Method for estimating range and speed of multiple targets for vehicle-mounted radar

Abstract

The application discloses a vehicle-mounted radar multi-target distance and speed estimation method, which comprises the following steps: obtaining a baseband signal matrix Y according to the number of targets; taking the baseband signal matrix Y as input, and obtaining the estimation of the distance dimension frequency and the speed dimension frequency of the baseband signal of each target through a Newton-backtracking straight line search method in a relaxation iteration; and determining the distance and speed of each target according to the estimation of the distance dimension frequency and the speed dimension frequency of the baseband signal of each target.

Description

Technical Field

[0001] This invention belongs to the field of vehicle-mounted radar signal processing, specifically relating to a method for estimating the range and velocity of multiple targets in vehicle-mounted radar based on the Newton-backtracking straight-line search method. Background Technology

[0002] Frequency Modulated Continuous Wave (FMCW) radar has a long history. Compared to pulse radar, its ranging range is limited, but it possesses many advantages that pulse radar lacks, such as: low power consumption; high short-range detection resolution; and uninterrupted transmission and reception, unlike pulse radar systems which require complex transceivers. Because FMCW radar transmits continuously, the average power equals the peak power, making it more suitable for solid-state or other peak power-limited transmitters. In particular, solid-state transmitters can promote the development of low-cost radar systems. Furthermore, continuous wave systems do not experience blind spots due to distance or speed limitations. These advantages have made FMCW radar a popular choice for automotive radar and it plays a crucial role in advanced driver assistance systems (ADAS).

[0003] In advanced driver assistance systems (ADAS), three main sensors are used: FMCW radar, lidar, and cameras. Cameras suffer from limitations: their detection performance is dependent on ambient lighting and susceptible to weather conditions. LiDAR, on the other hand, remains hampered by its high cost and difficult deployment. Therefore, FMCW radar addresses some of the shortcomings of cameras and lidar, while offering advantages such as ease of implementation, relatively simple structure, small size, light weight, and low cost. FMCW radar provides range and velocity estimation for multiple targets, requiring high-performance multi-target range and velocity estimation algorithms based on vehicle-mounted radar.

[0004] Researchers have used 2D FFT algorithms to calculate the distance and velocity information of multiple targets. However, in real-world scenarios, the targets detected by this algorithm may be overwhelmed by noise, and its estimation accuracy needs improvement. Some algorithms also approach the estimation of distance and velocity of multiple targets from the perspective of sparse parameter estimation, but these algorithms have high time and space complexity, and their estimation performance needs further improvement. The current challenge we face is that algorithms for estimating the distance and velocity of multiple targets need to have good estimation performance, especially in scenarios with adjacent targets or low signal-to-noise ratio scenarios. Summary of the Invention

[0005] In view of this, the main objective of the present invention is to provide a method for estimating the range and velocity of multiple targets using vehicle-mounted radar.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] This invention provides a method for estimating the range and velocity of multiple targets using vehicle-mounted radar. The method includes:

[0008] Obtain the baseband signal matrix Y based on the target quantity;

[0009] Using the baseband signal matrix Y as input, estimates of the range and velocity frequencies of the baseband signal for each target are obtained through a relaxation iteration based on the Newton-backtracking linear search method.

[0010] Based on the estimated range-dimensional frequency and velocity-dimensional frequency of the baseband signal of each target. Determine the distance and speed of each target.

[0011] In the above scheme, obtaining the baseband signal matrix Y based on the target quantity specifically means: when the target quantity is K, obtaining the baseband signal matrix Y. Y k It is the baseband signal matrix associated with the k-th target, f Bk f is the range-dimensional frequency of the baseband signal associated with the k-th target. Dk It is the velocity-dimensional frequency of the baseband signal associated with the k-th target, a k It is the complex amplitude value of the baseband signal associated with the k-th target.

[0012] In the above scheme, if the vehicle-mounted radar is a sawtooth frequency-modulated continuous wave signal, the baseband signal has the following mathematical model: Where n = 0, ..., N-1, n represents the nth sample within a single pulse, and N represents the total number of samples within a single pulse; q = 0, ..., Q-1, q represents the qth pulse within a frame, and Q represents the total number of pulses within a frame; where e(n, q () represents additive white Gaussian noise; where T is the period of the pulse sequence, B is the bandwidth, and f is the frequency. c f is the carrier frequency. s Where c is the sampling frequency within a single pulse, Rk is the speed of light, and v is the distance to the k-th target. k To determine the velocity of the k-th target, establish the baseband signal matrix. y(n, q) is the element in the nth row and qth column of Y.

[0013] In the above scheme, the baseband signal matrix Y is used as input, and the range and velocity frequency estimates of the baseband signal of each target are obtained through the relaxation iteration based on the Newton-backtracking linear search method. This can be achieved through the following steps:

[0014] 2.1: Determine the old value of the loss function;

[0015] 2.2: Reconstructing the baseband signal matrix Y k ;

[0016] 2.3: Using the Newton-backtracking linear search method and the baseband signal matrix Y k Obtain the estimate

[0017] 2.4: Obtaining the estimator based on the maximum likelihood criterion

[0018] 2.5: Determine the new value of the loss function;

[0019] 2.6: Determine whether the loss function has converged. If it has converged, proceed to step 2.7; otherwise, repeat step 2.1.

[0020] Step 2.7: Let like Then the estimation of the distance dimension frequency and the velocity dimension frequency is complete; otherwise, proceed to step 2.2.

[0021] In the above scheme, the reconstructed baseband signal matrix Y k for:

[0022] In the above scheme, determining the old value of the loss function specifically involves:

[0023]

[0024] In the above scheme, the method of searching a straight line using Newton-backtracking and the baseband signal matrix Y... k Obtain the estimate Specifically:

[0025] In the above scheme, the objective function is:

[0026] In the above scheme, the Jacobian vector g and Hessian matrix H of the objective function are specifically: Let The objective function is then f(x) = a H a, Jacobian vector g is: That,

[0027] The Hessian matrix H is represented as follows: in,

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] In the above scheme, the step of obtaining the estimate based on the maximum likelihood criterion... Specifically, based on the maximum likelihood estimation criterion... Where H is the conjugate transpose symbol, * is the conjugate symbol, and vector w1(f Bk ) and w2(f Dk The expression form of ) is: The sampling period is within a single pulse, and the T in the upper right corner of the parentheses is the transpose symbol.

[0034] Compared with existing technologies, this invention decomposes the distance and velocity estimation problem of multiple targets into the distance and velocity estimation problem of a single target, introduces the maximum likelihood estimation criterion, transforms the target distance and velocity estimation problem into an unconstrained optimization problem, and introduces the well-known Newton iteration algorithm to perform refined parameter estimation, thereby improving the accuracy of the estimation. Attached Figure Description

[0035] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and, together with their descriptions, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0036] Figure 1 This is a flowchart illustrating a method for estimating the range and velocity of multiple targets using vehicle-mounted radar, as provided in an embodiment of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0038] This invention provides a method for estimating the range and velocity of multiple targets using vehicle-mounted radar, such as... Figure 1 As shown, the method includes:

[0039] Step 1: When the actual number of targets is K, obtain the baseband signal matrix Y. Y k It is the baseband signal matrix associated with the k-th target, f Bkf is the range-dimensional frequency of the baseband signal associated with the k-th target. Dk α is the velocity-dimensional frequency of the baseband signal associated with the k-th target. k It is the complex amplitude value of the baseband signal associated with the k-th target;

[0040] Specifically, in step 1.1, let the number of targets K = 3, and the mathematical model of the baseband signal y(n, q) is shown in equation (1), where n = 0, ... . N-1, q=0, ..., Q-1, set the total number of samples within a single pulse N=48, the number of pulses within a frame Q=48, and the carrier frequency f c =76GHz, pulse period T=50us, waveform bandwidth B=150MHz, sampling frequency f within a single pulse s =1.28MHz, set three targets: R1=20.5m, v1=-10.5m / s; R2=39.5m, v2=10.5m / s; R3=40.5m, v3=11.5m / s, where target 2 and target 3 are adjacent and have similar speeds; set the signal-to-noise ratio (SNR) to -20dB to simulate a low SNR environment.

[0041] Step 1.2: Establish the baseband signal matrix Then the element in the nth row and qth column of Y is y(n, q).

[0042] Step 2: Initialize all parameter estimates using the baseband signal matrix Y as input. If the value is 0, the range-dimensional frequency and velocity-dimensional frequency of the baseband signal are estimated using the Newton-backtracking linear search method in the following relaxation iteration:

[0043] Step 2.1: Initialization

[0044] Step 2.2: Initialization Let l = 1; l is the loop variable, indicating which inner loop it is in, used to distinguish between the old and new values ​​of the loss function, and incremented by 1 before the end of each loop; k represents the k-th objective, that is, the parameters of the k-th objective are estimated by the current inner loop. The target number assumed by the outer loop is incremented by 1 before the end of each outer loop, which is different from the actual target number K.

[0045] Step 2.3: Let Where mod represents the modulo operation;

[0046] Step 2.4: Calculate the old value Φ of the loss function l The calculation formula is as follows:

[0047]

[0048] Step 2.5: According to Reconstructing the baseband signal matrix Y k ;

[0049] Step 2.6: Define the parameter vector to be estimated as: x = [f Bk f Dk ] T objective function The estimator was obtained by using the Newton-backtracking linear search method.

[0050] Step 2.6.1: For the baseband signal matrix Y k Perform a 2-D FFT to obtain f Bk and f Dk The initial value is obtained as x1 = [f Bk f Dk ] T Initialize the parameters η = 0.3 and β = 0.7, and let i = 1; i is the loop variable, indicating the current loop number; 77 and β are hyperparameters, which are set manually based on experience and used in step 2.6.3. Specifically, 77 is used as the weight coefficient and β is used as the callback factor.

[0051] Step 2.6.2: According to Calculate the Jacobian vector g of the objective function, according to Calculate the Hessian matrix H;

[0052] in,

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Step 2.6.3: Determine the step size using the backtracking linear search method: Initialize the step size μ = 1. If the condition is not met, i.e., f(x) i -μH -1 g)<f(x i )-ημg T H -1 If g is the step size, then adjust the step size μ = βμ and repeat the step size search process until a suitable step size μ is found, such that f(x) = βμ.i -μH -1 g)≥f(x i )-ημg T H -1 g;

[0060] Step 2.6.4: Update the parameter vector x using the step size μ determined by the backtracking line search process. i+1 =x i -μH -1 g;

[0061] Step 2.6.5: Let the convergence threshold ∈ = 10 -8 To determine whether the algorithm has converged, i.e., if |μH -1 Stop iteration when g|<∈, and output the optimal solution. Skip to step 2.7; otherwise, let i = i + 1, return to step 2.6.2, and proceed to the next iteration.

[0062] Step 2.7: Based on the maximum likelihood criterion, refer to... The estimated quantity was calculated.

[0063] Step 2.8: Reference Calculate the new value Φ of the loss function l+1 ;

[0064] Step 2.9: Let the convergence threshold ξ = 10 -7 Determine whether the loss function converges:

[0065]

[0066] The symbol tr() represents the trace of the matrix. If convergence is achieved, proceed to step 2.10; if convergence is not achieved, let l = l + 1 and proceed to step 2.3.

[0067] Step 2.10: Let like If so, proceed to step three; otherwise, skip to step 2.2.

[0068] Step 3: Obtain frequency pair information for each target [f] B f D After that, reference style Based on the relationship between frequency and distance / velocity in two dimensions, the distance and velocity of each target are calculated, thus completing the multi-target distance and velocity estimation task.

[0069] In the simulation experiments, this invention was compared with the 2D FFT algorithm and the traditional RELAX algorithm. For the 2D FFT algorithm, the zero-padding factor zp was set to 8; since the traditional RELAX algorithm is based on the zero-padding 2D FFT, the zero-padding factor zp was also set to 8. The calculation results were rounded to two decimal places, and the estimation results of the different algorithms are shown below:

[0070] Table 1 Estimation Results

[0071]

[0072] The performance metric for estimation is the mean deviation of the estimation, defined as follows:

[0073]

[0074]

[0075] Where μ ΔR μ is the mean bias of the multi-target distance estimation. Δv This represents the mean deviation of the multi-target velocity estimation. R is the estimated distance to the k-th target. k This represents the true distance to the k-th target. v is the estimated velocity of the k-th target. k Let be the true velocity of the k-th target. The estimation performance of the comparison algorithm and the present invention is shown in the table below:

[0076] Table 2 Estimated Performance Comparison

[0077] 2-D FFT algorithm, zp=8 0.377 0.177 Traditional RELAX algorithm, zp=8 0.133 0.053 This invention 0.110 0.050

[0078] The above results demonstrate the mean deviations of the comparative algorithm and the present invention for multi-target distance and velocity estimation; in multi-target environments with adjacent targets, the estimation performance of the present invention is optimal. Compared with the traditional RELAX algorithm, the present invention reduces the mean deviation of multi-target distance estimation by 17.3% and the mean deviation of multi-target velocity estimation by 5.7%.

[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention.

Claims

1. A method for estimating the range and velocity of multiple targets using vehicle-mounted radar, characterized in that, The method includes: Obtain the baseband signal matrix based on the target quantity. ; With the baseband signal matrix As input, estimates of the range and velocity frequencies of the baseband signal for each target are obtained through a relaxation iteration based on the Newton-backtracking linear search method. ; Based on the estimated range-dimensional frequency and velocity-dimensional frequency of the baseband signal of each target. Determine the distance and speed of each target; With the baseband signal matrix As input, estimates of the range and velocity frequencies of the baseband signal for each target are obtained through a relaxation iteration based on the Newton-backtracking linear search method. This can be achieved through the following steps: Step 2.1: Initialization ; Step 2.2: Initialization ,make ; It is a loop variable that indicates which inner loop it is in, used to distinguish between the old and new values ​​of the loss function, and is incremented by 1 before the end of each loop. k Indicates the first k The target is the parameter estimation of the k-th target in the current inner loop; The target number assumed by the outer loop is incremented by 1 before the end of each outer loop iteration, distinguishing it from the actual target number. K ; Step 2.3: Let , where mod represents the modulo operation; Step 2.4: Calculate the old value of the loss function The calculation formula is as follows: Step 2.5: According to Reconstructing the baseband signal matrix ; Step 2.6: Define the parameter vector to be estimated as follows: objective function The estimator was obtained by using the Newton-backtracking linear search method. ,make Then the objective function is ; Step 2.6.1: Baseband signal matrix Perform a 2-D FFT to obtain and The initial value is obtained. Initialization parameters and ,make ; i This is the loop variable, indicating which iteration is currently in. η and β These are all hyperparameters, used in step 2.6.

3. Specifically, η As weighting coefficients, β As a callback factor; Step 2.6.2: According to Calculate the Jacobian vector of the objective function. ,according to Calculate the Hessian matrix ; in, , , , , , , , , , , ; Is and the The complex amplitude of the baseband signal related to a target. Is and the The velocity dimension of the baseband signal related to the target is frequency. Is and the The range-dimensional frequency of the baseband signal associated with each target; Step 2.6.3: Determine the step size using the backtracking linear search method: Initialize the step size If the conditions are not met, that is Then adjust the step size. Repeat the step size search process until a step size is found. , making ; Step 2.6.4: Use the step size determined by the backtracking line search process Update the parameter vector: ; Step 2.6.5: Set the convergence threshold To determine whether the algorithm has converged, i.e., if... Stop iterating and output the optimal solution. If yes, skip to step 2.7; otherwise, let... Return to step 2.6.2 and proceed to the next iteration; Step 2.7: Based on the maximum likelihood criterion, refer to... The estimated quantity was calculated. ;in H The sign for conjugate transpose. The conjugate symbol is used for vectors. and The expression form is: , , The sampling period within a single pulse, indicated by the upper right corner of the parentheses. It is the transpose symbol; Step 2.8: Reference Calculate the new value of the loss function ; Step 2.9: Set the convergence threshold Determine whether the loss function converges: The symbol tr() represents the trace of the matrix. If convergence is achieved, step 2.10 is executed; otherwise, let... And proceed to step 2.3; Step 2.10: Let ,like If so, proceed to step 3; otherwise, skip to step 2.

2.

2. The method for estimating the range and velocity of multiple targets using vehicle-mounted radar according to claim 1, characterized in that, The baseband signal matrix is ​​obtained based on the target quantity. Specifically: when the target quantity is At that time, the baseband signal matrix is ​​obtained. , ; Is and the The baseband signal matrix associated with each target.

3. The method for estimating the range and velocity of multiple targets using vehicle-mounted radar according to claim 2, characterized in that, The vehicle-mounted radar uses a sawtooth frequency-modulated continuous wave signal, and the baseband signal has the following mathematical model: ;in , Indicates the first pulse within a single pulse Second sampling, Indicates the total number of samples within a single pulse; , Indicates the first in the frame One pulse, Indicates the total number of pulses within a frame; in This represents additive white Gaussian noise; where The period of the pulse sequence. For bandwidth, For carrier frequency, The sampling frequency within a single pulse. At the speed of light, For the first Distance to each target For the first The speed of each target is used to establish the baseband signal matrix. , That is The Line number The elements of the column.

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