Method for detecting living body in automobile cabin based on fusion point cloud tracking and machine learning algorithm SVM (Support Vector Machine)

Abstract

The invention provides an in-vehicle living body detection method based on fusion point cloud tracking and a machine learning algorithm SVM, and the method comprises the steps: collecting in-vehicle signals through a millimeter radar, carrying out the slow time dimension and fast time dimension preprocessing of data, extracting target point cloud data and an accumulated amplitude phase matrix, and carrying out the in-vehicle living body detection through the millimeter radar. And then a fusion point cloud and a machine learning algorithm SVM are used to predict results of a static target and a dynamic target. According to the method, the living body is judged by adopting the 3D point cloud and the machine learning SVM method through a dynamic and static distinguishing mode, and the method has good detection performance for the living body target left in the vehicle under the conditions of motion or sleep and static.

Description

Technical Field

[0001] The present invention relates to the field of automotive electronics technology, and particularly relates to a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM. Background Art

[0002] With the rapid development of the automotive industry and the increasing emphasis of consumers on the safety performance of automobiles, in-vehicle living body detection has become a new focus of research and development in automobile factories. The occurrence of various accidents has also sounded the alarm, and in-vehicle living body detection has become a new requirement that automobile factories need to consider. In order to effectively prevent accidents such as living bodies being left in the vehicle by accident, major automobile factories have invested in research and development to explore the use of advanced technologies for in-vehicle living body monitoring. With the technological progress of millimeter-wave radars, the application of millimeter-wave radars for living body detection has gradually come into people's view. To solve this problem, major automobile factories are all researching and developing living body detection radars.

[0003] Millimeter-wave radar technology has gradually become the preferred solution for in-vehicle living body detection due to its advantages such as strong penetration, good anti-interference performance, and high measurement accuracy. In the prior art, methods for in-vehicle living body detection using millimeter-wave radars have been proposed, such as the invention patent (application number 202311611730.0, application date November 29, 2023) disclosed by Dai Junjie et al. This method processes the millimeter-wave radar echo signal, extracts the target phase information, and uses the variational mode decomposition (VMD) algorithm to filter the continuous phase information, separates the breathing and heartbeat information, and then determines whether there is a living body target by calculating the breathing signal frequency.

[0004] However, the above method has many limitations in practical applications. First, its versatility is poor, requiring the radar to detect directly against the chest cavity of the living body target, which is difficult to meet in the actual vehicle environment because the in-vehicle space is limited and the installation position of the radar is restricted by many factors. Second, when the target has limb movements, the collected phase information is extremely vulnerable to interference, resulting in detection failure. Especially under strict time requirement conditions, such as quickly and accurately determining whether there is a living body in the vehicle, this method may not meet the real-time requirement.

[0005] Therefore, the existing methods for in-vehicle living body detection based on millimeter-wave radars face many challenges in practical applications and are difficult to meet the requirements of actual vehicle mass production. In order to achieve the real-time performance, anti-interference performance, and versatility of in-vehicle living body detection, a new technical solution is urgently needed to overcome the deficiencies of the prior art. Summary of the Invention

[0006] To solve the above problems existing in the prior art, the purpose of the present invention is to provide a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM. By fusing point cloud tracking and the machine learning algorithm, this method can more accurately determine whether there is a living body target in the vehicle, and combines dynamic and static living body detection methods, having good detection performance for the living body targets left in the vehicle whether they are moving or sleeping and stationary.

[0007] Specifically, when the target is moving, 3D point cloud is used for tracking to determine whether there is a living body; when the target is stationary, the breathing and heartbeat of the living body target will still generate micro-scattering signals. This micro-motion signal is the key to distinguishing a living body from a non-living body. The information extracted from the traditional single intermediate frequency signal according to the near-field phase approximation is easily affected by environmental noise in the real environment, resulting in poor accuracy of living body detection. By extracting the breathing micro-motion scattering signal of the target, it is determined whether there is a living body.

[0008] The present invention realizes the above purpose through the following technical solutions:

[0009] A method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM, the method comprising the following steps:

[0010] Step S1: After the vehicle is turned off and locked externally, initialize and start the radar, emit a continuous linear frequency modulation signal to detect the area inside the vehicle, and synchronously collect the ADC echo signal of the millimeter wave radar;

[0011] Step S2: Preprocess the collected ADC echo signal;

[0012] Step S3: Extract 3D point cloud data from the preprocessed data;

[0013] Step S4: Extract the amplitude-phase matrix corresponding to the 3D point cloud data;

[0014] Step S5: Process the fused 3D point cloud data, and determine whether there is a living body target in the vehicle through the 3D point cloud data features;

[0015] Step S6: Use the machine learning algorithm SVM to perform prediction and classification processing on the collected amplitude-phase matrix data, and output the result of whether there is a living body target;

[0016] Step S7: Fuse and judge the living body detection classification result predicted by the machine learning algorithm SVM and the living body detection result in the 3D point cloud mode, and output the result of whether there is a living body target in the vehicle.

[0017] According to a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, in step S3, the execution process of processing the current data frame signal to generate 3D point cloud data in the fast time dimension specifically includes the following steps:

[0018] Step A1: Perform 1D distance FFT processing. Perform one-dimensional FFT algorithm processing on the collected ADC echo signal. According to the relationship between distance and frequency R = c / 2f, obtain target information at different distances and obtain the distance FFT spectrum, where c is the speed of light, f is the frequency of the intermediate frequency signal, and R is the distance of the target;

[0019] Step A2: Perform static background removal. Use the circle fitting method to process the distance FFT data in each frame. Find the center of the circle of each frame of IQ data and subtract each data by this center;

[0020] Step A3: Doppler FFT. Perform 2D Doppler FFT processing on the data obtained after static background removal, and calculate amplitude information based on the obtained 2D Doppler data, thereby forming a distance-Doppler detection matrix;

[0021] Step A4: Perform SOGO-CFAR target detection. Then perform two-dimensional SOGO-CFAR processing on the detection matrix to obtain the distance and speed information of the target points;

[0022] Step A5: Perform MVDR algorithm angle estimation. Use the wave velocity synthesis method MVDR algorithm to calculate the azimuth and elevation angles of the target to obtain the 3D point cloud data in the fast time dimension.

[0023] According to a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, in step S3, the execution process of reconstructing 1D FFT data to generate 3D point cloud data in the slow time dimension specifically includes the following steps:

[0024] Step B1: Reconstruct the 1D FFT data. Extract the 1D FFT data of a chirp with a fixed serial number from each frame of received data, and extract continuous K chirps within consecutive K frame periods as a new data frame;

[0025] Step B2: Perform static background removal. Use the circle fitting method to process the reconstructed 1D FFT data. Find the center of the circle of each frame of IQ data and subtract each data by this center;

[0026] Step B3: Perform Doppler FFT processing. Perform 2D Doppler FFT processing on the data obtained after static background removal, and calculate amplitude information based on the obtained 2D Doppler data, thereby forming a distance-Doppler detection matrix;

[0027] Step B4: Perform SOGO-CFAR target detection, and then perform two-dimensional SOGO-CFAR processing on the detection matrix to obtain the distance and velocity information of the target points;

[0028] Step B5: Perform angle estimation using the MVDR algorithm. The MVDR algorithm of the wave velocity synthesis method is used to calculate the azimuth and elevation angles of the target to obtain the 3D point cloud data of the target in the slow time dimension;

[0029] Step B6: Fuse the 3D point cloud data, and merge the 3D point cloud data in the slow time dimension and the 3D point cloud data in the fast time dimension.

[0030] According to a method for in-vehicle living body detection based on fused point cloud tracking and machine learning algorithm SVM provided by the present invention, in the steps A5 and B5, the mathematical expression of the MVDR beamforming algorithm is as follows:

[0031] The received signal model function is expressed as the following formula:

[0032]

[0033] where x(t) is an M×1 received signal vector, k is the number of signal sources, a(θ k ) is the direction vector of the k-th signal source, θ k is the incoming wave direction of the k-th signal, s k (t) is the signal of the k-th signal source, and n(t) is the additive noise;

[0034] The objective function formula is expressed as the following formula:

[0035] J(w) = w H Rw + λ(w H a(θ d ) - 1)

[0036] where w is the weight vector, R = R[x(t)x H (t)] is the covariance matrix of the received signal, λ is the Lagrange multiplier, and θ d is the desired signal direction;

[0037] Taking the derivative of J(w) with respect to w and setting it to zero, the optimal weight vector can be obtained as:

[0038]

[0039] The output signal after beamforming is:

[0040]

[0041] According to an in-vehicle living body detection method based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, in step S4, the generation processing flow of the amplitude-phase feature matrix specifically includes the following steps:

[0042] Step C1: Select the data frames of a fixed channel in all antenna receiving channels, extract the chirp data of a fixed serial number from each frame of received data for 1D distance FFT operation to obtain 1D FFT data;

[0043] Step C2: Calculate the modulus value of the 1D FFT data to obtain amplitude information, and use the arctangent method to calculate the phase to form an amplitude-phase feature matrix.

[0044] According to an in-vehicle living body detection method based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, in step S5, the processed 3D point cloud data after fusion specifically includes the following steps:

[0045] Step D1: Data screening, perform data screening on the processed 3D point cloud data after fusion;

[0046] Step D2: Data caching, perform circular caching on the filtered 3D point cloud data;

[0047] Step D3: Data clustering, use the Mean Shift algorithm to perform clustering processing on the processed 3D point cloud data after fusion, and extract the feature information of the clusters after clustering;

[0048] Step D4: Cluster tracking, use the extended Kalman filter to perform filtering and aircraft tracking processing on the center points of the clusters after clustering;

[0049] Step D5: Region judgment, divide the in-vehicle space into multiple living body detection regions according to the spatial layout inside the vehicle cabin and the installation position of the radar;

[0050] Step D6: Presence detection strategy, based on the cluster information after clustering, filter out the clusters with fewer target points in the clusters, and mark the filtered clusters and the target points in the clusters as noise, and do not participate in subsequent judgments; after completing the screening of noise targets, based on the set detection ranges of multiple target partitions, count the data points in the clusters, count the total number of targets existing in each partition and the sum of the amplitudes of the targets in this partition; after completing the statistics of the number and amplitude sum of all target regions, it is necessary to further sum up the number of targets and the amplitude sum statistics in multiple detection partitions to obtain all_cnt and all_amp_cnt data, and finally make a decision whether there is a living body target through the threshold method.

[0051] A method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention. In step D3, the Mean Shift algorithm is optimized, specifically including the following steps:

[0052] Let x be a data point about x in a d-dimensional space. There are n data points x 1 , x 2 , …, x n . The probability density estimation of the kernel function K(x) at the data point x is given by the following formula:

[0053]

[0054] where K(x) is a kernel function, which is a symmetric function about x;

[0055] where the Mean Shift vector is defined by the following formula:

[0056]

[0057] where g(x) = k(x) p , p is a constant. Usually, g(x) is also a kernel function, and generally g(x) = K(x). When K(x) is a Gaussian kernel function, g(x) is also a Gaussian kernel function.

[0058] According to a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, the clustering optimization of the Mean Shift algorithm specifically includes:

[0059] Grouping of 3D point cloud data: Randomly divide 50 frames of point cloud data into groups of 10 frames each, and a total of 5 groups of 3D point cloud data are split;

[0060] Clustering of grouped data: Use the Mean Shift algorithm to cluster the 5 groups of 3D point cloud data respectively;

[0061] Merging of clustering clusters: Calculate the pairwise correlation of the 5 groups of clustered clusters, and merge the two clusters with higher similarity.

[0062] According to a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, in step S6, the machine learning algorithm SVM is executed, specifically including the following steps:

[0063] Step E1: Training of model parameters. Divide the pre-collected data into a training set and a test set and input them into the SVM model for training;

[0064] Step E2: Extract the trained SVM classifier model parameters and the prepared amplitude-phase matrix data;

[0065] Step E3: Data preprocessing, perform a moving average filtering algorithm on the cached multi-frame amplitude-phase matrix data column by column; further normalize the processed data to between -1 and 1;

[0066] Step E4: Predict the amplitude-phase time series formed by the amplitude matrix data of all range cells, classify the amplitude-phase feature matrix using the pre-trained SVM classification model parameters, and count the results. Save the number of times a living target is predicted in all current input prediction results, and save the current number of successful predictions in a circular buffer;

[0067] Step E5: Statistically analyze the classification results in the circular buffer for 5 consecutive frames, and decide whether there is a living target in the classification through a threshold comparison method.

[0068] According to a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM provided by the present invention, in step S6, the machine learning algorithm SVM using a Gaussian kernel function is used to process non-linear classification problems, and the Gaussian kernel function is defined by the following formula:

[0069] K(x i ,x j )=exp(-γ∥x i -x j ∥ 2 )

[0070] where γ > 0 is a parameter that controls the range of the function;

[0071] For the case of linear inseparability, the optimization objective of SVM is to minimize where ξ i is a slack variable used to handle inseparable data points, and c > 0 is a penalty parameter;

[0072] where the constraint condition is: y i (w·x i +b)≥1-ξ i ,ξ i ≥0,i=1,2,…,n;

[0073] Introduce Lagrange multipliers α i and μ i , and construct a Lagrangian function, expressed as the following formula:

[0074]

[0075] For w, b, and ξi Calculate the partial derivative, set the result to zero, and obtain: α i + μ i = C. Substitute these results into the Lagrangian function to obtain the dual problem:

[0076] Maximize Subject to the constraints 0 ≤ α i ≤ C,

[0077] For the decision function, solve the dual problem to obtain the optimal solution α * and calculate b * which can be calculated through any support vector that satisfies and is expressed by the following formula:

[0078]

[0079] The final decision function is expressed by the following formula:

[0080]

[0081] For the SVM with Gaussian kernel function, the decision function is expressed by the following formula:

[0082]

[0083] It can be seen that a method for in-vehicle living body detection based on the fusion of point cloud tracking and machine learning algorithms provided by the present invention has significant beneficial effects compared with the prior art, specifically as follows:

[0084] 1. Stable detection of moving and stationary living bodies: The present invention realizes the stable detection of moving and stationary living bodies in the vehicle cabin by fusing two living body detection methods, dynamic and static. For dynamic target detection, signal processing is carried out using the current frame 1D FFT data and the reconstructed 1D FFT data accumulated over multiple frames, which greatly improves the sensitivity of detecting the speed of moving targets and effectively captures the dynamic characteristics of moving living bodies. Clustering and segmentation of the 3D point cloud data accumulated over multiple frames can highly restore the contour and volume size of the real target. Combining with the layout of the vehicle cabin to divide the detection area, counting the number of target points, amplitude, etc. in the area, and comparing with a preset threshold, thus accurately determining whether there is a living body target. This method has a high suppression and filtering effect on non-living body interference and improves the accuracy of detection.

[0085] 2. Improve the stability and accuracy of static in - vivo detection: For static in - vivo targets, the present invention innovatively uses the method of extracting the breathing micro - motion scattering signal of the target for judgment. By constructing an amplitude - phase feature matrix and extracting the breathing micro - motion scattering signal of the target, the problem of poor detection accuracy caused by environmental noise interference in traditional methods is avoided. By training the SVM algorithm model, the extracted micro - motion amplitude - phase feature matrix is directly classified to determine whether there is an in - vivo target. This method not only improves the detection stability and accuracy of static in - vivo targets, but also reduces the algorithm complexity, improves the generality, and is especially more applicable in complex environments.

[0086] 3. Parallel operation to improve detection efficiency: The present invention uses two completely different algorithms and ideas, dynamic and static, to perform parallel operations, making full use of computing resources and improving detection efficiency. Through parallel processing, it can quickly respond to the in - vehicle in - vivo detection requirements and provide real - time guarantee for in - vehicle safety.

[0087] 4. Enhance the robustness and reliability of the system: The present invention forms complementary advantages by integrating multiple detection technologies and algorithms, enhancing the robustness and reliability of the system. No matter facing what kind of complex in - vehicle environment or in - vivo state, it can maintain stable detection performance and provide strong technical support for vehicle safety.

[0088] In summary, a method for in - vehicle in - vivo detection based on the fusion of point - cloud tracking and machine - learning algorithm SVM provided by the present invention can comprehensively and accurately detect in - vivo targets in the vehicle cabin, providing an important technical guarantee for vehicle safety.

[0089] The following further elaborates on the present invention in detail with reference to the accompanying drawings and specific embodiments. Brief Description of the Drawings

[0090] Figure 1 is a flowchart of an embodiment of a method for in - vehicle in - vivo detection based on the fusion of point - cloud tracking and machine - learning algorithm SVM of the present invention.

[0091] Figure 2 is an algorithm flowchart for generating fused 3D point - cloud data in an embodiment of a method for in - vehicle in - vivo detection based on the fusion of point - cloud tracking and machine - learning algorithm SVM of the present invention.

[0092] Figure 3 is a flowchart for generating an amplitude - phase feature matrix in an embodiment of a method for in - vehicle in - vivo detection based on the fusion of point - cloud tracking and machine - learning algorithm SVM of the present invention.

[0093] Figure 4 is a schematic diagram of the division of the in - vehicle detection area in an embodiment of a method for in - vehicle in - vivo detection based on the fusion of point - cloud tracking and machine - learning algorithm SVM of the present invention.

[0094] Figure 5 This is a flowchart of an algorithm for determining the existence of a living target inside a vehicle through 3D point cloud data in an embodiment of a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM of the present invention.

[0095] Figure 6 This is a flowchart of the optimization of the Mean Shift clustering algorithm in an embodiment of a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM of the present invention.

[0096] Figure 7 This is a flowchart of a strategy for determining the existence of a living target inside a vehicle through 3D point cloud data in an embodiment of a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM of the present invention.

[0097] Figure 8 This is a flowchart of an algorithm for determining the existence of a living target inside a vehicle through the machine learning algorithm SVM in an embodiment of a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM of the present invention.

[0098] Figure 9 This is a signal feature map of a living target inside a vehicle in an embodiment of a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM of the present invention.

[0099] Figure 10 This is an amplitude-phase feature map used for inputting into the machine learning algorithm SVM in an embodiment of a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM of the present invention. Detailed implementation manners

[0100] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without making creative efforts based on the embodiments in the present invention fall within the protection scope of the present invention.

[0101] Referring to "embodiments" herein means that the specific features, structures, or characteristics described in conjunction with the embodiments may be included in at least one embodiment of the present application. The phrase appears in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art explicitly and implicitly understand that the embodiments described herein can be combined with other embodiments.

[0102] SeeFigure 1 , this embodiment provides a method for in-vehicle living body detection based on the fusion of point cloud tracking and the machine learning algorithm SVM. This method includes the following steps:

[0103] Step S1: After the vehicle is turned off and locked externally, initialize and start the radar, emit a continuous linear frequency modulation signal to detect the interior area of the vehicle, and synchronously collect the ADC echo signals of the millimeter-wave radar, with a periodic interval of 50 ms each time;

[0104] Step S2: Preprocess the collected ADC echo signals;

[0105] Step S3: Extract 3D point cloud data from the preprocessed data;

[0106] Step S4: Extract the amplitude-phase matrix corresponding to the 3D point cloud data;

[0107] Step S5: Process the fused 3D point cloud data, and judge whether there is a living body target in the vehicle through the characteristics of the 3D point cloud data;

[0108] Step S6: Use the machine learning algorithm SVM to perform prediction and classification processing on the collected amplitude-phase matrix data, and output the result of whether there is a living body target;

[0109] Step S7: Fuse and judge the living body detection classification result predicted by the machine learning algorithm SVM and the living body detection result in the 3D point cloud mode, and output the result of whether there is a living body target in the vehicle.

[0110] As Figure 2 shown, in step S3, the execution processing flow for generating 3D point cloud data in the fast time dimension by processing the current data frame signal specifically includes the following steps:

[0111] Step A1: Perform 1D distance FFT processing. Perform a one-dimensional FFT algorithm on the collected ADC echo signals. According to the relationship between distance and frequency R = c / 2f, the target information at different distances can be obtained to obtain the distance FFT spectrum, where c is the speed of light, f is the frequency of the intermediate frequency signal, and R is the distance of the target;

[0112] Step A2: Perform static background removal. Use the circle fitting method to process the distance FFT data in each frame, and find the center of the circle of each frame of IQ data and subtract each data by this center.

[0113] Step A3: Doppler FFT. Perform 2D Doppler FFT processing on the data obtained after static background removal processing, and calculate the amplitude information based on the obtained 2D Doppler data to form a distance-Doppler detection matrix;

[0114] Step A4: Perform SOGO-CFAR target detection, and then perform two-dimensional SOGO-CFAR processing on the detection matrix to obtain the distance and velocity information of the target points;

[0115] Step A5: Perform MVDR algorithm angle estimation, and use the wave velocity synthesis method MVDR algorithm to calculate the azimuth and elevation angles of the target to obtain the fast-time dimension point cloud data.

[0116] As Figure 2 shown, in step S3, the execution processing flow of generating the slow-time dimension 3D point cloud data from the reconstructed 1D FFT data specifically includes the following steps:

[0117] Step B1: Reconstruct the 1D FFT data. Extract the 1D FFT data of a chirp with a fixed serial number from each frame of received data, and extract continuous K chirps within a continuous K-frame period as a new data frame. For example, extract continuous 64 chirps within a continuous 64-frame period as a new data frame, and perform signal processing to obtain the point cloud data accumulated in multiple frames. In this embodiment, it is called the slow-time dimension 3D point cloud data to improve the sensitivity of point cloud detection for small movements inside the car cabin;

[0118] Step B2: Perform static background removal. Use the circle fitting method to process the reconstructed 1D FFT data by finding the center of the circle of each frame of IQ data and subtracting each data from the center of the circle;

[0119] Step B3: Perform Doppler FFT processing. Perform 2D Doppler FFT processing on the data obtained after static background removal processing, and calculate the amplitude information based on the obtained 2D Doppler data to form a range-Doppler detection matrix;

[0120] Step B4: Perform SOGO-CFAR target detection, and then perform two-dimensional SOGO-CFAR processing on the detection matrix to obtain the distance and velocity information of the target points;

[0121] Step B5: Perform MVDR algorithm angle estimation. Use the wave velocity synthesis method MVDR (Minimum Variance Distortionless Response) algorithm to calculate the azimuth and elevation angles of the target to obtain the target slow-time dimension 3D point cloud data;

[0122] Step B6: Fuse the 3D point cloud data, and merge the slow-time dimension 3D point cloud data and the fast-time dimension 3D point cloud data.

[0123] Further, in step B1, reconstructing the 1D FFT (Fast Fourier Transform) data is to recover the time-domain signal from the frequency-domain signal. FFT is an efficient algorithm for calculating the discrete Fourier transform (DFT), which converts the time-domain signal into the frequency-domain signal for easy analysis of the spectral characteristics of the signal. The inverse transform of FFT (IFFT, Inverse Fast Fourier Transform) is used to convert the frequency-domain signal back to the time-domain signal, thereby realizing the reconstruction of the 1D FFT data.

[0124] Further, in steps A2 and B2, the purpose of this step is to remove the echoes of the static or fixed background from the radar echo data for more accurate detection and analysis of dynamic targets. In radar signal processing, the received raw radar signal is first subjected to a fast Fourier transform (FFT) to convert the time-domain signal into the frequency-domain signal. In this way, it is easier to analyze the frequency components of the signal.

[0125] Among them, the circle fitting method is a mathematical method for finding the best-fitting circle in a two-dimensional dataset. In radar signal processing, this method can be applied to IQ data (i.e., in-phase and quadrature-phase data), which are usually represented as points on a two-dimensional plane. Through the circle fitting method, the "center of the circle" of the IQ dataset can be determined, and this center of the circle roughly represents the echo center of the static background.

[0126] For the IQ representation of each frame of radar echo data, the circle fitting method is applied to find the center of the circle of that frame of data, and this center of the circle represents the main echo position of the static background in that frame. The center of the circle is usually determined by minimizing the sum of the squares of the distances from the data points to the fitted circle. Once the center of the circle of each frame of data is determined, each data point in that frame is subtracted by this center of the circle. This operation is actually background removal because subtracting the center of the circle is equivalent to removing the main echo component of the static background. In this way, the influence of the static background on the detection of dynamic targets can be significantly reduced, and the sensitivity and accuracy of the radar system can be improved.

[0127] Further, in steps A3 and B3, the data after static background removal processing is a time series. For each radar pulse echo, there is a corresponding range bin (or range cell) data. These data are organized into a two-dimensional array, where one row represents a radar pulse echo and one column represents a range bin. Apply a two-dimensional fast Fourier transform (2D FFT) to this two-dimensional array. The 2D FFT will perform a transform simultaneously in the range and pulse (or time) dimensions, thereby obtaining range-Doppler frequency domain data. The FFT in the range dimension can reveal the distribution of targets at different ranges, while the FFT in the pulse dimension reveals the distribution of targets at Doppler frequencies (i.e., velocities). Extract the amplitude information from the 2D FFT results, usually by calculating the modulus of complex elements. The amplitude matrix represents the signal strength under different combinations of range and velocity, and is the basis of the range-Doppler detection matrix. Take the amplitude matrix as the range-Doppler detection matrix, where the rows represent range bins and the columns represent Doppler frequencies (or velocities). This matrix can be used to detect and analyze the distribution of targets at different ranges and velocities.

[0128] Further, in steps A4 and B4, SOGO-CFAR is a constant false alarm rate (CFAR) detection technique used to detect targets in radar echo data. The CFAR technique can automatically adjust the detection threshold according to the background noise level to maintain a constant false alarm probability. SOGO-CFAR is particularly suitable for non-uniform clutter environments. It sets the detection threshold by selecting the highest average power among surrounding cells as a reference, thereby improving the target detection performance in complex environments.

[0129] In radar data, targets usually appear as bright spots in the range-Doppler (or velocity) two-dimensional space. The two-dimensional SOGO-CFAR processing applies the CFAR technique in this two-dimensional space to simultaneously obtain the range and velocity information of targets. In this embodiment, by comparing the signal strength of each cell with the threshold value calculated from surrounding cells, it can be determined which cells contain target signals.

[0130] Further, in steps A5 and B5, the mathematical principle and advantages of the MVDR algorithm in angle estimation are as follows:

[0131] The mathematical expression of the MVDR beamforming algorithm is as follows, and the received signal model function is expressed as the following formula:

[0132]

[0133] where \(x(t)\) is an \(M\times1\) received signal vector, \(k\) is the number of signal sources, \(a(\theta\) k ) is the direction vector of the \(k\)th signal source, \(\theta\) k is the incoming wave direction of the \(k\)th signal, \(s\)k (t) is the signal of the k-th signal source, and n(t) is the additive noise.

[0134] The objective function formula is expressed as the following formula:

[0135] J(w) = w H Rw + λ(w H a(θ d ) - 1)

[0136] where w is the weight vector, R = E[x(t)x H (t)] is the covariance matrix of the received signal, λ is the Lagrange multiplier, and θ d is the direction of the desired signal;

[0137] Taking the derivative of J(w) with respect to w and setting it to zero, the optimal weight vector can be obtained as:

[0138]

[0139] The output signal after beamforming is:

[0140]

[0141] Among them, the advantages of the MVDR algorithm are as follows:

[0142] High resolution, can distinguish signal sources with small angular intervals, and has good signal processing effect in multipath environments; strong adaptability, can adjust the weight vector according to the received signal environment, adapt to different interference noises, and does not require prior knowledge of the statistical characteristics of signals and interferences; good robustness, has a certain tolerance for model errors and measurement noises, strong versatility, and can work stably in complex environments; significant signal enhancement, enhances the strength of the desired signal, suppresses interference noises, improves the signal-to-noise ratio, and is conducive to the detection and processing of weak signals.

[0143] As Figure 3 shown, in step S4, the generation processing flow of the amplitude-phase feature matrix specifically includes the following steps:

[0144] Step C1: 1-dimensional distance FFT. For the ADC data of the echo signal, select the data frame of a fixed channel in all antenna receiving channels, and extract the chirp data with a fixed serial number from each frame of received data for 1-dimensional distance FFT operation to obtain the 1-dimensional FFT data;

[0145] Step C2: Amplitude-phase information calculation. Calculate the modulus value of the 1D FFT data obtained from signal processing to get the amplitude information, and use the arctangent method to calculate the phase, thus forming an amplitude-phase feature matrix. Among them, after 1D FFT, half of the distance units, a total of 64 distance units, are taken. The calculation of amplitude-phase information is arranged in order, obtaining a total of 128 data for amplitude and phase. Cache the currently extracted amplitude-phase sequence in chronological order, with a total of 128 frames cached, forming an amplitude-phase feature matrix of 128 rows and 128 columns.

[0146] As Figure 5 shown, in step S5, process the fused 3D point cloud data, which specifically includes the following steps:

[0147] Step D1: Data screening. Screen the fused 3D point cloud data. The screening principle is to filter based on the target distance, speed, horizontal angle, vertical angle, and the maximum and minimum ranges of amplitude, removing invalid data with large speed, small amplitude, and outside the car cabin.

[0148] Step D2: Data caching. Circularly cache the filtered 3D point cloud data. After caching 50 frames, perform further processing. The accumulated 3D cloud data can greatly improve the quality of target point cloud information and facilitate the implementation of subsequent in-vehicle detection strategies.

[0149] Step D3: Data clustering. Use the Mean Shift algorithm to perform clustering on the fused 50-frame 3D point cloud data, and extract the feature information of the clusters after clustering, mainly including the length, width, height of the cluster, the coordinates of the cluster center point, the number of target points included in the cluster, and the accumulated sum of amplitudes of all points included in the current cluster.

[0150] Step D4: Cluster tracking. Use the Extended Kalman Filter to perform filtering and aircraft tracking on the center point of the cluster after clustering; based on the boundary conditions of the car space distribution, it can provide a basis for judging whether the target enters or leaves the car.

[0151] As Figure 4 shown, step D5: Region judgment. According to the space layout inside the car cabin and the installation position of the radar, divide the inside of the car cabin into multiple in-vehicle detection regions. For example, divide the inside of the car cabin into 8 in-vehicle detection regions such as the driver's seat area, co-driver's seat area, left footrest area, middle footrest area, right footrest area, rear left seat area, rear middle seat area, and rear right seat area, with region numbers 0, 1, 2, 3, 4, 5, 6, 7.

[0152] Step D6: Presence detection strategy. As Figure 7As shown in the figure, based on the clustered cluster information, filter out the clusters with fewer target points in the clusters, and mark the filtered clusters and the target points in the clusters as noise, and no longer participate in subsequent judgments; after completing the screening of noise targets, based on the set 8 target partition detection ranges, count the data points in the clusters, and count the total number of targets in each partition and the sum of the amplitudes of the targets in that partition; after completing the statistics of the number and amplitude sum of all target areas, it is necessary to further sum the number of targets and amplitude sum statistically in the 8 detection partitions to obtain the all_cnt and all_amp_cnt data. Finally, make a decision whether there is a living target through the threshold method. For example, judge whether there is a living target by judging whether all_cnt and all_amp_cnt are both greater than the preset threshold 1 and threshold 2 and other conditions; through noise target filtering and target data partition statistics, the interference of non-living targets in different positions such as skylights, windows, and armrests can be greatly reduced.

[0153] Furthermore, as Figure 6 shown in the figure, in step D3, optimize the Mean Shift algorithm, which specifically includes the following steps:

[0154] The Mean Shift algorithm is an iterative algorithm based on non-parametric probability density estimation and is commonly used in fields such as clustering and image segmentation.

[0155] Let x be a data point about x in a d-dimensional space. There are n data points x 1 , x 2 , …, x n in the d-dimensional space. The probability density estimate of the kernel function K(x) at the data point x is the following formula:

[0156]

[0157] where K(x) is a kernel function, usually a symmetric function about x, such as a Gaussian kernel function.

[0158] where the Mean Shift vector is defined as the following formula:

[0159]

[0160] where g(x) = k(x) p , p is a constant. Usually, g(x) is also a kernel function. Generally, g(x) = K(x). When K(x) is a Gaussian kernel function, g(x) is also a Gaussian kernel function.

[0161] The iterative process of the Mean Shift algorithm:

[0162] Given an initial point x 0, in each iteration, calculate the Mean Shift vector m(x) of the current point, and then update the current point to x = x + m(x). Continuously repeat this process until the convergence condition is met.

[0163] The convergence condition can usually be set to that the norm of the Mean Shift vector is less than a certain threshold, or the number of iterations reaches a certain value. The Mean Shift algorithm makes the data points move in the direction of increasing probability density through continuous iteration, and finally converges to the local maximum points of the probability density. These local maximum points can be regarded as the clustering centers of the data.

[0164] In this embodiment, the clustering optimization of the Mean Shift algorithm: Obviously, directly performing iterative clustering on 50 frames of 3D point cloud data on an embedded platform will consume a large amount of computing resources and may not be suitable for lightweight processors. In this embodiment, algorithm optimization is carried out during the use of the algorithm, specifically including:

[0165] Grouping of 3D point cloud data: Randomly split the 50-frame point cloud data, with 10 frames of data as a group, and a total of 5 groups of 3D point cloud data are split;

[0166] Data grouping and clustering: Use the Mean Shift algorithm to cluster the 5 groups of 3D point cloud data respectively;

[0167] Clustering cluster merging: Calculate the pairwise correlation of the 5 groups of clustered clusters, and merge the two clusters with higher similarity.

[0168] As Figure 8 shown, in step S6, execute the machine learning algorithm SVM, which specifically includes the following steps:

[0169] Step E1: Training of SVM model parameters. Divide the pre-collected data into a training set and a test set and input them into the SVM model for training. Stop training after the prediction accuracy of the trained SVM model parameters for the test set data is greater than 99%;

[0170] Step E2: Extract the trained SVM classifier model parameters and the prepared amplitude-phase matrix data;

[0171] Step E3: Data preprocessing. Perform a moving average filtering algorithm on the cached 128-frame amplitude-phase matrix data column by column; further normalize the processed data to between -1 and 1.

[0172] The normalization formula is:

[0173]

[0174] Among them, n = 1, 2, …, N, where N represents the number of columns of the amplitude-phase matrix, Xn represents the time series of the n-th column of the amplitude-phase matrix, Xnmin represents the minimum value of the time series, Xnmax represents the maximum value of the time series, and Yn represents the normalized time series.

[0175] Step E4: Predict the amplitude-phase time series formed by the amplitude matrix data of all range cells. A total of 128 outputs are predicted. Use the pre-trained SVM classification model parameters to classify the 128 inputs of the amplitude-phase feature matrix, and count the results. Save the number of times of all predicted living targets in the current 128 input prediction results, and save the current prediction success times in the circular buffer. The maximum buffer stores 5 frames of prediction results.

[0176] Step E5: Count the classification results in the circular buffer of 5 consecutive frames, and decide whether there is a living target under classification through the threshold comparison method. Making a decision on whether there is a living target finally by counting the data of the SVM classification results of multiple consecutive frames has a good interference suppression effect and avoids the misjudgment problem of the living presence detection caused by occasional classification errors.

[0177] Furthermore, in step S6, the machine learning algorithm SVM using the Gaussian kernel function is used to handle non-linear classification problems. The Gaussian kernel function is defined by the following formula:

[0178] K(x i ,x j ) = exp(-γ∥x i -x j ∥ 2 )

[0179] Among them, γ > 0 is a parameter that controls the range of the function.

[0180] For the linearly inseparable case, the optimization objective of SVM is to minimize where ξ i is the slack variable used to handle inseparable data points, and c > 0 is the penalty parameter.

[0181] Among them, the constraint condition is: y i (w·x i +b) ≥ 1 - ξ i ,ξ i ≥ 0, i = 1, 2, …, n.

[0182] Introduce the Lagrange multipliers α i and μ i , and construct the Lagrangian function, which is expressed by the following formula:

[0183]

[0184] For w, b, and ξ i Calculate the partial derivatives and set the results to zero to obtain: α i + μ i = C. Substitute these results into the Lagrangian function to obtain the dual problem:

[0185] Maximize Subject to the constraint 0 ≤ α i ≤ C,

[0186] The decision function. Solve the dual problem to obtain the optimal solution α * and calculate b * , which can be calculated through any support vector that satisfies and is expressed by the following formula:

[0187]

[0188] The final decision function is expressed by the following formula:

[0189]

[0190] For the SVM with a Gaussian kernel function, the decision function is expressed by the following formula:

[0191]

[0192] By introducing the SVM algorithm with a kernel function as an advanced machine learning technique, it plays an important role in this patent. Through the innovation and application of the SVM algorithm, this patent provides new ideas and methods for the development of related technical fields.

[0193] As Figure 9 shown, the respiratory feature signals are collected only under the condition that the living target is stationary, and are the signal graphs before and after smoothing respectively. These signals can be classified by the SVM algorithm of the S machine learning method.

[0194] As Figure 10 shown, it is the extracted amplitude-phase feature matrix, with a total of 128 samples arranged in order row by row for each frame. The data frames are stacked in chronological order, forming a feature matrix of size 128x128 in total. Among them, the time series formed by columns is used as the prediction object, with a total of 128 data for prediction input.

[0195] In summary, a method for in-vehicle living body detection based on the fusion of point cloud tracking and machine learning algorithms provided in this embodiment can comprehensively and accurately detect living body targets in the vehicle cabin, providing an important technical guarantee for vehicle safety.

[0196] Furthermore, by integrating dynamic and static in-vivo detection methods, the present invention achieves stable detection of moving and stationary in-vivo objects in the vehicle cabin. For dynamic object detection, signal processing is performed using the current frame 1D FFT data and the reconstructed 1D FFT data accumulated over multiple frames, greatly improving the sensitivity of detecting the speed of moving objects and effectively capturing the dynamic characteristics of moving in-vivo objects. Clustering and segmentation of the 3D point cloud data accumulated over multiple frames can highly restore the contour and volume size of the real object. By combining with the layout of the vehicle cabin to divide the detection area, the number of target points and amplitude within the area are statistically analyzed and compared with a preset threshold to accurately determine whether there is an in-vivo object target. This method has a high suppression and filtering effect on non-in-vivo interference and improves the detection accuracy.

[0197] Furthermore, for static in-vivo object targets, the present invention innovatively uses the method of extracting the breathing micro-motion scattering signal of the target for judgment. By constructing an amplitude-phase feature matrix to extract the breathing micro-motion scattering signal of the target, the problem of poor detection accuracy caused by environmental noise interference in traditional methods is avoided. By training the SVM algorithm model, the extracted micro-motion amplitude-phase feature matrix is directly classified to determine whether there is an in-vivo object target. This method not only improves the detection stability and accuracy of static in-vivo object targets, but also reduces the algorithm complexity and improves the generality, especially the applicability in complex environments is stronger.

[0198] Furthermore, the present invention uses two completely different algorithms and ideas, dynamic and static, to perform operations in parallel, making full use of computing resources and improving the detection efficiency. Through parallel processing, it can quickly respond to the in-vehicle in-vivo detection requirements and provide real-time guarantee for in-vehicle safety.

[0199] Furthermore, by integrating multiple detection technologies and algorithms, the present invention forms complementary advantages, enhancing the robustness and reliability of the system. Regardless of the complex in-vehicle environment or in-vivo state, it can maintain stable detection performance and provide strong technical support for vehicle safety.

[0200] The above embodiments are only the preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantive changes and substitutions made by those skilled in the art based on the present invention belong to the scope of protection required by the present invention.

Claims

1. A method for detecting living bodies in a car cabin based on fusion point cloud tracking and machine learning algorithm SVM, characterized in that: The method comprises the following steps: Step S1: after the vehicle is turned off and locked externally, the radar is initialized and started, a continuous linear frequency modulation signal is emitted to detect the area inside the vehicle, and the ADC echo signal of the millimeter wave radar is synchronously collected; Step S2: pre-processing the collected ADC echo signal; Step S3: extracting 3D point cloud data from the preprocessed data; Step S4: extracting an amplitude phase matrix corresponding to the 3D point cloud data; Step S5: Processing the fused 3D point cloud data, and judging whether there is a living target in the car based on the features of the 3D point cloud data; Step S6: using the machine learning algorithm SVM to perform prediction and classification processing on the collected amplitude and phase matrix data, and outputting the result of whether there is a living target; Step S7: Fusion the liveness detection classification result predicted by the machine learning algorithm SVM with the liveness detection result in the 3D point cloud mode to determine whether there is a live target in the vehicle.

2. The method according to claim 1, characterized in that In step S3, the execution process of processing the current data frame signal to generate fast time dimension 3D point cloud data specifically includes the following steps: Step A1: Perform 1D distance FFT processing, perform 1D FFT algorithm processing on the collected ADC echo signal, obtain target information at different distances according to the relationship between distance and frequency R=c / 2f, and obtain the distance FFT spectrum, where c is the speed of light, f is the frequency of the intermediate frequency signal, and R is the distance of the target; Step A2: Perform static background removal, use the circle fitting method to process the distance FFT data in each frame, by finding the center of each frame of IQ data and subtracting the center from each data; Step A3: Doppler FFT, performing 2D Doppler FFT processing on the data obtained after the static background removal processing, and calculating amplitude information based on the obtained 2D Doppler data, thereby forming a range-Doppler detection matrix; Step A4: Perform SOGO-CFAR target detection, and then perform two-dimensional SOGO-CFAR processing on the detection matrix to obtain the distance and speed information of the target point; Step A5: Perform angle estimation using the MVDR algorithm, and use the wave velocity synthesis method MVDR algorithm to calculate the azimuth and elevation angles of the target to obtain fast time-dimensional point cloud data.

3. The method according to claim 2, characterized in that In step S3, the execution process of reconstructing the 1-dimensional FFT data to generate the slow-time 3D point cloud data specifically includes the following steps: Step B1: reconstruct the 1D FFT data, extract the 1D FFT data of a chirp with a fixed sequence number in each frame of received data, and extract K consecutive chirps as new data frames in a continuous K frame period; Step B2: Perform static background removal, and process the reconstructed 1D FFT data using a circle fitting method by finding the center of each frame of IQ data and subtracting the center from each data; Step B3: performing Doppler FFT processing, performing 2D Doppler FFT processing on the data obtained after the static background removal processing, and calculating amplitude information based on the obtained 2D Doppler data, thereby forming a range-Doppler detection matrix; Step B4: Perform SOGO-CFAR target detection, and then perform two-dimensional SOGO-CFAR processing on the detection matrix to obtain the distance and speed information of the target point; Step B5: perform angle estimation using the MVDR algorithm, and use the MVDR algorithm, a wave velocity synthesis method, to calculate the azimuth and elevation angles of the target to obtain the target slow-time dimension 3D point cloud data; Step B6: Fusing 3D point cloud data, merging the slow-time dimension 3D point cloud data and the fast-time dimension 3D point cloud data.

4. The method according to claim 3, characterized in that: In steps A5 and B5, the mathematical expression of the MVDR beamforming algorithm is as follows: The received signal model function is expressed as the following formula: Where x(t) is the M x 1 received signal vector, k is the number of signal sources, and a(θ k ) is the direction vector of the kth signal source, θ k is the direction of the kth signal, s k (t) is the signal of the kth source, n(t) is the additive noise; The objective function formula is expressed as the following formula: J(w)=w H Rw+λ(w H a(θ d )-1) Where w is the weight vector, R = E[x(t)x H (t)] is the covariance matrix of the received signal, λ is the Lagrange multiplier, θ d is the expected signal direction; Taking the derivative of J(w) with respect to w and setting it to zero, we can get the optimal weight vector: The output signal after beamforming is:

5. The method according to claim 1, characterized in that In step S4, the generation process of the amplitude-phase characteristic matrix specifically includes the following steps: Step C1: Select a data frame of a fixed channel from all antenna receiving channels, extract a chirp data with a fixed sequence number from each frame of received data, perform a 1D distance FFT operation, and obtain 1D FFT data; Step C2: Calculate the modulus of the 1-dimensional FFT data to obtain amplitude information, use the inverse tangent phase method to calculate the phase, and construct an amplitude-phase feature matrix.

6. The method according to claim 1, characterized in that In step S5, the fused 3D point cloud data is processed, specifically including the following steps: Step D1: Data screening, data screening of the fused 3D point cloud data; Step D2: data caching, cyclic caching of the filtered 3D point cloud data; Step D3: Data clustering: using the mean shift algorithm to cluster the fused 3D point cloud data and extract the characteristic information of the clusters after clustering; Step D4: Cluster tracking, using an extended Kalman filter to filter the cluster center points after clustering and perform aircraft tracking processing; Step D5: Area determination: according to the spatial layout of the car cabin and the installation position of the radar, the car cabin is divided into multiple living body detection areas; Step D6: There is a detection strategy. Based on the cluster information after clustering, the clusters with fewer target points in the cluster are filtered out, and the filtered clusters and the target points in the clusters are marked as noise, which will not participate in subsequent judgments; after completing the noise target screening, the data points in the cluster are counted based on the set multiple target partition detection ranges, and the total number of targets in each partition and the amplitude sum of the targets in the partition are counted; after completing the number, amplitude and statistics of all target areas, it is necessary to further sum the number and amplitude sum of the targets counted in multiple detection partitions to obtain all_cnt and all_amp_cnt data, and finally use the threshold method to decide whether there is a living target.

7. The method according to claim 6, characterized in that In step D3, the mean shift algorithm MeanShift is optimized, specifically including the following steps: Let x be a data point about x in d-dimensional space. There are n data points x1, x2, …, x in d-dimensional space. n , the probability density of the kernel function K(x) at the data point x is estimated as follows: Among them, K(x) is a kernel function, which is a symmetric function about x; Among them, the Mean Shift vector is defined as the following formula: Where g(x) = k(x) p , p is a constant, usually g(x) is also a kernel function, generally take g(x) = K(x), when K(x) is a Gaussian kernel function, g(x) is also a Gaussian kernel function.

8. The method according to claim 1, characterized in that The clustering optimization of the mean shift algorithm Mean Shift specifically includes: 3D point cloud data grouping: 50 frames of point cloud data are randomly divided into 5 groups of 3D point cloud data, with 10 frames of data as a group; Data grouping and clustering: The Mean Shift algorithm is used to cluster the 5 groups of 3D point cloud data respectively; Cluster merging: The correlation between the five clusters is calculated pairwise, and the two clusters with higher similarity are merged.

9. The method according to claim 1, characterized in that: In step S6, executing the machine learning algorithm SVM specifically includes the following steps: Step E1: Model parameter training, by dividing the pre-collected data into a training set and a test set and inputting them into the SVM model for training; Step E2: extracting the trained SVM classifier model parameters and the prepared amplitude-phase matrix data; Step E3: Data preprocessing, performing moving average filtering algorithm processing on the cached multi-frame amplitude phase matrix data by column; further normalizing the processed data to between positive and negative 1; Step E4: The amplitude matrix data of all distance units constitute an amplitude phase time series for prediction, and the amplitude phase feature matrix is ​​classified using the pre-trained SVM classification model parameters, and the result process is counted, and the number of times all living targets are predicted in the current multiple input prediction results is saved, and the current number of successful predictions is saved in the circular cache; Step E5: Count the classification results in the circular buffer of 5 consecutive frames, and decide whether there is a living target under the classification by threshold comparison method.

10. The method according to claim 1, characterized in that In step S6, a machine learning algorithm SVM using a Gaussian kernel function is used to process nonlinear classification problems. The Gaussian kernel function is defined as the following formula: K(x i ,x j )=exp(-γ∥x i -x j ∥ 2 ) Among them, γ>0 is a parameter that controls the scope of the function; For the case of linear inseparability, the optimization goal of SVM is to minimize where ξ i is a slack variable used to deal with inseparable data points, and c>0 is a penalty parameter; The constraints are: i (w·x i +b)≥1-ξ i ,ξ i ≥0,i=1,2,…,n; Introducing the Lagrange multiplier α i and μ i , construct the Lagrangian function, expressed as the following formula: For e, b and ξ i Calculate the partial derivative and set it to zero to get: α i +μ i =C, substituting these results into the Lagrangian function, we get the dual problem: maximize The constraint is 0≤α i ≤C, Decision function, solve the dual problem to get the optimal solution α * , and calculate b * , can be satisfied by any The support vector is calculated and expressed as the following formula: The final decision function is expressed as the following formula: For the SVM with Gaussian kernel function, the decision function is expressed as the following formula:

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