Frequency-modulated continuous wave laser radar distance measurement and speed measurement frequency spectrum estimation method
The frequency beat signal of the FM continuous wave lidar is processed through variational modular mode decomposition and coherent spectrum methods, which solves the problems of fence effect and spectrum leakage, and achieves high-precision and high-resolution ranging and speed measurement.
Patent Information
- Application Number
- CN202510280480.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-11
- Publication Date
- 2025-07-08
AI Technical Summary
The prior art has reduced measurement accuracy and resolution caused by fence effect, spectrum leakage and noise interference in FM LiDAR, and the existing frequency correction algorithm has large calculation amounts and limited accuracy.
Variable mode decomposition and coherent spectrum methods are used to perform variational mode decomposition of the original beat frequency signal, reconstruct the signal, and then perform windowed Fourier transform and frequency modulation Z transform. Combined with coherent spectrum refinement, the distance velocity information of the target is accurately solved.
It effectively suppresses modal aliasing, improves signal-to-noise ratio, enhances measurement resolution and accuracy, and improves the accuracy of distance measurement and speed measurement.
Smart Images
Figure CN120275932A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of ranging and velocity measurement signal processing for frequency modulated continuous wave lidar, and specifically relates to a method for estimating the ranging and velocity measurement spectrum of frequency modulated continuous wave lidar. Background Art
[0002] With the rapid development of technologies such as autonomous driving, robots, and drones, frequency modulated continuous wave lidar, with its characteristics of being able to measure distance and velocity simultaneously, having strong anti-interference ability, high measurement resolution, and being easy to integrate, is used as a high-precision sensor and plays a crucial role in providing environmental perception, achieving real-time measurement, and enhancing the autonomous decision-making ability of the system.
[0003] The FMCW frequency modulated continuous wave lidar calculates the distance and velocity information by obtaining the difference frequency between the transmitted signal and the echo signal. The estimation of the intermediate frequency directly affects the measurement result. In practical applications, the fast Fourier transform (FFT) is often used to estimate the spectrum of the beat frequency signal. The frequency resolution of directly using FFT is
[0004]
[0005] where f s is the signal sampling rate and N is the number of FFT points. The frequency error range of direct FFT is In response to the fence effect, a suitable spectrum refinement method should be selected to estimate the frequency values in the gaps between adjacent frequency points, and the calculation resolution of the measurement is reflected here. In actual signal processing, due to the truncation of the infinite-time signal, "spectrum leakage" occurs, which also affects the extraction of the intermediate frequency signal. To reduce the measurement error, a suitable frequency correction algorithm needs to be adopted to accurately estimate the frequency value of the intermediate frequency signal. In terms of spectrum estimation, although the simplest zero-padding method in the time domain can improve the frequency resolution, it will introduce a large amount of calculation, and the accuracy of the estimation result is limited. The energy centroid method can effectively correct the frequency but cannot refine the spectrum and improve the frequency resolution. Summary of the Invention
[0006] The present invention discloses a method for estimating the ranging and velocity measurement spectrum of frequency modulated continuous wave lidar, which uses VMD denoising and a spectrum refinement method based on the coherent spectrum to improve the measurement accuracy and resolution degraded by the fence effect, spectrum leakage, and noise interference.
[0007] The technical solution for achieving the object of the present invention is: a method for estimating the ranging and velocity measurement spectrum of frequency modulated continuous wave lidar, and the specific steps are as follows:
[0008] Step 1: Perform variational mode decomposition and reconstruction on the original beat frequency signal to obtain a denoised reconstructed signal;
[0009] Step 2: Perform windowed Fourier transform on the reconstructed signal to obtain a coarse spectrum, and perform chirp Z transform centered on the peak of the coarse spectrum to obtain the first refined spectrum;
[0010] Step 3: Perform spectrum refinement based on the coherent spectrum centered on the peak of the first refined spectrum to obtain the final coherent spectrum;
[0011] Step 4: Accurately calculate the range-velocity information of the target according to the coherent spectrum.
[0012] Preferably, perform variational mode decomposition and reconstruction on the original beat frequency signal to obtain the reconstructed signal. The specific process is as follows:
[0013] Step 1.1: Decompose the beat frequency signal f(t) into k modal functions ν k (t), and each modal function ν k (t) is concentrated in the frequency domain at the center frequency ω k . To minimize the modal bandwidth, construct the objective function:
[0014]
[0015] where K represents the optimal decomposition layer number, ν k (t) represents the k-th modal signal, ω k is the center frequency of the k-th mode, δ(t) is the unit impulse function, and ||·||2 represents the L2 norm;
[0016] At the same time, the objective function satisfies the constraint conditions:
[0017]
[0018] Step 1.2: Introduce the Lagrange multiplier λ(t) and the second-order penalty factor α to transform the constrained variational problem into an unconstrained variational problem, specifically:
[0019]
[0020] Step 1.3: Continuously update the modal signal, center frequency, and Lagrange multiplier in the frequency domain using the alternating direction multiplier method to seek the optimal solution of the objective function. The specific process is as follows:
[0021] Convert the modal signal ν k (t) to the frequency domain signal and update:
[0022]
[0023] Calculate the new center frequency in the frequency domain:
[0024]
[0025] Update the Lagrange multiplier in the frequency domain:
[0026]
[0027] where τ is the step size, which is used to control the update speed;
[0028] After each update of the modal signal, central frequency, and Lagrange multiplier, calculate the sample entropy of each mode:
[0029]
[0030] When the average sample entropy of all modes is less than the sample entropy stability threshold, k reaches the optimal decomposition level; otherwise, continue to alternately update the modal signal, central frequency, and Lagrange multiplier repeatedly until convergence or the optimal decomposition level is reached to obtain each mode;
[0031] Superimpose the k modal components in the time domain to obtain the reconstructed signal R(t).
[0032] Preferably, perform a windowed Fourier transform on the reconstructed signal to obtain a coarse spectrum, and perform a chirp Z-transform centered on the peak of the coarse spectrum to obtain a first refined spectrum. The specific process is as follows:
[0033] Step 2.1: Perform a windowed Fourier transform on the reconstructed signal R(t):
[0034]
[0035] where ω is the angular frequency, the general variable u is used to distinguish from the time variable t, R(u) represents the value of the reconstructed signal at time u, g(u - t) is a moving window function centered on t, t is the time offset parameter, indicating sliding the window function along the time axis. By sliding the time window t, calculate the windowed Fourier transform spectrum of the entire signal
[0036] Step 2.2: Discretize the reconstructed signal after the windowed Fourier transform to obtain a discretized reconstructed signal R(n) of length N;
[0037] Step 2.3: Centered on the maximum value R0_WFT of , perform a Z-transform on the discretized reconstructed signal R(n) processed by the windowed Fourier transform, expressed as:
[0038]
[0039] Take any sampling point z among the k spectral sampling points on the Z-plane k ,
[0040] z k = AW -k
[0041] Among them, A represents a complex constant for scaling, and W is a rotation factor on the unit circle;
[0042] The complex numbers A and W are represented in polar form, that is
[0043]
[0044] where A0 represents the modulus of the complex number A, θ0 is the phase angle of the complex number A, W0 represents the modulus of the complex number W, is the phase angle of the complex number W;
[0045] Perform a chirp Z-transform on the reconstructed signal R(n) in discrete form after windowed Fourier transform processing to obtain the first refined spectrum, which is expressed as:
[0046]
[0047] where N represents the length of R(n), τ d represents the time delay, f0 represents the starting frequency, and k represents the index of the spectrum sampling point.
[0048] Preferably, perform spectrum refinement based on the coherent spectrum with the peak of the first refined spectrum as the center to obtain the final coherent spectrum, specifically:
[0049]
[0050] Preferably, accurately calculate the range-velocity information of the target according to the coherent spectrum, and the specific formula is:
[0051]
[0052] where T is the modulation period, c is the speed of light, B is the modulation bandwidth, f bu and f bd are the beat frequencies of the upper and lower frequency bands on the coherent spectrum respectively, and λ is the modulation wavelength.
[0053] Compared with the prior art, the significant advantages of the present invention are as follows: (1) In the data preprocessing of the present invention, variational mode decomposition is performed on the beat signal, which has the characteristics of self - adaptation and non - recursion. This algorithm realizes the decomposition of the original signal by constructing and solving a variational problem, and can effectively avoid problems such as mode aliasing, over - envelope, under - envelope, and boundary effects. It has advantages such as good complex data decomposition accuracy and good anti - noise interference. The decomposition layer number k is automatically evaluated by sample entropy, the curve stability and change trend are analyzed, and the optimal layer number is judged, so as to achieve a better decomposition effect and effectively suppress mode aliasing. By decomposing noise and signal through variational mode decomposition, the signal - to - noise ratio can be enhanced to a certain extent, effectively increasing the measurement range of the frequency - modulated continuous - wave lidar. (2) According to the characteristics of the difference frequency signal, the present invention makes full use of the frequency and phase information of the beat signal, and introduces a modulation term factor containing this phase information to eliminate the phase that changes with frequency when demodulating the target distance and speed by the frequency difference method. The introduction of the modulation factor changes the shape of the spectrum, but does not affect the positioning of the original spectral peak. After modulation, the distribution of the frequency components of the spectrum is more compact, generating a more concentrated spectral peak, which helps to improve the measurement resolution and improve the ranging and velocity - measuring accuracy.
[0054] The following further describes the present invention in detail with reference to the accompanying drawings. Description of the Drawings
[0055] Figure 1 Schematic diagram of ranging and velocity - measuring of the frequency - modulated continuous - wave lidar constructed for the present invention.
[0056] Figure 2 Frame diagram of the spectrum estimation method proposed by the present invention.
[0057] Figure 3 Schematic diagram of the discrete power spectrum of the present invention.
[0058] Figure 4 Schematic diagram of the coherence spectrum of the present invention.
[0059] Figure 5 Schematic diagram of the frequency - modulated Z - transform coherence theory model proposed by the present invention.
[0060] Figure 6 Frequency - distance comparison diagram of the spectrum estimation method proposed by the present invention and the WFT.
[0061] Figure 7 Ranging effect diagrams of two targets located at 1.02 m and 1.03 m using different algorithms.
[0062] Figure 8 Ranging effect diagrams of two targets located at 1.025 m and 1.028 m using different algorithms.
[0063] Figure 9Generate ranging effect diagrams for two targets located at 17.00m and 17.01m using different algorithms.
[0064] Figure 10 Generate ranging effect diagrams for two targets located at 17.001m and 17.004m using different algorithms. Detailed implementation manners
[0065] Some technical details of the present invention will be further described in detail below. The present invention will be further described in detail with reference to the accompanying drawings.
[0066] As Figures 1 - 2 shown, the concept of the present invention is: a frequency-modulated continuous-wave lidar ranging and velocity measurement spectrum estimation method, which resolves target distance and velocity information by performing spectrum estimation on the beat signal formed by the interference mixing of the transmitted signal and the received signal. The variational mode decomposition is used to decompose the beat signal, and a penalty factor α is introduced to control the mode overlap degree and the sparsity of the signal decomposition during the decomposition process. The decomposition layer number k is automatically evaluated by sample entropy, and the curve stability and change trend are analyzed to determine the optimal layer number, so as to achieve a better decomposition effect and effectively suppress mode aliasing. The specific steps are as follows:
[0067] Step 1: Perform variational mode decomposition and reconstruction on the original beat signal to obtain a reconstructed signal;
[0068] Step 1.1: Decompose the beat signal f(t) into k modal functions ν k (t), and each modal function ν k (t) is concentrated in the center frequency ω k in the frequency domain. To minimize the modal bandwidth, construct the objective function:
[0069]
[0070] where K represents the optimal decomposition layer number, ν k (t) represents the k-th modal signal, ω k is the center frequency of the k-th mode, ||·||2 represents the L2 norm; δ(t) is the unit impulse function, is the kernel function of the Hilbert transform, and the convolution term is equivalent to performing the Hilbert transform on ν k (t) to obtain the analytic signal; the exponential modulation term is equivalent to translating the modal signal v k (t) to the baseband center for analyzing the bandwidth characteristics.
[0071] At the same time, the objective function satisfies the constraint condition:
[0072]
[0073] Step 1.2: To solve the above-mentioned constrained optimization problem, transform the constrained variational problem into an unconstrained variational problem, and introduce the Lagrange multiplier λ(t) and the second-order penalty factor α:
[0074]
[0075] Step 1.3: Continuously update the modal signal, the center frequency, and the Lagrange multiplier in the frequency domain by using the alternating direction method of multipliers to seek the optimal solution of the objective function.
[0076] Convert the modal signal ν k (t) to the frequency domain and update:
[0077]
[0078] After the update calculate the new center frequency in the frequency domain:
[0079]
[0080] Update the Lagrange multiplier in the frequency domain:
[0081]
[0082] where τ is the step size used to control the update speed;
[0083] Step 1.4: After each update of the modal signal, the center frequency, and the Lagrange multiplier, calculate the sample entropy of each mode:
[0084]
[0085] When the average sample entropy of all modes is less than the sample entropy stability threshold, k reaches the optimal decomposition level.
[0086] Step 1.5: Obtain each mode by repeatedly and alternately updating the modal signal, the center frequency, and the Lagrange multiplier until convergence or the optimal decomposition level is reached;
[0087] Superimpose the k modal components in the time domain to obtain the reconstructed signal R(t).
[0088] Step 2: Perform a windowed Fourier transform on the reconstructed signal to obtain the coarse spectrum as Figure 3 shown, and perform a chirp Z-transform centered on the coarse spectrum peak to obtain the first refined spectrum.
[0089] Step 2.1: Perform a windowed Fourier transform on the reconstructed signal R(t):
[0090]
[0091] Among them, ω is the angular frequency, the general variable u is used to distinguish the time variable t, R(u) represents the value of the reconstructed signal at time u, g(u - t) is a moving window function centered on t, t is the time offset parameter, indicating the sliding of the window function along the time axis. By sliding the time window t, the windowed Fourier transform spectrum of the entire signal is calculated.
[0092] Step 2.2: The reconstructed signal after windowed Fourier transform is discretized. The reconstructed signal R(n) in discrete form with a length of N after windowed Fourier transform processing is expressed as:
[0093]
[0094] where f0 is the starting frequency, B is the modulation bandwidth, τ d is the time delay.
[0095] Taking the maximum value R0_WFT as the center, the Z-transform is performed on the reconstructed signal R(n) in discrete form after windowed Fourier transform processing, which is expressed as:
[0096]
[0097] Taking any sampling point z among the k spectral sampling points on the Z-plane k ,
[0098] z k = AW -k
[0099] where A represents a complex constant for scaling, and W is a rotation factor on the unit circle.
[0100] The complex numbers A and W are represented in polar coordinate form, that is
[0101]
[0102] where A0 represents the modulus of the complex number A, θ0 is the phase angle of the complex number A, W0 represents the modulus of the complex number W, is the phase angle of the complex number W.
[0103] Performing a chirp Z-transform on the reconstructed signal R(n) in discrete form after windowed Fourier transform processing, the first refined spectrum is obtained, which is expressed as:
[0104]
[0105] where N represents the length of R(n), τ d represents the time delay, f0 represents the starting frequency, and k represents the index of the spectral sampling point.
[0106] Step 3: Perform spectrum zooming based on the coherent spectrum with the first zoomed spectrum peak as the center to obtain the final coherent spectrum.
[0107] Analyzing the characteristics of the first zoomed spectrum, it is easy to know that the phase and frequency of R(z k ) both change with τ d , that is, the phase of R(z k ) is related to the frequency, and the phase does not change independently of the frequency. Therefore, in order to make full use of the target information, when demodulating the target range and velocity by the frequency difference method, a modulation term factor containing this phase information can be introduced to eliminate this frequency-varying phase, that is, compensation is performed using the phase coherence property.
[0108] Perform phase coherence compensation on the first zoomed spectrum. The modulation factor is usually selected as:
[0109]
[0110] where
[0111] The specific compensation term is:
[0112]
[0113] The coherent spectrum after multiplying the zoomed spectrum by the modulation term factor is:
[0114]
[0115] Taking the real part gives:
[0116]
[0117] As Figure 4 shown, the coherent spectrum at this time is equivalent to multiplying the original frequency-modulated Z-transform zoomed spectrum by a cosine term containing phase information at each frequency point. The introduction of the cosine term changes the shape of the zoomed spectrum but does not affect the positioning of the zoomed spectrum peak. The distribution of the frequency components of the modulated coherent spectrum is more compact, producing a more concentrated spectrum peak, which helps to improve the measurement resolution and the ranging and velocity measurement accuracy.
[0118] Step 4: Accurately calculate the range and velocity information of the target according to the coherent spectrum.
[0119] As Figure 5 shown, the specific formula for calculating the target range and velocity according to the coherent spectrum is:
[0120]
[0121] where c is the speed of light, T is the modulation period, B is the modulation bandwidth, f bu and fbd They are the beat frequencies of the frequency sweep up and down on the coherent spectrum respectively, and λ is the modulation wavelength.
[0122] Figure 6 It is the frequency-distance comparison diagram between the spectrum estimation method proposed by the present invention and the windowed Fourier transform.
[0123] Figure 7 They are the ranging effect diagrams of two targets located at 1.02 m and 1.03 m using different algorithms. Figure 7 (a) is the windowed Fourier transform. Figure 7 (b) is the chirp Z transform. Figure 7 (c) is the method of the present invention.
[0124] Figure 8 They are the ranging effect diagrams of two targets located at 1.025 m and 1.028 m using different algorithms. Figure 8 (a) is the windowed Fourier transform. Figure 8 (b) is the chirp Z transform. Figure 8 (c) is the method of the present invention.
[0125] Figure 9 They are the ranging effect diagrams of two targets located at 17.00 m and 17.01 m using different algorithms. Figure 9 (a) is the windowed Fourier transform. Figure 9 (b) is the chirp Z transform. Figure 9 (c) is the method of the present invention.
[0126] Figure 10 They are the ranging effect diagrams of two targets located at 17.001 m and 17.004 m using different algorithms. Figure 10 (a) is the windowed Fourier transform. Figure 10 (b) is the chirp Z transform. Figure 10 (c) is the method of the present invention.
[0127] The frequency-modulated continuous-wave lidar spectrum estimation method proposed by the present invention will be a ranging and velocity measurement method with high precision and high resolution.
Claims
1. A frequency-modulated continuous-wave lidar ranging and velocity measurement spectrum estimation method, characterized in that, The specific steps are as follows: Step 1: Perform variational mode decomposition and reconstruction on the original beat frequency signal to obtain a reconstructed signal with noise reduction; Step 2: Perform windowed Fourier transform on the reconstructed signal to obtain a coarse spectrum, and perform chirp Z transform centered on the peak of the coarse spectrum to obtain the first refined spectrum; Step 3: Perform spectrum refinement based on the coherence spectrum centered on the peak of the first refined spectrum to obtain the final coherence spectrum; Step 4: Accurately calculate the range-velocity information of the target according to the coherence spectrum.
2. The frequency-modulated continuous-wave lidar ranging and velocity measurement spectrum estimation method according to claim 1, wherein Perform variational mode decomposition and reconstruction on the original beat frequency signal to obtain a reconstructed signal. The specific process is as follows: Step 1.1: Decompose the beat frequency signal f(t) into k modal functions ν k (t), where each modal function ν k (t) is concentrated in the frequency domain at the center frequency ω k . To minimize the modal bandwidth, construct the objective function: where K represents the optimal decomposition level, and ν k (t) represents the k-th modal signal, ω k is the central frequency of the k-th mode, δ(t) is the unit impulse function, and ·2 represents the L2 norm; Meanwhile, the objective function satisfies the constraint conditions: Step 1.2: Introduce the Lagrange multiplier λ(t) and the second-order penalty factor α to transform the constrained variational problem into an unconstrained variational problem, specifically: Step 1.3: Continuously update the modal signal, central frequency, and Lagrange multiplier in the frequency domain using the alternating direction method of multipliers to seek the optimal solution of the objective function. The specific process is as follows: Convert the modal signal ν k (t) to a frequency-domain signal and update: Calculate the new central frequency in the frequency domain: Update the Lagrange multiplier in the frequency domain: where τ is the step size used to control the update speed; After each update of the modal signal, central frequency, and Lagrange multiplier, calculate the sample entropy of each mode: When the average sample entropy of all modes is less than the sample entropy stability threshold, k reaches the optimal decomposition level. Otherwise, continue to alternately update the modal signal, central frequency, and Lagrange multiplier repeatedly until convergence or reaching the optimal decomposition level to obtain each mode; Superimpose the k modal components in the time domain to obtain the reconstructed signal R(t).
3. The frequency-modulated continuous-wave lidar ranging and velocity measurement spectrum estimation method according to claim 1, wherein Perform windowed Fourier transform on the reconstructed signal to obtain a coarse spectrum, and perform chirp Z transform centered on the peak of the coarse spectrum to obtain the first refined spectrum. The specific process is as follows: Step 2.1: Perform windowed Fourier transform on the reconstructed signal R(t): Among them, ω is the angular frequency, the general variable u is used to distinguish the time variable t, R(u) represents the value of the reconstructed signal at time u, g(u - t) is a moving window function centered on t, t is the time offset parameter, indicating the sliding of the window function along the time axis. By sliding the time window t, the windowed Fourier transform spectrum of the entire signal is calculated. Step 2.2: Discretize the reconstructed signal after windowed Fourier transform to obtain a reconstructed signal R(n) in discrete form with a length of N; Step 2.3: Centering around the maximum value R0_WFT of , perform a Z-transform on the reconstructed signal R(n) in discrete form after windowed Fourier transform processing, which is expressed as: Take any sampling point z among the k spectral sampling points on the Z-plane k , z k = AW -k where A represents the complex constant for scaling, and W is the rotation factor on the unit circle; The complex numbers A and W are represented in polar coordinate form, that is where \(A_0\) represents the modulus of the complex number \(A\), \(\theta_0\) is the phase angle of the complex number \(A\), and \(W_0\) represents the modulus of the complex number \(W\), is the phase angle of the complex number \(W\); Perform chirp Z transform on the discrete reconstructed signal R(n) after windowed Fourier transform processing to obtain the first refined spectrum, denoted as: where N represents the length of R(n), τ d represents the time delay, f0 represents the starting frequency, and k represents the index of the spectral sampling points.
4. The frequency-modulated continuous-wave lidar ranging and velocity measurement spectrum estimation method according to claim 1, wherein Perform spectrum refinement based on the coherence spectrum centered on the peak of the first refined spectrum to obtain the final coherence spectrum, specifically:
5. The frequency-modulated continuous-wave lidar ranging and velocity measurement spectrum estimation method according to claim 1, wherein Accurately calculate the range-velocity information of the target according to the coherence spectrum. The specific formula is: where T is the modulation period, c is the speed of light, B is the modulation bandwidth, f bu and f bd are the beat frequencies of the upper and lower frequency bands on the coherent spectrum, respectively, and λ is the modulation wavelength.