A method for suppressing interference of vehicle-mounted millimeter wave radar based on sparse and low-rank model

Abstract

The application discloses a kind of vehicle-mounted millimeter wave radar interference suppression methods based on sparse and low rank model, comprising: the low rank and sparse characteristics of useful signal and interference signal in radar receiver demodulation filtered intermediate frequency signal are utilized, and low rank sparse optimization model is constructed;After maximum minimum non-convex sparse penalty and low rank factor decomposition are carried out to the low rank sparse optimization model, interference signal and useful signal are separated by the aid of alternating direction multiplier method and iterative optimization is realized.Thereby, explicit detection of interference component is avoided, and compared with prior art, the power loss of target signal will be greatly reduced.

Description

Technical Field

[0001] This invention relates to a method for suppressing interference in vehicle-mounted millimeter-wave radar based on a sparse and low-rank model, belonging to the field of anti-interference for vehicle-mounted radar. Background Technology

[0002] Autonomous driving technology has become a mainstream development trend in automobiles, and millimeter-wave radar, with its high measurement accuracy, small size, low power consumption, and all-weather operation, has become one of the key sensors in autonomous driving assistance systems. As more and more vehicles on the road are equipped with multiple radar sensors, the probability of mutual interference between radars has also greatly increased.

[0003] Interference signals can lead to false alarms or missed alarms, both of which severely reduce the safety and stability of vehicle operation. Existing technology one uses a constant false alarm rate detector (CFAR) in the time-frequency domain to detect interference, then sets the interference component to zero. Existing technology two proposes a low-pass filter interference detection technique that, upon detecting interference, marks the interference component as missing data, and then recovers the useful signal based on a sparse model.

[0004] However, accurate interference detection is the key to achieving good recovery results in the interference detection and suppression method at the receiver. If a certain level of accuracy is not achieved, too much useful signal will be discarded, resulting in power loss in the recovered target signal. Summary of the Invention

[0005] Objective: To overcome the shortcomings of existing technologies, and addressing the problem of inaccurate detection or precise removal of interference during interference suppression, which leads to power loss in the target signal, this invention provides an interference suppression method for vehicle-mounted millimeter-wave radar based on a sparse and low-rank model. This method separates useful signals from interference signals, thereby eliminating the need for detection of interference components.

[0006] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0007] In a first aspect, the present invention provides a method for suppressing interference from vehicle-mounted millimeter-wave radar based on a sparse and low-rank model, comprising:

[0008] By utilizing the low-rank and sparse characteristics of the useful and interference signals in the intermediate frequency signal after demodulation and filtering by the radar receiver, a low-rank sparse optimization model is constructed.

[0009] After applying the minimax nonconvex sparsity penalty and low-rank factor decomposition to the low-rank sparse optimization model, the useful signal and interference signal are separated by iterative optimization using the alternating direction multiplier method.

[0010] In some embodiments, a low-rank sparse optimization model is constructed by utilizing the low-rank and sparse characteristics of the useful and interference signals in the intermediate frequency signal after demodulation and filtering by the radar receiver, including:

[0011] Construct a model of the intermediate frequency signal after demodulation and filtering by the radar receiver;

[0012] Based on the demodulated and filtered intermediate frequency signal model of the radar receiver, a low-rank sparse optimization model is constructed.

[0013] Furthermore, in some embodiments, constructing a model of the intermediate frequency signal after demodulation and filtering by the radar receiver includes:

[0014] The radar transmitted signal p(t) is represented as:

[0015]

[0016] In the formula, j represents an imaginary number, and f0, k, and T represent the starting frequency, modulation slope, and duration of the signal, respectively.

[0017] The target's echo signal is a delayed version of the radar's transmitted signal. The beat frequency signal x(t) of multiple targets acquired by the radar is represented as:

[0018]

[0019] In the formula, M represents the number of targets, a i τ i and f b,i These represent the scattering coefficient of the i-th target, the time delay of the echo signal, and the beat frequency, respectively.

[0020] If echo signals from several targets cross-interference during radar reception, the received signals, after demodulation and low-pass filtering, will have the following intermediate frequency (IF) signal model from the radar receiver:

[0021]

[0022] In the formula, s(t) represents the intermediate frequency signal after demodulation and filtering by the radar receiver, i(t) represents the remaining component of the interference signal after demodulation and filtering by the radar receiver, and n(t) is additive white Gaussian noise.

[0023] s int (t) represents the interference signal. The complex conjugate of the radar transmitted signal p(t) and the interference signal s int (t) are multiplied for demodulation, h lpf (t) represents a low-pass filter, which performs a convolution operation on the demodulated signal to achieve filtering.

[0024] Furthermore, in some embodiments, a low-rank sparse optimization model is constructed based on the demodulated and filtered intermediate frequency signal model of the radar receiver, including:

[0025] The intermediate frequency signal model after demodulation and filtering by the radar receiver is converted into a discrete signal by time-interval sampling. The measured values ​​of all time samples are represented in vector form as follows:

[0026] s = x + i + n (4)

[0027] In the formula, the four vectors are represented as s = [s0, s1, ..., s2]. N-1 ] T The vector representing the target is x = [x0, x1, ..., xn]. N-1 ] T The vector representing interference is i = [i0, i1, ..., i...]. N-1 ] T The vector representing noise is n = [n0, n1, ..., n]. N-1 ] T N is the number of discrete signal sampling points;

[0028] vector Transform into Hankel matrix Where N = m + n - 1, m and n are the number of rows and columns of the matrix, respectively; then the Hankel matrix S is expressed as:

[0029]

[0030] In the formula, This represents the Hankel matrix transformed from the vector within the parentheses; for the matrix constructed from the target beat frequency signal... The number of targets M << m, M << n, and the matrix The rank of the matrix is ​​the number of the target complex exponents. It is a low-rank matrix;

[0031] In the case of cross-interference, the interference signal i(t) after being demodulated and low-pass filtered by the radar receiver is usually short in duration, and manifests as one or more spikes on the relevant chrip signal, exhibiting sparsity in the time domain; therefore, the vector i representing the interference component is a sparse vector.

[0032] The low-rank sparse optimization model used to separate useful signals from interference signals in measurement data is expressed as follows:

[0033]

[0034] In the formula, It is the rank operation, representing a matrix. The number of non-zero singular values, σi Representative matrix The singular values; η is the l0 norm, representing the number of non-zero elements in vector i. η≥0 is an adjustment parameter that balances the loss function and the regularization term. ε represents the error coefficient.

[0035] Furthermore, in some embodiments, the vehicle-mounted millimeter-wave radar interference suppression method based on sparse and low-rank models further includes:

[0036] Since the rank and l0 norm sparse minimization problem is difficult to solve directly through optimization, the kernel norm and l1 norm are used to replace the rank operation and l0 norm respectively for relaxation. Thus, the low-rank sparse optimization model of equation (6) is re-expressed as:

[0037]

[0038] In the formula, It is the nuclear norm, representing the matrix. The sum of singular values, It is the l1 norm, representing the sum of the absolute values ​​of the non-zero elements in vector i.

[0039] In some embodiments, the low-rank sparse optimization model is subjected to a minimax nonconvex sparsity penalty and a low-rank factor decomposition, including:

[0040] The MCP penalty function is defined as follows: in:

[0041]

[0042] Where λ and γ represent the parameters of the MCP penalty function, and setting different values ​​for λ and γ will change the shape of the MCP penalty function;

[0043] The MCP penalty function is used as the l1 norm;

[0044] The low-rank sparse optimization model, after applying low-rank factorization with nuclear norm relaxation and the MCP penalty function, is expressed as follows:

[0045]

[0046] In the formula, U and V represent intermediate parameters. The F-norm is defined as follows: P represents the square root of the sum of squares of each term in the matrix. λ,γ (i) represents the MCP penalty function for vector i, (*) H This represents the conjugate transpose.

[0047] In some embodiments, iterative optimization using the alternating direction multiplier method is employed to separate useful signals from interference signals, including:

[0048] The augmented Lagrangian function corresponding to the optimization problem in equation (9) is expressed as:

[0049]

[0050] In the formula, β and μ are regularization parameters, and w and Z are Lagrange multiplier vectors and matrices, which simplify to:

[0051]

[0052] Based on the augmented Lagrangian function, the optimization problem of equation (11) is transformed into solving the following subproblems using the ADMM iterative method:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Where k represents the number of iterations;

[0060] To obtain the update of x, we take the first derivative of equation (12) and get:

[0061]

[0062] In the formula Hankel matrix The Moore-Penrose generalized inverse matrix is ​​defined as follows:

[0063] The closed-form solution to the optimization subproblem (13) is expressed as:

[0064]

[0065] In the formula, i = 1, 2, ..., N, introduced This is a soft thresholding operator, where sign(t) is the sign function, and the intermediate parameters t and α represent the values ​​in the equation. and

[0066] The closed-form solutions for U and V are given by making the first derivatives of equations (14) and (15) zero, i.e.:

[0067]

[0068]

[0069] The updates to U and V are obtained from equations (22) and (23):

[0070]

[0071]

[0072] In the formula, E represents the identity matrix; (*) -1 Represents reciprocal operations;

[0073] Equations (18), (19), (22), (23), (16), and (17) are calculated sequentially and the process is repeated, continuously updating x, i, U, V, w, and Z. During the iteration, the regularization parameters β and μ need to be gradually increased to increase the accuracy of the recovered signal. After several iterations, x, representing the target vector, and i, representing the interference vector, are recovered from the prior data, thereby achieving the separation of the useful target signal and the interference signal.

[0074] In a second aspect, the present invention provides an on-board millimeter-wave radar interference suppression device based on a sparse and low-rank model, including a processor and a storage medium.

[0075] The storage medium is used to store instructions;

[0076] The processor is configured to operate according to the instructions to execute the method according to the first aspect.

[0077] Thirdly, the present invention provides an apparatus comprising,

[0078] Memory;

[0079] processor;

[0080] as well as

[0081] Computer programs;

[0082] The computer program is stored in the memory and configured to be executed by the processor to implement the method described in the first aspect above.

[0083] Fourthly, the present invention provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0084] Beneficial Effects: The vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model provided by this invention has the following advantages: Based on the low-rank and sparse characteristics of the useful and interfering signals in the echo signal, this invention designs an optimization problem based on a low-rank and sparse model to separate the useful and interfering signals, thereby eliminating the need for detecting the interfering components. This invention can significantly reduce the noise floor in the signal frequency domain, increase recovery accuracy, and effectively suppress mutual interference between radars.

[0085] This invention addresses the problem of interference suppression in complex scenarios with multiple targets and multiple sources of interference without requiring prior interference detection. It utilizes the low-rank and sparse characteristics of both the useful and interfering signals in the intermediate frequency (IF) signal to construct a low-rank sparse optimization model. Simultaneously, it uses the Alternating Directional Multiplier (ADMM) method for iterative optimization while employing the Minimal Maximal Nonconvex Sparse Penalty (MCP) to separate the useful and interfering signals.

[0086] The method proposed in this invention transforms the interference suppression problem into an optimization problem based on a low-rank and sparse model, thereby avoiding explicit detection of interference components. Compared with existing technologies, the power loss of the target signal will be significantly reduced. Introducing the MCP non-convex sparsity penalty into the optimization model will also effectively increase the recovery accuracy. Attached Figure Description

[0087] Figure 1 This is a schematic diagram illustrating crosstalk interference affecting an FMCW signal according to an embodiment of the present invention.

[0088] Figure 2 This is a schematic diagram of the beat frequency signals of the target signal and the interference signal according to an embodiment of the present invention;

[0089] Figure 3 This is a schematic diagram of an interference scenario according to an embodiment of the present invention;

[0090] Figure 4 This is a time-domain diagram of an intermediate frequency signal contaminated by interference according to an embodiment of the present invention;

[0091] Figure 5 This is a frequency domain comparison diagram of the interfered signal and the reference signal according to an embodiment of the present invention;

[0092] Figure 6 This is a comparison diagram of the intermediate frequency signal after interference suppression and the reference intermediate frequency signal according to an embodiment of the present invention;

[0093] Figure 7 This is a frequency domain comparison diagram of the interfered signal, the signal after interference suppression, and the reference signal according to an embodiment of the present invention.

[0094] Figure 8The SINR values ​​after interference suppression using various methods at different signal-to-noise ratios according to an embodiment of the present invention;

[0095] Figure 9 The |ρ| value is the result of interference suppression using various methods at different signal-to-noise ratios according to an embodiment of the present invention. Detailed Implementation

[0096] The present invention will be further described below with reference to the accompanying drawings and embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be used to limit the scope of protection of the present invention.

[0097] In the description of this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0098] In the description of this invention, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0099] Example 1

[0100] Firstly, this embodiment provides a vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model, including:

[0101] By utilizing the low-rank and sparse characteristics of the useful and interference signals in the intermediate frequency signal after demodulation and filtering by the radar receiver, a low-rank sparse optimization model is constructed.

[0102] After applying the minimax nonconvex sparsity penalty and low-rank factor decomposition to the low-rank sparse optimization model, the useful signal and interference signal are separated by iterative optimization using the alternating direction multiplier method.

[0103] In some embodiments, a low-rank sparse optimization model is constructed by utilizing the low-rank and sparse characteristics of the useful and interference signals in the intermediate frequency signal after demodulation and filtering by the radar receiver, including:

[0104] Construct a model of the intermediate frequency signal after demodulation and filtering by the radar receiver;

[0105] Based on the demodulated and filtered intermediate frequency signal model of the radar receiver, a low-rank sparse optimization model is constructed.

[0106] In some embodiments, a vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model includes:

[0107] Step 1: Establish and analyze the signal model

[0108] Figure 1 These are curves showing the random time-varying frequency variations of each signal. Figure 2 It is a curve showing the change in beat frequency over time after each signal is mixed with the transmitted signal. (B) LPF f is the bandwidth of the low-pass filter. LPF t is the cutoff frequency of the low-pass filter. int This represents the duration of the interference. As shown in the diagram, only interference signals within the receiver's bandwidth will affect the echo signal. A schematic diagram of a road interference scenario is shown below. Figure 3 As shown.

[0109] The linear frequency modulated signal p(t) transmitted by the frequency modulated continuous wave (FMCW) radar can be expressed as:

[0110]

[0111] In the formula, f0, k, and T represent the starting frequency, modulation slope, and duration of the signal, respectively. The reflected signal from the target is a delayed version of the radar's transmitted signal; therefore, the beat frequency signal x(t) of multiple targets acquired by the radar can be expressed as:

[0112]

[0113] In the formula, M represents the number of targets, a i τ i and f b,i Let represent the scattering coefficient of the i-th target, the time delay of the echo signal, and the beat frequency, respectively. If the echo signals from several targets cross-interfere during radar reception, the received signal, after demodulation and low-pass filtering, can be expressed as:

[0114]

[0115] In the formula, s int (t) represents the interference signal. The complex conjugate of the radar transmitted signal p(t) and the interference signal s int (t) are multiplied for demodulation, h lpf(t) represents a low-pass filter, which performs a convolution operation on the demodulated signal to achieve filtering. i(t) represents the remaining component of the interference signal after demodulation and filtering by the radar receiver, and n(t) is additive white Gaussian noise, representing clutter signals such as system noise, environmental noise, and measurement errors.

[0116] Step 2: Construct a low-rank sparse optimization model

[0117] By sampling the signal model in equation (3) at intervals to convert it into a discrete signal, and representing the measured values ​​of all time samples in vector form, equation (3) can be rewritten as:

[0118] s = x + i + n (4)

[0119] In the formula, the four vectors are represented as s = [s0, s1, ..., s2]. N-1 ] T x = [x0, x1, ..., x N-1 ] T i = [i0, i1, ..., i N-1 ] T n = [n0, n1, ..., n N-1 ] T N is the number of discrete signal sampling points. To facilitate the construction of a low-rank sparse optimization model, the one-dimensional vector generated by the interference-contaminated signal is converted into the form of a Hankel matrix. For the vector in equation (4) It can be converted into a Hankel matrix. Where N = m + n - 1. Then the Hankel matrix S can be expressed as:

[0120]

[0121] In the formula, This represents the Hankel matrix transformed from the vector within the parentheses. For the matrix constructed from the target beat frequency signal... The number of targets M << m, M << n, and the matrix The rank of the matrix is ​​the number of the objective complex exponents. It is a low-rank matrix.

[0122] In cross-interference scenarios, the interference signal i(t), after demodulation and low-pass filtering by the radar receiver, typically has a short duration, manifesting as one or more spikes on the relevant cross signal, exhibiting sparsity in the time domain. Therefore, the vector i representing the interference component in equation (4) is a sparse vector. In summary, the low-rank sparse optimization model used to separate the useful signal and the interference signal from the measurement data can be expressed as:

[0123]

[0124] In the formula, It is the rank operation, representing a matrix. The number of non-zero singular values ​​(i.e., the rank of the matrix), σ i Representative matrix The singular values; η is the l0 norm, representing the number of non-zero elements in vector i. η≥0 is an adjustment parameter that balances the loss function and the regularization term. ε represents the error coefficient.

[0125] Since the rank and l0 norm sparsity minimization problem is difficult to solve directly through optimization, the kernel norm and l1 norm are generally used to replace the rank operation and l0 norm for relaxation, respectively. Thus, equation (6) can be rewritten as:

[0126]

[0127] In the formula, It is the nuclear norm, representing the matrix. The sum of singular values, It is the l1 norm, representing the sum of the absolute values ​​of the non-zero elements in vector i.

[0128] Step 3: Non-convex regularized sparse and low-rank factorization

[0129] The MCP penalty function, with its favorable properties of being fast, having small bias, being sparsity, and being continuous, is chosen to provide sparsity for the estimated signal. Its definition is... in:

[0130]

[0131] Setting different values ​​for parameters λ and γ will change the shape of the MCP penalty function;

[0132] When the parameter γ→1, the non-convex penalty function MCP converges to a hard threshold penalty, while when γ→∞, the function can be used as the l1 norm. Therefore, the estimator obtained by the MCP penalty function is asymptotically unbiased, and the estimation result will be more accurate than that of the l1 norm penalty.

[0133] In the optimization model (7), due to the Hankel matrix The dimensionality is large, and Singular Value Decomposition (SVD) is usually expensive and time-consuming. To reduce the overall computational complexity, this invention adopts a low-rank factorization algorithm. From the perspective of the optimization process, the algorithm does not require SVD decomposition during the iterative process, but only needs to solve the linear least squares problem. In summary, the optimization model (7) can be expressed as follows after applying the nuclear norm relaxation factorization and the MCP penalty function:

[0134]

[0135] Step 4: Use ADMM to solve optimization problems

[0136] The augmented Lagrangian function corresponding to the optimization problem in equation (9) can be expressed as:

[0137]

[0138] In the formula, β and μ are regularization parameters, and w and Z are Lagrange multiplier vectors and matrices. Equation (10) can be simplified to:

[0139]

[0140] Based on the augmented Lagrange function, the ADMM iterative method can be used to transform the optimization problem of equation (11) into solving the following subproblems:

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] To obtain the update of x, we need to take the first derivative of equation (12) above, which gives us:

[0148]

[0149] In the formula Hankel matrix The Moore-Penrose generalized inverse matrix is ​​defined as follows:

[0150] The closed-form solution to the optimization subproblem (13) can be expressed as:

[0151]

[0152] In the formula, i = 1, 2, ..., N, introduced For soft thresholding, sign(t) is the sign function.

[0153] Next, the closed-form solutions for U and V can be given by making the first derivatives of equations (14) and (15) zero, that is:

[0154]

[0155]

[0156] The updates to U and V can be obtained from equations (22) and (23):

[0157]

[0158]

[0159] In the formula, E represents the identity matrix; (*) -1 It represents reciprocal operations.

[0160] By sequentially calculating equations (18), (19), (22), (23), (16), and (17) and iterating this process, x, i, U, V, w, and Z can be continuously updated. During the iteration process, the regularization parameters β and μ need to be gradually increased to improve the accuracy of the recovered signal. After several iterations, x, representing the target component, and i, representing the interference component, are recovered from the prior data, thereby achieving the separation of the target component and the interference component.

[0161] Step 5: Simulation Verification and Comparison

[0162] This invention simulates a scenario where a victim radar is jammed by multiple FWCW radars to verify the effectiveness of the aforementioned algorithm in suppressing interference. Table 1 lists the relevant parameters used to simulate the victim radar and multiple jamming radar systems. Point targets with scattering coefficients of 0.5, 0.03, and 0.4 were placed at distances of 40m, 70m, and 100m from the victim radar, respectively.

[0163] Table 1 Radar System Parameters

[0164]

[0165]

[0166] The echo signal carrying target information and the signal emitted by the jamming radar are simultaneously received by the victim radar. After mixing and filtering with the transmitted signal at the receiver, it is evident that the jamming signal, as an additive signal, directly affects the overall intermediate frequency signal (e.g., ...). Figure 4 (As shown). The distance information of the target can be obtained by performing a Fast Fourier Transform (FFT) on the filtered intermediate frequency signal, such as... Figure 5 As shown, the reference signal is an undisturbed signal containing only target information. Since the target at 70m is a weak target with a low scattering coefficient, the increased noise floor in the range profile under strong interference makes it almost impossible to observe.

[0167] For the method of this invention, the initial regularization parameters are set to τ = 0.02, β = 0.2, and μ = 0.02. During the iteration process, the regularization parameters β and μ are increased to 1.03 times their original values ​​every ten iterations. When the relative error reaches δ = 1 × 10⁻⁶, the regularization parameters are further increased. -3 At this point, the iteration exits, yielding the final separation result. The useful signal containing target information separated from the echo signal is also presented in the form of an intermediate frequency signal, such as... Figure 6 As shown, the interference on the intermediate frequency signal has been successfully eliminated, as indicated in the corresponding distance profile ( Figure 7 In the image, even a weak target located at 70m is clearly visible. This demonstrates that the method of this invention achieves good interference suppression in scenarios with multiple targets and multiple interferences.

[0168] To facilitate comparison of the method of this invention with other interference suppression methods, this invention introduces two indicators to quantitatively evaluate the interference suppression performance of various methods: Signal-to-Interference-plus-Noise Ratio (SINR) and Correlation Coefficient ρ. The definitions of these two performance evaluation indicators are as follows:

[0169]

[0170]

[0171] In the formula, s0 represents the reference signal free from noise and interference, s b The signal is represented by ||·||², which is the l2 norm operator. The correlation coefficient ρ is in complex form. The magnitude of ρ ranges from 0 to 1, and it can be used to reflect the similarity between the reference signal and the recovered signal. Therefore, the larger the values ​​of |ρ| and SINR, the better the interference suppression performance of the method.

[0172] To demonstrate the superiority of the signal separation method introduced in this invention, interference suppression methods such as interference component removal and reconstruction, and adaptive filtering are used for comparison. Interference component removal and reconstruction methods include CFAR-Z, CFAR-AC, and CFAR-B. All three methods use CFAR detection in the time-frequency domain to determine the location of interference. The former directly sets the interference component to zero, the second method uses the amplitude and phase information of the undisturbed signal to recover the interference-contaminated signal, and the latter reconstructs the signal in the frequency domain based on the Burg algorithm. For the adaptive filtering (ANC) method, the threshold is adaptively adjusted to accurately detect the interference component and then set it to zero.

[0173] After using the above methods to suppress cross-interference, performance was compared using equations (24) and (25). Under different input signal-to-noise ratios, the SINR and |ρ| of each method were as follows:Figure 8 , Figure 9 As shown. When SNR = -10dB, the signal separation method using the l1 norm as the sparsity penalty function has slightly higher performance indicators than the method of this invention. At other signal-to-noise ratios, the method of this invention can clearly demonstrate better interference suppression performance.

[0174] Example 2

[0175] Secondly, based on Embodiment 1, this embodiment provides a vehicle-mounted millimeter-wave radar interference suppression device based on a sparse and low-rank model, including a processor and a storage medium.

[0176] The storage medium is used to store instructions;

[0177] The processor is configured to operate according to the instructions to execute the method according to Embodiment 1.

[0178] Example 3

[0179] Thirdly, based on Embodiment 1, this embodiment provides a device, including,

[0180] Memory;

[0181] processor;

[0182] as well as

[0183] Computer programs;

[0184] The computer program is stored in the memory and configured to be executed by the processor to implement the method described in Embodiment 1.

[0185] Example 4

[0186] Fourthly, based on Embodiment 1, this embodiment provides a storage medium on which a computer program is stored, and when the computer program is executed by a processor, it implements the method described in Embodiment 1.

[0187] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0188] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0189] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0190] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0191] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for suppressing interference from vehicle-mounted millimeter-wave radar based on a sparse and low-rank model, characterized in that, The method includes: By utilizing the low-rank and sparse characteristics of the useful and interference signals in the intermediate frequency signal after demodulation and filtering by the radar receiver, a low-rank sparse optimization model is constructed. After applying the minimax nonconvex sparsity penalty and low-rank factor decomposition to the low-rank sparse optimization model, the useful signal and interference signal are separated by iterative optimization using the alternating direction multiplier method. Specifically, a low-rank sparse optimization model is constructed by utilizing the low-rank and sparse characteristics of the useful and interference signals in the intermediate frequency signal after demodulation and filtering by the radar receiver, including: Construct a model of the intermediate frequency signal after demodulation and filtering by the radar receiver; Based on the demodulated and filtered intermediate frequency signal model of the radar receiver, a low-rank sparse optimization model is constructed, including: The intermediate frequency signal model after demodulation and filtering by the radar receiver is converted into a discrete signal by time-interval sampling. The measured values ​​of all time samples are represented in vector form as follows: s = x + i + n (4) In the formula, the four vectors are represented as s = [s0, s1, ..., s2]. N-1 ] T The vector representing the target is x = [x0, x1, ..., xn]. N-1 ] T The vector representing interference is i = [i0, i1, ..., i...]. N-1 ] T The vector representing noise is n = [n0, n1, ..., n]. N-1 ] T N is the number of discrete signal sampling points; vector Transform into Hankel matrix Where N = m + n - 1, m and n are the number of rows and columns of the matrix, respectively; then the Hankel matrix S is expressed as: In the formula, represents the Hankel matrix transformed from the vector within the parentheses; for the matrix constructed from the target beat frequency signal the number of targets M << m, M << n, and the matrix has a rank equal to the number of target complex exponentials, and the matrix is a low-rank matrix; In the case of cross-interference, the interference signal i(t) after being demodulated and low-pass filtered by the radar receiver is usually short in duration, and manifests as one or more spikes on the relevant chrip signal, exhibiting sparsity in the time domain; therefore, the vector i representing the interference component is a sparse vector. The low-rank sparse optimization model used to separate useful signals from interference signals in measurement data is expressed as follows: In the formula, It is the rank operation, representing a matrix. The number of non-zero singular values, σ i Representative matrix The singular values; yes The norm represents the number of non-zero elements in vector i. η≥0 is an adjustment parameter that balances the loss function and the regularization term. ε represents the error coefficient.

2. The vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model according to claim 1, characterized in that, Constructing a model of the intermediate frequency signal after demodulation and filtering by the radar receiver includes: The radar transmitted signal p(t) is represented as: In the formula, j represents an imaginary number, and f0, k, and T represent the starting frequency, modulation slope, and duration of the signal, respectively. The target's echo signal is a delayed version of the radar's transmitted signal. The beat frequency signal x(t) of multiple targets acquired by the radar is represented as: In the formula, M represents the number of targets, a i τ i and f b,i These represent the scattering coefficient of the i-th target, the time delay of the echo signal, and the beat frequency, respectively. If echo signals from several targets cross-interference during radar reception, the received signals, after demodulation and low-pass filtering, will have the following intermediate frequency (IF) signal model from the radar receiver: In the formula, s(t) represents the intermediate frequency signal after demodulation and filtering by the radar receiver, i(t) represents the remaining component of the interference signal after demodulation and filtering by the radar receiver, and n(t) is additive white Gaussian noise. s int (t) represents the interference signal. The complex conjugate of the radar transmitted signal p(t) and the interference signal s int (t) are multiplied for demodulation, h lpf (t) represents a low-pass filter, which performs a convolution operation on the demodulated signal to achieve filtering.

3. The vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model according to claim 1, characterized in that, Also includes: Due to rank sum The norm sparsity minimization problem is difficult to solve directly using optimization; it relies on the kernel norm and... Norms replace rank operations and Using the norm for relaxation, the low-rank sparse optimization model of equation (6) is re-expressed as: In the formula, It is the nuclear norm, representing the matrix. The sum of singular values, yes The norm represents the sum of the absolute values ​​of the non-zero elements in vector i.

4. The vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model according to claim 3, characterized in that, The low-rank sparse optimization model is subjected to minimax nonconvex sparsity penalty and low-rank factor decomposition, including: The MCP penalty function is defined as follows: in: Where λ and γ represent the parameters of the MCP penalty function, and setting different values ​​for λ and γ will change the shape of the MCP penalty function; The MCP penalty function is used as Norm; The low-rank sparse optimization model, after applying low-rank factorization with nuclear norm relaxation and the MCP penalty function, is expressed as follows: In the formula, U and V represent intermediate parameters. The F-norm is defined as follows: P represents the square root of the sum of squares of each term in the matrix. λ,γ (i) represents the MCP penalty function for vector i, (*) H This represents the conjugate transpose.

5. The vehicle-mounted millimeter-wave radar interference suppression method based on a sparse and low-rank model according to claim 4, characterized in that, Iterative optimization using the alternating direction multiplier method to separate useful signals from interference signals includes: The augmented Lagrangian function corresponding to the optimization problem in equation (9) is expressed as: In the formula, β and μ are regularization parameters, and w and Z are Lagrange multiplier vectors and matrices, which simplify to: Based on the augmented Lagrangian function, the optimization problem of equation (11) is transformed into solving the following subproblems using the ADMM iterative method: Where k represents the number of iterations; To obtain the update of x, we take the first derivative of equation (12) and get: In the formula Hankel matrix The Moore-Penrose generalized inverse matrix is ​​defined as follows: The closed-form solution to the optimization subproblem (13) is expressed as: In the formula, i = 1, 2, ..., N, introduced This is a soft thresholding operator, where sign(t) is the sign function, and the intermediate parameters t and α represent the values ​​in the equation. and τ is the regularization parameter; The closed-form solutions for U and V are given by making the first derivatives of equations (14) and (15) zero, i.e.: The updates to U and V are obtained from equations (22) and (23): In the formula, E represents the identity matrix; (*) -1 Represents reciprocal operations; Equations (18), (19), (22), (23), (16), and (17) are calculated sequentially and the process is repeated, continuously updating x, i, U, V, w, and Z. During the iteration, the regularization parameters β and μ need to be gradually increased to increase the accuracy of the recovered signal. After several iterations, x, representing the target vector, and i, representing the interference vector, are recovered from the prior data, thereby achieving the separation of the useful target signal and the interference signal.

6. A vehicle-mounted millimeter-wave radar interference suppression device based on a sparse and low-rank model, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the method according to any one of claims 1 to 5.

7. A computer device, characterized in that, include: Memory; processor; as well as Computer programs; The computer program is stored in the memory and configured to be executed by the processor to implement the method as described in any one of claims 1 to 5.

8. A storage medium, characterized in that, It stores a computer program thereon, which, when executed by a processor, implements the method described in any one of claims 1 to 5.

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