A high-speed target acceleration estimation method based on biorthogonal fourier transform

Abstract

This application discloses a high-speed target acceleration estimation method based on biorthogonal Fourier transform. First, the received echo signal is subjected to an FFT transform in the fast clock dimension. Then, a Keystone transform is performed in the slow clock dimension to correct for range travel, stretching and compressing the echo signal. Next, a moving target detection (MTD) method is used to coarsely estimate the target velocity, obtaining an ambiguous target velocity, and Doppler filtering is applied in the frequency domain to improve the signal-to-noise ratio. Then, the Doppler frequency of the signal is compensated based on the estimated value. Next, based on the Keystone transform, a biorthogonal basis opening is performed on the echo signal using a BFT transform to estimate acceleration and compensate for target acceleration. Finally, the MTD method is used to de-ambiguate the range and velocity, obtaining the precise target velocity and range. This method can increase the linear dynamic range of signal processing and improve the improvement factor; it also solves the problem that the Keystone transform alone cannot eliminate the effects of acceleration when analyzing accelerating targets.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and in particular relates to a method for estimating the acceleration of high-speed targets based on biorthogonal Fourier transform. Background Technology

[0002] With the development of radar detection technology, guidance technology is playing an increasingly important role, and precision guidance technology is playing an increasingly crucial part. Radar seekers, due to their superior target tracking and acquisition capabilities, have become a vital component of radar detectors. To meet the accuracy requirements of radar measurements, signals need to have a large time and bandwidth. Modern radars mostly employ linear frequency modulated (LFM) pulse signals through pulse compression processing to balance radar range resolution and detection power. LFM pulse radars have significant advantages in target tracking and acquisition, and also perform well in clutter suppression, thus they are widely used in radar systems.

[0003] The signal processing of traditional radar systems generally involves matched filtering and Moving Target Detection (MTD) of the target echo, concentrating the signal energy within a range and velocity cell to complete the coherent accumulation process. According to the design principles of traditional PD radars, the target's range movement cannot exceed half a range resolution cell during the coherent accumulation time. When the coherent accumulation time is long, the signal bandwidth is large, or the target's speed is high, this requirement is often not met. Therefore, pulse echoes exhibiting range cell movement are a major factor affecting radar detection performance. For high-speed targets moving at a constant velocity, many detection methods have been proposed in existing technologies, but all have certain limitations.

[0004] Radon first proposed using MTD (Mean Transformer) to detect parameters of high-speed targets. Although it can directly obtain information such as the target's velocity and range, when the target's speed is too high, the target echo frequency expands in the Doppler frequency cell during multi-pulse coherent accumulation processing. The target Doppler frequency will span multiple frequency cells, resulting in a limited linear dynamic range for target processing and potential clutter interference. Perry proposed the Keystone Transform, which eliminates the linear range offset of all moving targets through scaling. This method does not require knowledge of the target's velocity information. However, because the target has acceleration, the signal energy after pulse compression cannot be concentrated in a single range cell, which means that the influence of the moving target's acceleration cannot be eliminated when performing Keystone Transform detection alone. Zhang Shouhong et al. performed motion compensation and matching accumulation by comprehensively processing multiple distance units and combining time-frequency analysis. They were able to eliminate the effects of Doppler frequency shift and cross-distance unit influence simultaneously using Doppler filter banks with different rotation angles. However, multiple Doppler filters were used to complete motion compensation during detection. The search for the power coefficients of each filter took a long time. Furthermore, the accumulation efficiency was too low due to the small improvement factor during compensation, which led to the diffusion of accumulated energy and made it impossible to complete target detection or accurate velocity measurement.

[0005] The Biorthogonal Fourier Transform (BFT) is a target acceleration estimation algorithm based on the Keystone Transform. It opens the signal using a biorthogonal basis to obtain the frequency modulation slope density spectrum, a density distribution similar to a spectrum. Through BFT, a single-slope spectrum LFM signal will appear as a corresponding single-impulse function. For an accelerating target with known velocity binding conditions, this algorithm performs a Medium-Degree of Deposition (MTD) on the Keystone-transformed signal, defuzzifies the velocity based on the binding velocity information to obtain a velocity estimate, and then applies BFT to the velocity-compensated signal to obtain the slope density spectrum, calculating the target acceleration. Summary of the Invention

[0006] The purpose of this invention is to solve the problem that the Keystone transform alone cannot eliminate the influence of acceleration in high-speed target detection. It provides a high-speed target acceleration estimation method based on biorthogonal Fourier transform, which is mainly applied to high-speed moving target detection under active LFM radar.

[0007] To achieve the objective of this invention, a method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform is disclosed, comprising the following steps:

[0008] Step 1: After receiving the radar echo signal, the receiver first performs a Fast Fourier Transform (FFT) on the echo signal in the fast clock dimension; then it performs a Keystone Transform in the slow clock dimension to correct the range travel, stretching and compressing the echo signal.

[0009] Step 2: Roughly estimate the target velocity using Moving Target Detection (MTD) to obtain the blurred target velocity, and perform Doppler filtering on the signal in the frequency domain to improve the signal-to-noise ratio; then compensate the Doppler frequency of the signal based on the estimated value.

[0010] Step 3: Based on the Keystone transform, use the biorthogonal Fourier transform (BFT) to open the biorthogonal basis of the echo signal, estimate the acceleration, and compensate for the target acceleration.

[0011] Step 4: Use Moving Target Detection (MTD) to deblur the distance and velocity and obtain the target's precise velocity and distance.

[0012] Furthermore, step 1 specifically includes the following steps:

[0013] Step 1-1: Arrange the echo signals received by the radar into a two-dimensional matrix of fast time and slow time;

[0014] Steps 1-2: Perform FFT transformation on the fast clock dimension of the received echo signal;

[0015] Steps 1-3: Perform a keystone transform on the slow clock dimension of the echo signal to eliminate the first-order term coupling frequency and time in the echo signal. Then, align the envelope of each pulse with the first pulse using an inverse fast Fourier transform (IFFT), thereby achieving range travel correction for the target. The keystone transform refers to performing variable substitution, and the specific formula is as follows:

[0016]

[0017] In the formula, t m τ represents the slow clock dimension. m The virtual slow time domain after the Keystone transform is defined as f0, where f is the carrier frequency of the LFM signal and f represents the fast time frequency domain. When f > 0, the slow clock dimension is stretched; when f < 0, the slow clock dimension is compressed, and the degree of transformation is related to the magnitude of the absolute value of the frequency. The Keystone transform makes ft... m A rectangular domain on the plane becomes f-τ m An inverted trapezoidal domain on a plane.

[0018] Furthermore, step 2 specifically includes the following steps:

[0019] Step 2-1: Moving target detection MTD performs pulse compression on echo signals within multiple pulse repetition intervals within the same coherent processing time.

[0020] Step 2-2: Perform Doppler filtering on the echo signal in the frequency domain to filter out clutter signals;

[0021] When the target's speed is too high, Doppler ambiguity occurs in the radar system, causing a change in the target's Doppler frequency; let the transformed target Doppler frequency become f. d1 The actual Doppler frequency is f d2 If || is the absolute value operator, then the expression is:

[0022]

[0023] In the formula, k is the Doppler ambiguity number, and f r The difference between the target's actual frequency and the Doppler frequency;

[0024] Steps 2-3: Perform spectral analysis on the slow clock dimension data sequence within each range cell to complete the target detection process on the range-Doppler matrix data.

[0025] Furthermore, step 3 specifically includes the following steps:

[0026] Step 3-1: After the echo signal undergoes Keystone transformation, the target acceleration is estimated by using Biorthogonal Fourier Transform (BFT). The echo signal is then subjected to a biorthogonal basis opening.

[0027] Step 3-2: Extract the frequency modulation slope of the corresponding linear frequency modulated (LFM) signal from the biorthogonal spectrum of the signal. Estimate the target acceleration by identifying the peak position in the slope spectrum. The formula for calculating the target acceleration is:

[0028]

[0029] In the formula, 'a' represents the target's acceleration, in m / s². 2 , x is the peak position of the slope spectrum obtained by discrete biorthogonal Fourier transform (DBFT), λ represents the radar pulse wavelength, f0 is the carrier frequency of the LFM signal, and f represents the fast time frequency domain.

[0030] Furthermore, the BFT processing procedure for the echo signal in step 3-1 is as follows:

[0031] Let the frequency modulation slope of the signal be k, the amplitude be A, and the signal expression be f(t).

[0032] f(t) = Aexp(jKt) 2 )

[0033] In the formula, j represents the imaginary unit, t is the time unit, and exp represents an exponential function with base e. Then, the biorthogonal Fourier transform amplitude spectrum F(ω) of the signal is:

[0034] F(ω)=BFT[f(t)]=2πAδ(ω-k)

[0035] BFT represents the biorthogonal Fourier transform of the signal, δ represents the Dirac function, and ω is the frequency domain representation of the time domain t; the expression f is the combination of M LFM signals with different frequency modulation slopes. m (t) is

[0036]

[0037] Then the BFT transform amplitude spectrum F of the combined signal m (ω) is

[0038]

[0039] In the formula, K m A represents the frequency modulation slope of the m-th LFM signal. m This represents the amplitude of the m-th LFM signal.

[0040] Furthermore, step 4 is detailed below:

[0041] The repetition period of the LFM waveform pulse transmitted by the active LFM radar is T. r c represents the speed of light in a vacuum, λ represents the radar pulse wavelength, and its maximum unambiguous range R ami Maximum unambiguous speed V ami They are respectively

[0042]

[0043] When the target's reflection distance N r and reflection speed N v satisfy

[0044]

[0045] In the formula, R and V represent the actual distance and velocity of the target, respectively. Therefore, the processed target distance and velocity information is:

[0046] R = R m +N r R ami V = V m +N r V ami

[0047] In the formula, R m and V mThis indicates the actual distance and velocity values ​​of the target measured after the radar signal is de-ambigued through moving target detection.

[0048] Compared with the prior art, the significant advancements of this invention are: 1) increasing the linear dynamic range of signal processing; 2) using a set of Doppler filters to make it closer to the optimal filter and improve the improvement factor; 3) effectively suppressing clutter interference and solving the problem that the Keystone transform alone cannot eliminate the effects of acceleration when analyzing accelerated targets.

[0049] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0050] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0051] Figure 1 This is a flowchart illustrating the technical implementation of the present invention.

[0052] Figure 2 This is a schematic diagram of the MTD data processing structure;

[0053] Figure 3 This is a schematic diagram of the MTD processing results for the echo signal;

[0054] Figure 4 This is a schematic diagram illustrating the distance traveled by a high-speed target.

[0055] Figure 5 Simulation results of MTD detection of high-speed target echo signals;

[0056] Figure 6 This is a simulation diagram illustrating the effect of the residual Doppler frequency on the DBFT. Detailed Implementation

[0057] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] To achieve the above objectives, the present invention provides the following technical solution, with specific steps as follows:

[0059] Step 1: After receiving the radar echo signal, the receiver first performs a Fast Fourier Transform (FFT) on the echo signal in the fast clock dimension; then it performs a Keystone Transform in the slow clock dimension to correct the range travel, stretching and compressing the echo signal.

[0060] Step 2: Roughly estimate the target velocity using Moving Target Detection (MTD) to obtain the blurred target velocity, and perform Doppler filtering on the signal in the frequency domain to improve the signal-to-noise ratio; then compensate the Doppler frequency of the signal based on the estimated value.

[0061] Step 3: Based on the Keystone transform, use the biorthogonal Fourier transform (BFT) to open the biorthogonal basis of the echo signal, estimate the acceleration, and compensate for the target acceleration.

[0062] Step 4: Use Moving Target Detection (MTD) to deblur the distance and velocity and obtain the target's precise velocity and distance.

[0063] This invention proposes an acceleration detection method based on biorthogonal Fourier transform. It uses BFT to estimate acceleration based on keystone transform, uses the acceleration estimate to compensate for the target echo signal, corrects the target Doppler cell movement phenomenon, and finally performs MTD to detect the target's distance and velocity.

[0064] Step 1 specifically involves: The echo signals received by the radar can be arranged into a fast-time-slow-time two-dimensional matrix. An FFT transformation is performed on the fast clock dimension of the received echo signals, followed by a keystone transformation. This is a linear transformation, essentially a stretching and compression of the slow clock dimension. The keystone transformation is essentially variable substitution.

[0065]

[0066] In the formula τ m For the virtual slow time domain after the Keystone transform, when f > 0, the slow clock dimension is stretched; when f < 0, the slow clock dimension is compressed, and the degree of transformation is related to the magnitude of the absolute value of the frequency. The Keystone transform makes ft m A rectangular domain on the plane becomes f-τ m An inverted trapezoidal domain on a plane.

[0067] The Keystone transform is essentially a scaling transform. In practical radar systems, the echo signal is sampled at a fixed sampling frequency, and the data are discrete points. τ m For the defined virtual time, no sampled values ​​exist at that moment. Therefore, interpolation is needed to transform the trapezoidal data after Keystone transformation into a rectangular data arrangement. s(f,t) m) is obtained by performing a Fourier transform on each pulse echo signal, and then using a Keystone transform to convert s(f,t) into s(f,t). m Transformed into s(f,τ) m Then, the frequency domain expression of the echo signal after Keystone transformation is:

[0068]

[0069] As can be seen from the above formula, the Keystone transform eliminates the first-order term that couples frequency and time, and after IFFT, the envelopes of each pulse are aligned at the first pulse, thus achieving target range movement correction.

[0070] Step 2 specifically involves MTD processing, which involves two dimensions of the echo signal: a fast clock dimension and a slow clock dimension. The radar samples the signal for each pulse repetition period to form the fast clock dimension. The clock dimension corresponding to the same sampling point of multiple PRI (Pulse Repetition Interval) echo signals within a CPI (Coherent Processing Time) is the slow clock dimension. MTD processes the pulse-compressed echo signals of multiple PRIs within the same CPI, which is essentially a Doppler filtering process on the first range gate data to the Mth range gate data in the fast clock dimension. M represents the number of sampling points of the echo signal within a PRI, N represents the number of PRIs within a CPI, and S(n,m) represents the m-th data point of the nth PRI of the echo signal. Each row corresponds to all data within each PRI of the signal, and each column corresponds to the echo signals of each PRI at the same sampling point. MTD directly performs spectral analysis on the slow-time data sequence within each range cell, thus replacing filtering processing. Target detection is performed directly on the range-Doppler matrix data.

[0071] Step 3 specifically involves the biorthogonal Fourier transform (BFT), which expands the signal using a biorthogonal function to obtain the frequency modulation slope density spectrum. This is a transform algorithm that does not require searching for the modulation frequency. For a zero-initial-frequency LFM signal, the slope spectrum obtained through the BFT is a singer function, and its peak position corresponds to the frequency modulation slope of the LFM signal. The slope spectrum obtained by the BFT is a density distribution similar to a spectrum, suitable for analyzing the constituent signals of multiple LFM signals with different frequency modulation slopes. The continuous-form BFT expression is:

[0072]

[0073] Let the frequency modulation slope of the signal be k, and the amplitude be A. The signal expression is:

[0074] f(t) = Aexp(jKt) 2 )

[0075] The amplitude spectrum of the bioorthogonal Fourier transform of the signal is:

[0076] F(ω)=BFT[f(t)]=2πAδ(ω-k)

[0077] The expression for the combination of N LFM signals with different frequency modulation slopes is:

[0078]

[0079] The amplitude spectrum of the BFT transform of the signal is then:

[0080]

[0081] This transform possesses linear additivity, conjugate symmetry, and slant shift properties. Since the signals sampled by the radar system are discrete values, this paper uses the discrete biorthogonal Fourier transform (DFT) to analyze the signals. Corresponding to the Fourier transform kernel exp(-jwt), which is used for the spectral expansion of the processed signal, the biorthogonal Fourier transform kernel exp(-jwt)... 2 The DBFT expression is derived from the frequency modulation slope density spectrum expansion of the signal. Referring to the Discrete Fourier Transform (DFT), circular convolution is used to obtain the following expression:

[0082]

[0083] The echo signal expression of a high-speed, accelerating target is:

[0084]

[0085] The frequency domain expression of the echo pulse compression signal is:

[0086]

[0087] The signal expression after performing the Keystone transform on the above equation is:

[0088]

[0089] In the formula, γ = 2a / λ. For the two-dimensional matrix of the echo signal in the fast-time frequency domain and slow-time domain, with the distance frequency f constant, the quadratic term in the signal caused by acceleration is:

[0090]

[0091] The above formula can be viewed as using a slow time T r The LFM signal has intervals, and γf0 / (f0+f) represents the frequency modulation slope. Therefore, DBFT can be used to analyze this signal, and the target acceleration can be estimated by identifying the peak locations in the slope spectrum. After formula transformation, the acceleration calculation formula is:

[0092]

[0093] In the formula, x represents the peak position of the slope spectrum obtained through DBFT. However, when the initial frequency of the LFM signal is not 0, the peak of the BFT result will be broadened, reducing the accuracy of the analysis results. Therefore, the initial frequency of the signal to be analyzed should be kept as low as possible. As can be seen from the above formula, the Doppler frequency of a high-speed target will cause the initial frequency of the signal to be non-zero. Therefore, it is necessary to compensate for the Doppler frequency before performing DBFT analysis on the target acceleration.

[0094] Step 4 specifically involves the following: When the repetition frequency of the transmitted waveform pulse is very high, the echo generated by a transmitted pulse may take several cycles to be received, causing confusion in the radar's transmit and receive pulse correspondence, thus resulting in range ambiguity. Similarly, when the repetition frequency is not high enough, the target's Doppler frequency shift will be greater than the repetition frequency of the transmitted pulse, with a phase difference of nf. r The Doppler frequency will be read as the same frequency, thus producing a speed ambiguity phenomenon.

[0095] The LFM waveform pulse repetition period transmitted by the active LFM radar is Tr, and its maximum unambiguous range and velocity are respectively...

[0096]

[0097] When the goal is satisfied

[0098]

[0099] In the formula, R and V represent the actual distance and velocity of the target, respectively. Therefore, the processed target distance and velocity information is:

[0100] R = R m +N r R ami V = V m +N r V ami

[0101] In the formula, R m and V m This indicates the actual distance and velocity values ​​of the target measured after the radar signal is de-ambigued through moving target detection.

[0102] like Figure 1 As shown, Figure 1This is a flowchart of a high-speed target acceleration estimation method based on biorthogonal Fourier transform. The specific implementation process is as follows: First, after the receiver receives the radar echo signal, it performs a Fast Fourier Transform (FFT) on the echo signal in the fast clock dimension. Then, it performs a Keystone Transform in the slow clock dimension to correct range travel, stretching and compressing the echo signal. Next, it uses Moving Target Detection (MTD) to coarsely estimate the target velocity, obtaining an ambiguous target velocity, and performs Doppler filtering in the frequency domain to improve the signal-to-noise ratio. Then, it compensates for the Doppler frequency of the signal based on the estimated value. Then, based on the Keystone Transform, it uses a biorthogonal Fourier Transform (BFT) to open the biorthogonal basis of the echo signal, performs acceleration estimation, and compensates for target acceleration. Finally, it uses MTD to complete range-velocity deambiguation and obtain the precise target velocity and range. This invention combines the advantages and disadvantages of the Keystone Transform algorithm in both uniform and accelerating target scenarios, greatly improving the energy accumulation efficiency of uniform targets and effectively reducing the impact of acceleration.

[0103] like Figure 2 As shown, Figure 2 This is a schematic diagram of the MTD data processing structure. MTD processing involves two dimensions: the fast clock dimension and the slow clock dimension of the echo signal. The radar samples the signal for each pulse repetition period to form the fast clock dimension. The clock dimension corresponding to the same sampling point of multiple PRI echo signals within a CPI is the slow clock dimension. The data structure for moving target detection processing is as follows: Figure 2 As shown.

[0104] MTD processes the pulse-compressed echo signals from multiple PRIs within the same CPI, which is to... Figure 2 The process of performing Doppler filtering on each column of data. Figure 2 In this diagram, M represents the number of sampling points of the echo signal within a PRI, N represents the number of PRIs within a CPI, and S(n,m) represents the data of the m-th point of the n-th PRI of the echo signal. Each row corresponds to all the data within each PRI of the signal, and each column corresponds to the echo signal of each PRI under the same sampling point.

[0105] MTD (Moving Target Detection) is a technique that uses a Doppler filter bank to suppress various clutter signals, thereby improving the radar's ability to detect moving targets in cluttered environments. MTD is a bandpass filter bank, meaning it has multiple inputs and multiple outputs. While it can be implemented using an FIR (First-In, Second-Out) filter bank, it is generally implemented using FFT (First-In, Second-Out) processing. This involves performing FFT on the same range cells of different pulse echo signals, resulting in N inputs and N outputs. Targets are then detected and identified from these N outputs. If a target is present, the output with the largest peak value will appear; this likely represents the target's position. Based on this position information, the Doppler value of the moving target can be obtained. In an MTD radar system, the difference between moving targets and clutter lies in their velocity. The different velocities cause unequal Doppler frequencies in the echo signals, allowing for the differentiation between clutter and moving targets. Moving target detection not only filters out clutter but also distinguishes targets moving at different speeds, significantly improving the ability to detect moving targets in cluttered environments.

[0106] like Figure 3 As shown, Figure 3 The results are simulations of the echo signal processed by MTD. Figure 3 This is the MTD result of the target echo signal under a 22µs waveform obtained through Matlab simulation. The target velocity is 102m / s and the distance is 600m. At this time, the peak value of the result after MTD is located at the 200th distance cell and the 39th Doppler cell.

[0107] like Figure 4 As shown, Figure 4 This diagram illustrates the relationship between the range movement of a high-speed target and the change in the signal envelope. When the target exhibits acceleration, the echo signal contains a quadratic phase term caused by the acceleration. Increased target velocity and acceleration lead to more significant inter-pulse envelope changes, resulting in energy diffusion. Therefore, to improve accumulation gain, range movement correction and acceleration compensation are required for the target echo before moving target detection.

[0108] like Figure 5 As shown, Figure 5 The images show simulation results of MTD (Mean Transmission Detection) of high-speed target echo signals. The left and right images are the top and front views of the MTD detection results, respectively. Due to the influence of acceleration, the target exhibits Doppler diffusion in addition to range travel during the coherent accumulation time. Figure 5This indicates that the signal spectrum extends not only in the range dimension but also across multiple Doppler frequency units, leading to severe energy diffusion and a decrease in accumulated gain. The MTD result is no longer a sharp peak, making it impossible to analyze the target's motion information. In actual measurements, the target's velocity information cannot be precisely known. Therefore, when the target velocity is unknown, a rough estimate of the target velocity can be made by directly performing MTD after the Keystone transform, and then the Doppler frequency of the signal can be compensated based on the estimate before performing BFT analysis. Since only a rough estimate of the target's Doppler frequency is possible, and the Doppler frequency cannot be precisely compensated, the signal has an initial frequency. Therefore, the peak point generated after the BFT transform will be shifted and broadened, degrading detection performance. Matalab simulations verify the impact of the presence of an initial frequency in the signal after the Keystone transform on the performance of the biorthogonal Fourier transform algorithm.

[0109] Figure 6 (a) to (f) represent the residual velocities after compensation as 1 to 6 m / s and the acceleration as 200 m / s², respectively. 2 The impact of time on signal analysis. Figure 6 (a) The DBFT results are obtained when the residual velocity is 1 m / s. The estimated target acceleration is calculated to be 211.29 m / s². 2 The difference from the actual value is 11.29 m / s. 2 , Figure 6 (c) The DBFT results are obtained when the residual velocity is 3 m / s. The estimated target acceleration is calculated to be 234.13 m / s². 2 The difference from the actual value is 34.13 m / s. 2 , Figure 6 (e) The DBFT results are obtained when the residual velocity is 5 m / s. The estimated target acceleration is calculated to be 256.97 m / s². 2 The difference from the actual value is 56.97 m / s. 2 .right Figure 6 Analysis of the simulation results shows that for every 1 m / s increase in residual velocity, the difference between the measured and actual acceleration values ​​increases by approximately 11.29 m / s². 2 .

[0110] The biorthogonal Fourier transform requires the initial frequency of the transformed signal to be 0, therefore this method requires knowledge of the target's initial velocity. First, the Doppler frequency is compensated in the target echo signal. Performing a DBFT on the compensated signal yields the peak value of the target's acceleration.

[0111] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0112] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform, characterized in that, Includes the following steps: Step 1: After receiving the radar echo signal, the receiver first performs a Fast Fourier Transform (FFT) on the echo signal in the fast clock dimension; then it performs a Keystone Transform in the slow clock dimension to correct the range travel, stretching and compressing the echo signal. Step 2: Roughly estimate the target velocity using Moving Target Detection (MTD) to obtain the blurred target velocity, and perform Doppler filtering on the signal in the frequency domain to improve the signal-to-noise ratio; then compensate the Doppler frequency of the signal based on the estimated value. Step 3: Based on the Keystone transform, use the biorthogonal Fourier transform (BFT) to open the biorthogonal basis of the echo signal, estimate the acceleration, and compensate for the target acceleration. Step 4: Use Moving Target Detection (MTD) to deblur the distance and velocity and obtain the target's precise velocity and distance.

2. The method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1-1: Arrange the echo signals received by the radar into a two-dimensional matrix of fast time and slow time; Steps 1-2: Perform FFT transformation on the fast clock dimension of the received echo signal; Steps 1-3: Perform a keystone transform on the slow clock dimension of the echo signal to eliminate the first-order term coupling frequency and time in the echo signal. Then, align the envelope of each pulse with the first pulse using an inverse fast Fourier transform (IFFT), thereby achieving target range travel correction. The keystone transform refers to performing variable substitution, and the specific formula is as follows: In the formula, Represents the slow clock dimension. The virtual slow time domain after the Keystone transform is defined as follows: f0 is the carrier frequency of the LFM signal, and f represents the fast time frequency domain. When f > 0, the slow clock dimension is stretched; when f < 0, the slow clock dimension is compressed, and the degree of transformation is related to the magnitude of the absolute value of the frequency. The Keystone transform makes... A rectangular region on the plane becomes An inverted trapezoidal domain on a plane.

3. The method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2-1: Moving target detection MTD performs pulse compression on echo signals within multiple pulse repetition intervals within the same coherent processing time. Step 2-2: Perform Doppler filtering on the echo signal in the frequency domain to filter out clutter signals; When the target's speed is too high, Doppler ambiguity occurs in the radar system, causing a change in the target's Doppler frequency; let the transformed target Doppler frequency become... The actual Doppler frequency is If | is the absolute value operator, then the expression is: In the formula, k is the Doppler ambiguity number. The difference between the target's actual frequency and the Doppler frequency; Steps 2-3: Perform spectral analysis on the slow clock dimension data sequence within each range cell to complete the target detection process on the range-Doppler matrix data.

4. The method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3-1: After the echo signal undergoes Keystone transformation, the target acceleration is estimated by using Biorthogonal Fourier Transform (BFT). The echo signal is then subjected to a biorthogonal basis opening. Step 3-2: Extract the frequency modulation slope of the corresponding linear frequency modulated (LFM) signal from the biorthogonal spectrum of the signal. Estimate the target acceleration by identifying the peak position in the slope spectrum. The formula for calculating the target acceleration is: In the formula, 'a' represents the target's acceleration, in units of 1000 m / s. x represents the peak position of the slope spectrum obtained through Discrete Bioorthogonal Fourier Transform (DBFT). The wavelength of the radar pulse is represented by f0, the carrier frequency of the LFM signal is f, and f represents the fast time frequency domain.

5. The method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform according to claim 4, characterized in that, The BFT transformation process for the echo signal in step 3-1 is as follows: Let the frequency modulation slope of the signal be k, and the amplitude be A. The signal expression is... for In the formula, j represents the imaginary unit, t is the time unit, and exp represents an exponential function with base e. Then, the magnitude spectrum of the bioorthogonal Fourier transform of the signal... for BFT stands for Biorthogonal Fourier Transform of a signal. Represents the Dirac function, It is the frequency domain representation of the time domain t; The expression for the combination of M LFM signals with different frequency modulation slopes for The amplitude spectrum of the BFT transform of the combined signal for In the formula, This represents the frequency modulation slope of the m-th LFM signal. This represents the amplitude of the m-th LFM signal.

6. The method for estimating the acceleration of a high-speed target based on bioorthogonal Fourier transform according to claim 1, characterized in that, Step 4 is as follows: The repetition period of the LFM waveform pulse transmitted by the active LFM radar is c represents the speed of light in a vacuum. This represents the radar pulse wavelength and its maximum unambiguous range. Maximum unambiguous speed They are respectively When the target's reflection distance and reflection speed satisfy In the formula, R and V represent the actual distance and velocity of the target, respectively. Therefore, the processed target distance and velocity information is: In the formula, and This indicates the actual distance and velocity values ​​of the target measured after the radar signal is de-ambigued through moving target detection.

Images