u axis is less than or equal to the minimum projection distance u min , the current peak point is classified as the same group as the previous peak point, otherwise the current peak point is classified as the starting point of the next group. For the peak points in the same group, take the corresponding amplitude matrix |X αi (pu s )| is retained as a valid peak point, while the other peak points in the same group are discarded. According to this method, the amplitude matrix |X αi (pu s )| filters the peak points of each row to obtain the amplitude matrix |X αi (pu s )|. These effective peak points record the corresponding angle sampling value α i , u-axis projection value pu s and amplitude information.

[0083] S4. Extract the effective target energy line according to the effective peak point of each row, and perform smoothing filtering on the effective target energy line.

[0084] In a feasible implementation manner, extracting the effective target energy line according to the effective peak point of each row in step S4 includes:

[0085] S4.1. Extract all target energy lines based on the effective peak points of each row.

[0086] In some specific embodiments, the target energy line extraction process includes:

[0087] According to the effective peak points of each row, the closest effective peak points in different rows are sequentially associated with the same target energy line. Specifically, there are:

[0088] Record the index position information of the valid peak point in the first row;

[0089] For other rows, the valid peak point in the row closest to the valid peak point recorded in the previous row is sequentially associated with the valid peak point recorded in the previous row on the same target energy line.

[0090] According to this method, multiple target energy lines can be obtained, and each target energy line contains effective peak points in different rows.

[0091] S4.2. Filter out valid target energy lines from all target energy lines based on the set threshold value of the number of valid peak points.

[0092] For the target energy line obtained, the validity judgment needs to be made. As a feasible implementation method, the minimum number N of valid peak points on the target energy line is set. p , N p Satisfy 1≤N p ≤M. Determine in turn whether the number of effective peak points on each target energy line is greater than or equal to N p If the condition is met, it is a valid target energy line, otherwise it is an invalid target energy line. The number of valid target energy lines is the number of targets actually detected.

[0093] Step S4 further includes:

[0094] S4.3. Smoothing and filtering are performed on the amplitude of the effective target energy line to obtain a smooth effective target energy line. The filter may be a digital window function filter.

[0095] S6. Estimate the distance s of the corresponding target based on the angle sampling value and u-axis projection value of the effective peak point with the largest amplitude on each effective target energy line. obj and speed v obj .

[0096] For each effective peak point, the corresponding angle sampling value α is recorded i , u-axis projection value pu s In step S6, for each valid target energy value, obtain the angle sampling value α of the valid peak point with the largest amplitude. obj and the u-axis projection value u obj , calculate the distance estimate s of the corresponding target obj and the velocity estimate v obj The calculation method is:

[0097]

[0098] Where cot(·) represents the cotangent function.

[0099] The embodiment of the present application performs a refined modeling of the LFM radar echo signal r(t), which is expressed as follows:

[0100]

[0101] Among them, L is the number of targets in the scene to be detected, A i ,θ i , τ i With ξ i are the amplitude, phase, delay, and scale change factor of the echo component corresponding to the i-th target, ξ i Satisfaction relationship ξ i =1-η i ,in, v i is the target radial velocity.

[0102] It can be analyzed that according to the above refined echo model, the frequency modulation slope of the echo component corresponding to different target speeds is also different, and the frequency modulation slope value is Using FRFT processing, the echo signal is projected into the (α, u) domain, where α is directly linked to the echo signal's frequency modulation slope, and the u axis is directly related to both delay and frequency. By performing FRFT processing on the echo, the method of this application can calculate the distance and velocity information of multiple targets within a single echo cycle. This demonstrates the timeliness of this application's joint estimation of multi-target distance and velocity, as well as its adaptability to maneuverability.

[0103] Existing technologies assume that echoes from targets of varying speeds all have consistent frequency modulation slopes, making it difficult to simultaneously calculate the range and velocity information of multiple targets from a single cycle. To obtain range and velocity estimates for multiple targets, multi-cycle echoes must be processed together. However, due to averaging and inertial effects, changes in target maneuverability can lead to model mismatch and increased estimation errors. Furthermore, non-refined echo modeling can significantly affect the motion parameters of high- and ultra-high-speed targets, leading to increased parameter estimation bias and mismatch between echo range profiles.

[0104] In some embodiments, the device provided in the present application includes a processor and a storage medium, in which a computer program is stored. When the processor runs the computer program in the storage medium, the above-mentioned FRFT-based high-speed multi-target distance and speed joint estimation method is executed.

[0105] The computer program product provided herein, in some embodiments, includes a computer program that, when executed by a processor, performs the aforementioned FRFT-based high-speed multi-target range and velocity joint estimation method. As a feasible implementation, the computer program product can be recorded and stored on a computer-readable storage medium, such as a CD, USB flash drive, magnetic disk, or hard drive.

[0106] The embodiments of the present application also verify the performance of the proposed method.

[0107] 1) Simulation conditions

[0108] Assume that the detection scenario includes three hypersonic targets with true radial distances of 96.7 km, 97.0 km, and 98.4 km, respectively, and true radial velocities of Mach 4.00, Mach 9.25, and Mach 7.5, respectively. The amplitude gains of the corresponding echo components are all set to 1. The radar transmit signal is a broadband linear frequency-modulated pulse signal with a bandwidth of 500 MHz and a pulse width of 0.5 ms, using a modulation scheme where the frequency increases linearly with time. The input signal-to-noise ratio of the echo is set to -25 dB, the intermediate frequency sampling rate is set to 1.2 GHz, and the total number of sample points of the echo signal to be analyzed is 640,000. The range step size for the FRFT processing is set to 0.14 m, and the velocity step size is set to 0.25 Mach, resulting in a total of 60 search angles α. The simulation computer configuration includes a 3.8 GHz CPU and 16 GB of memory. Other parameters that have no substantial impact on the simulation results are not listed here.

[0109] 2.) Simulation content

[0110] Under the above simulation conditions, a radar echo signal is constructed and the echo signal is processed by FRFT using the method provided in this application. The FRFT processing results are recorded as follows: Figure 2-Figure 4 shown.

[0111] Figure 2 The simulation results of the FRFT transform amplitude at the first search angle are given. It can be seen from the results that three target peaks can be clearly seen in the FRFT transform results, and the highest peak of each target is accurately found according to the method of the present application. Figure 3 The simulation results of the two-dimensional FRFT transform amplitude in the velocity-distance dimension at all search angles are given, and the three target energy lines can be clearly distinguished. Figure 4 The amplitude-to-velocity curves of the three target energy lines are presented, and the velocity corresponding to the highest peak of each target energy line is accurately found using the method of this application. Table 1 shows the target distance-velocity joint estimation results of this method and the comparison results with the true values. The results show that this method accurately achieves multi-target distance-velocity joint estimation, and the estimated distance and velocity errors do not exceed the set distance and velocity step values.

[0112] Table 1 Target distance-speed joint estimation value and comparison with the true value

[0113]

[0114] Furthermore, the computer took 9.57 seconds to complete the entire simulation. It should be noted that the FRFT calculations for each search angle during the simulation were performed serially. However, in actual embedded hardware applications, each search angle can be calculated in parallel. Therefore, the method of this application is fast enough to meet real-time requirements in practical applications.

[0115] The present invention is not limited to the aforementioned specific embodiments, but extends to any new features or any new combination disclosed in this specification, as well as any new method or process steps or any new combination disclosed.

Claims

1. A high-speed multi-target distance and velocity joint estimation method based on FRFT, characterized in that: include: Perform down-conversion sampling on the radar echo signal to obtain a digital echo signal; Performing FRFT processing on the digital echo signal to obtain a processing result; Obtaining an amplitude matrix of the processing result, filtering the amplitude matrix according to a set threshold, and extracting peak points for each row; According to the set target minimum spacing, the peak points of each row are screened to obtain the retained valid peak points; Extracting the effective target energy line according to the effective peak point of each row includes: Extracting all target energy lines based on the valid peak points in each row, including: sequentially associating the closest valid peak points in different rows with the same target energy line based on the valid peak points in each row, including: recording the index position information of the valid peak points in the first row; for other rows, sequentially associating the valid peak points in the current row that are closest to the valid peak points recorded in the previous row with the valid peak points recorded in the previous row with the same target energy line; Filtering out effective target energy lines from all target energy lines according to a set effective peak point number threshold; performing smoothing filtering on the effective target energy lines; The distance and speed of the corresponding target are estimated based on the angle sampling value and the u-axis projection value of the effective peak point with the maximum amplitude on each of the effective target energy lines.

2. The high-speed multi-target distance and velocity joint estimation method based on FRFT as claimed in claim 1, characterized in that: Performing FRFT processing on the digital echo signal includes: Calculate the angle sampling value required for FRFT processing according to the set target speed change range and speed search step; According to the set radial distance resolution interval, calculate the u-axis sampling interval required for FRFT processing; Perform FRFT processing on the digital echo signal according to the angle sampling value and the u-axis sampling interval.

3. The high-speed multi-target distance and velocity joint estimation method based on FRFT as claimed in claim 1, characterized in that: The filtering the amplitude matrix according to the set threshold comprises: setting the threshold based on the average power of the processing result; The amplitudes in the amplitude matrix that are smaller than the threshold are set to zero.

4. The high-speed multi-target distance and velocity joint estimation method based on FRFT as claimed in claim 1, characterized in that: The step of screening the peak points of each row according to the set target minimum spacing includes: According to the set target minimum spacing, calculate the minimum projection spacing projected onto the u-axis; Only one peak point is retained as a valid peak point within the minimum projection spacing range in each row.

5. The high-speed multi-target distance and velocity joint estimation method based on FRFT as claimed in claim 4, characterized in that: The retaining only one peak point as a valid peak point within the minimum projection spacing range in each row includes: Grouping the peak points of each row based on the minimum projection distance; The peak point with the largest amplitude in each group is retained as the valid peak point.

6. A device comprising a processor and a storage medium, wherein the storage medium stores a computer program, characterized in that: When the processor runs the computer program in the storage medium, it executes the FRFT-based high-speed multi-target distance and velocity joint estimation method according to any one of claims 1 to 5.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the high-speed multi-target distance and velocity joint estimation method based on FRFT is executed.

Images