An image tracking method based on filtering algorithm
By combining particle filtering and Kalman filtering algorithms, the occlusion problem in target tracking is solved, improving the robustness and accuracy of target tracking and preventing target loss.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2024-06-29
- Publication Date
- 2026-06-19
AI Technical Summary
Existing target tracking technologies suffer from decreased tracking accuracy and precision due to factors such as lighting, scale changes, and target occlusion in motion scenarios, especially when occlusion occurs, making it easy to lose the target.
By combining particle filtering and Kalman filtering algorithms, target edge information is obtained through contour method, coarse tracking is performed using particle filtering, the KCF_DCF algorithm is used to obtain the particle filter position and scale response, the occlusion area is determined by weighted response coefficients, and Kalman filtering is used for prediction to improve positioning accuracy.
It improves the robustness and accuracy of target tracking, prevents target loss under occlusion conditions, and achieves stable tracking.
Smart Images
Figure CN118864509B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of image tracking technology, and in particular to an image tracking method based on a filtering algorithm. Background Technology
[0002] Target tracking technology is a comprehensive core technology integrating high-tech fields such as image processing, artificial intelligence, pattern recognition, and automatic control. It is one of the core problems in the field of computer vision and has wide applications in many areas, such as video surveillance, autonomous driving, military, and robot autonomous navigation. It tracks moving targets in video, capturing their features after identification, and then tracking them in the next frame of the video image, thereby achieving target monitoring and even aiming.
[0003] In practical applications, the complexity of motion scenes, leading to issues such as lighting, scale changes, and target occlusion, significantly impacts the accuracy and precision of target tracking. Therefore, addressing occlusion is one of the main challenges in target tracking.
[0004] Particle filtering and Kalman filtering are both filtering algorithms used for state estimation. They can infer the system's state even with measurement errors and system noise, and can also be applied to target tracking. Particle filtering estimates the state through particle weights and matches them in the image to obtain the target's position, thus achieving target tracking. During execution, target occlusion can occur. This can be addressed by dividing the target into regions, applying particle filtering, and then combining this with Kalman filtering for target localization to improve accuracy. Therefore, this paper proposes a localization method combining particle filtering and Kalman filtering, incorporating region response judgment to improve target tracking accuracy and enhance the robustness of the target tracking algorithm. Summary of the Invention
[0005] The purpose of this invention is to provide an image tracking method based on a filtering algorithm, which solves the occlusion problem in the target tracking process and improves the robustness of the target tracking system.
[0006] The technical solution adopted in the image tracking method based on filtering algorithm disclosed in this invention is as follows:
[0007] An image tracking method based on a filtering algorithm includes the following steps:
[0008] S1. Process the video images to obtain frame-by-frame image information;
[0009] S2. Read image frame information, set an initial search window from relevant frame images, determine the target object to be tracked, use the contour method to obtain the edge information of the target object to be tracked, use the Monte Carlo method to extract edge points for auxiliary particle filtering; use the Histogram of Oriented Gradients (HOG) method to extract the target features of the selected edge point region;
[0010] S3. Use the particle filter algorithm to perform coarse tracking of the target and obtain the preliminary positioning of the target.
[0011] S4. Use the KCF_DCF target tracking algorithm to obtain the position and scale response of the particle filter in each divided region;
[0012] S5. Compare and judge the regional response results, and use the weighted response coefficient L to judge the threshold. If it is greater than the set threshold, proceed to step S6; if it is less than the threshold, proceed to step S7.
[0013] S6. If the result is greater than the threshold, output the location result directly as the final result;
[0014] S7. If the value is less than the threshold, it is determined to be an occluded area, and Kalman filtering is performed on the particles in the unoccluded area for prediction. The prediction result is used as the target localization result.
[0015] As a preferred embodiment, step S2 specifically includes:
[0016] Select the target area by using B. k The rectangle represents the target region at time k. This rectangle serves as the search window. As the target moves and changes, the target lock and size are adjusted. Target analysis is performed within the rectangular region, and the contour method is used to obtain the target edge.
[0017] The Canny edge detection algorithm is used to extract the target edges; the region image is then smoothed using a two-dimensional Gaussian function, as shown below:
[0018]
[0019] The gradient vector is represented as:
[0020]
[0021] Finite difference spectroscopy is used to obtain the gradient magnitude and gradient direction of the data array, using P. x [i, j], P y [i, j] represents the array of partial derivatives in the x and y directions:
[0022] P x [i,j]=(I[i,j+1]-I[i,j]+I[i+1,j+1]-I[i+1,j]) / 2
[0023] P y [i,j]=(I[i,j]-I[i+1,j]+I[i,j+1]-I[i+1,j+1]) / 2
[0024] The gradient magnitude M[i,j] and gradient direction θ[i,j] of a pixel are represented as follows:
[0025]
[0026] θ[i,j]=arctan(P) y [i, j] / P x [i, j])
[0027] Non-maximum suppression refines the gradient magnitude:
[0028] N[i,j]=NMS(M[i,j],S[i,j])
[0029] S[i,j] is the fan-shaped region along the gradient direction of the pixel neighborhood center, which is also the execution region of nonmaximum suppression;
[0030] Non-maximum suppression subgraph N[i,j] is passed through high and low thresholds T h T l After segmentation, T is obtained h [i, j], T l [i, j], where T h [i, j] does not contain false edges. Using the Monte Carlo method, from Th... [ Extract auxiliary positioning points from [i, j].
[0031] As a preferred embodiment, step S3 specifically includes:
[0032] To initialize the particle set, firstly, for the initial N particles, sampled particles are generated based on the prior probability P(x0), which is the probability distribution of the moving target in the initial state.
[0033] As the video frames progress, for the state at time k (k = 1, 2, ...), sampling particles are generated from the importance probability density. Then the particle weights are calculated. Then normalization is performed;
[0034] Furthermore, the recursive method for particle weights is as follows:
[0035]
[0036] Resampling of particle set The resampled particle set is:
[0037] After performing k iterations on the above results, the state estimate at time k is obtained:
[0038]
[0039] As a preferred embodiment, step S4 specifically includes:
[0040] The target region is divided into left and right, and top and bottom regions. Taking the left region as an example, the samples include:
[0041] x = [x1, x2, ... x] n ] T
[0042] n represents the number of particles in the corresponding region. By multiplying by the cyclic matrix P on the left, the displacement can be obtained, thus yielding the cyclic matrix, which is the set of all displacements X:
[0043]
[0044] The set of all circular matrices can be represented diagonally by the Discrete Fourier Transform (DFT):
[0045]
[0046] Where F represents a constant matrix that is independent of the matrix. The Fourier transform of x, i.e.
[0047] The training objective of the KCF algorithm is to find a function f(z) = w T z, such that sample x i And the squared error of the regression objective is minimized, that is:
[0048]
[0049] The regularization parameter w, obtained by the regression method, is expressed as follows:
[0050]
[0051] Mapping the input of a linear problem to a nonlinear feature space, w can then be represented as a linear combination of samples:
[0052]
[0053] Where a i =[a1,a2,…,a n ] T As weight, For kernel functions, it can be represented as The weights are obtained through fast kernel regression using a circular matrix:
[0054]
[0055] in, For the kernel matrix K = C(k) xx The first row of the image, and the cyclic matrix generated by cyclically shifting the image z at the same position in the next frame, are then defined as follows:
[0056] K 2 =C(k) x2 )
[0057] Where k xz This represents the kernel correlation between x and z, and the regression function can be calculated as:
[0058] f(z))=(K z ) T α
[0059] Where f(z) is a vector that includes the output of all cyclic shifts of z, i.e., the complete detection response. Its discrete Fourier transform is then performed to obtain:
[0060]
[0061] As a preferred embodiment, step S5 specifically includes:
[0062] Divide the area into two parts each, left and right, and top and bottom.
[0063] By extracting auxiliary positioning particles, the particle response factors in each divided region were analyzed. Solve the problem;
[0064]
[0065] The larger the response factor value, the better the matching and tracking of the particles on the target; the smaller the response factor, the more likely the particles on the target are not being tracked or are being occluded.
[0066] Given a threshold L, if the response factor p < L, it indicates that the target particles in the region are not being tracked well, which means that occlusion has occurred; if the response factor p > L, it means that occlusion has not occurred in the region.
[0067] As a preferred embodiment, the specific steps of S7 include:
[0068] Extract regions where the response factor is greater than the threshold L, where the particle states are x = [x1, x2, ... x]. n- ], where n- represents the total number of particles in the region where the response factor is greater than the threshold, and the calculation is performed by Kalman filtering;
[0069] First, the prediction includes state prediction and covariance prediction, which are represented as follows:
[0070]
[0071] P(k|k)=AP(k|k-1)A T +Q
[0072] in It is the estimated value of the state vector at time t. A is the estimated value at time t, A represents the state transition matrix, describing the system state from the previous time to the current time, B is the input matrix, taking external factors into account in the state prediction, U(k|k-1) is the control input vector, P(k|k) is the predicted value of the state estimation covariance matrix, and Q represents the process noise covariance matrix. This quantity is introduced to avoid the influence of unmodeled noise in the process.
[0073] Secondly, the variables are updated through measurement, starting with the calculation of measurement residuals:
[0074] Y(k|k)=Z(k|k)-H k X(k|k)
[0075] Where Z(k|k) is the observed value at time t, Y(k|k) represents the difference between the observed value and the predicted value, and H... k The observation matrix describes the mapping of the state vector in the observation space, and then its covariance and residuals are calculated:
[0076] Where R represents the observation noise, the Kalman gain can be calculated from the covariance residual as follows:
[0077]
[0078] State update is represented as:
[0079]
[0080] The covariance update function is expressed as:
[0081] P(k+1|k)=(IK k H k )·P(k|k)
[0082] By updating the state values and covariance function, the next round of predictions can be made, and then corrections can be made based on the observations to achieve stable tracking results.
[0083] The beneficial effects of the image tracking method based on filtering algorithms disclosed in this invention are as follows: First, video images are processed to obtain frame-by-frame image information. The target object is determined based on the images of relevant frames. A particle filter algorithm is used for coarse tracking of the target to achieve preliminary localization. Then, the KCF_DCF target tracking algorithm is used to obtain the position and scale response of the particle filter in each segmented region. The region response results are compared and judged, and a threshold is determined using a weighted response coefficient L to finally obtain the target localization structure. Coarse localization using particle filtering achieves an efficient and effective localization method. Occlusion judgment is performed using contour region particles, thereby improving the target tracking accuracy after occlusion and preventing target loss. Attached Figure Description
[0084] Figure 1 This is a flowchart of an image tracking method based on a filtering algorithm according to the present invention.
[0085] Figure 2 This is an example of an image tracking method based on a filtering algorithm, using the original image.
[0086] Figure 3 yes Figure 2 A schematic diagram of extracting auxiliary particles for localization.
[0087] Figure 4 A comparative tracking effect diagram of an image tracking method based on a filtering algorithm.
[0088] Figure 5 This is a schematic diagram illustrating the tracking effect of an image tracking method based on a filtering algorithm. Detailed Implementation
[0089] The present invention will be further described and illustrated below with reference to specific embodiments and the accompanying drawings:
[0090] Please refer to Figure 1 An image tracking method based on a filtering algorithm includes the following steps:
[0091] S1. Process the video images to obtain frame-by-frame image information;
[0092] S2. Read image frame information, set an initial search window from relevant frame images, determine the target object to be tracked, use the contour method to obtain the edge information of the target object to be tracked, use the Monte Carlo method to extract edge points for auxiliary particle filtering; use the Histogram of Oriented Gradients (HOG) method to extract the target features of the selected edge point region;
[0093] Step S2 specifically includes:
[0094] Select the target area by using B. kThe rectangle represents the target region at time k. This rectangle serves as the search window. As the target moves and changes, the target lock and size are adjusted. Target analysis is performed within the rectangular region, and the contour method is used to obtain the target edge.
[0095] The Canny edge detection algorithm is used to extract the target edges; the region image is then smoothed using a two-dimensional Gaussian function, as shown below:
[0096]
[0097] The gradient vector is represented as:
[0098]
[0099] Finite difference spectroscopy is used to obtain the gradient magnitude and gradient direction of the data array, using P. x [i, j], P y [i, j] represents the array of partial derivatives in the x and y directions:
[0100] P x [i,j]=(I[i,j+1]-I[i,j]+I[i+1,j+1]-I[i+1,j) / 2
[0101] P y [i,j]=(I[i,j]-I[i+1,j]+I[i,j+1]-I[i+1,j+1]) / 2
[0102] The gradient magnitude M[i,j] and gradient direction θ[i,j] of a pixel are represented as follows:
[0103]
[0104] θ[i,j]=arctan(P) y [i, j] / P x [i, j])
[0105] Non-maximum suppression refines the gradient magnitude:
[0106] N[i,j]=NMS(M[i,j],S[i,j])
[0107] S[i,j] is the fan-shaped region along the gradient direction of the pixel neighborhood center, which is also the execution region of nonmaximum suppression;
[0108] Non-maximum suppression subgraph N[i,j] is passed through high and low thresholds T h T l After segmentation, T is obtained h [i, j], T l [i, j], where T h[i, j] does not contain false edges. Applying the Monte Carlo method from T... h Extract auxiliary positioning points from [i, j].
[0109] S3. Use the particle filter algorithm to perform coarse tracking of the target and obtain the preliminary positioning of the target.
[0110] To initialize the particle set, firstly, for the initial N particles, sampled particles are generated based on the prior probability P(x0), which is the probability distribution of the moving target in the initial state.
[0111] As the video frames progress, for the state at time k (k = 1, 2, ...), sampling particles are generated from the importance probability density. Then the particle weights are calculated. Then normalization is performed;
[0112] Furthermore, the recursive method for particle weights is as follows:
[0113]
[0114] Resampling of particle set The resampled particle set is:
[0115] After performing k iterations on the above results, the state estimate at time k is obtained:
[0116]
[0117] S4. Use the KCF_DCF target tracking algorithm to obtain the position and scale response of the particle filter in each divided region;
[0118] Step S4 specifically includes:
[0119] The target region is divided into left and right, and top and bottom regions. Taking the left region as an example, the samples include:
[0120] x = [x1, x2, ..., x] n ] T
[0121] n represents the number of particles in the corresponding region. By multiplying by the cyclic matrix P on the left, the displacement can be obtained, thus yielding the cyclic matrix, which is the set of all displacements X:
[0122]
[0123] The set of all circular matrices can be represented diagonally by the Discrete Fourier Transform (DFT):
[0124]
[0125] Where F represents a constant matrix that is independent of the matrix. The Fourier transform of x, i.e.
[0126] The training objective of the KCF algorithm is to find a function f(z) = w T z, such that sample x i And the squared error of the regression objective is minimized, that is:
[0127]
[0128] The regularization parameter w, obtained by the regression method, is expressed as follows:
[0129]
[0130] Mapping the input of a linear problem to a nonlinear feature space, w can then be represented as a linear combination of samples:
[0131]
[0132] Where a i =[a1,a2,...,a n ] T As weight, For kernel functions, it can be represented as The weights are obtained through fast kernel regression using a circular matrix:
[0133]
[0134] in, For the kernel matrix K = C(k) xx The first row of the image, and the cyclic matrix generated by cyclically shifting the image z at the same position in the next frame, are then defined as follows:
[0135] K z =C(k) xz )
[0136] Where k xz This represents the kernel correlation between x and z, and the regression function can be calculated as:
[0137] f(z)=(K z ) T α
[0138] Where f(z) is a vector that includes the output of all cyclic shifts of z, i.e., the complete detection response. Its discrete Fourier transform is then performed to obtain:
[0139]
[0140] S5. Compare and judge the regional response results, and use the weighted response coefficient L to judge the threshold. If it is greater than the set threshold, proceed to step S6; if it is less than the threshold, proceed to step S7.
[0141] The S5 steps specifically include:
[0142] Divide the area into two parts each, left and right, and top and bottom.
[0143] By extracting auxiliary positioning particles, the particle response factors in each divided region were analyzed. Solve the problem;
[0144]
[0145] The larger the response factor value, the better the matching and tracking of the particles on the target; the smaller the response factor, the more likely the particles on the target are not being tracked or are being occluded.
[0146] Given a threshold L, if the response factor p < L, it indicates that the target particles in the region are not being tracked well, which means that occlusion has occurred; if the response factor p > L, it means that occlusion has not occurred in the region.
[0147] S6. If the value is greater than the threshold, the location result will be output directly as the final result.
[0148] S7. If the value is less than the threshold, it is determined to be an occluded area and Kalman filtering is performed on the particles in the unoccluded area for prediction. The prediction result is used as the target localization result.
[0149] The specific steps in S7 include:
[0150] Extract regions where the response factor is greater than a threshold L, where the particle states are x = [x1, x2, ... x]. n- ], where n- represents the total number of particles in the region where the response factor is greater than the threshold, and the calculation is performed by Kalman filtering;
[0151] First, the prediction includes state prediction and covariance prediction, which are represented as follows:
[0152]
[0153] P(k|k)=AP(k|k-1)A T +Q
[0154] in It is the estimated value of the state vector at time t. A is the estimated value at time t, A represents the state transition matrix, describing the system state from the previous time to the current time, B is the input matrix, taking external factors into account in the state prediction, U(k|k-1) is the control input vector, P(k|k) is the predicted value of the state estimation covariance matrix, and Q represents the process noise covariance matrix. This quantity is introduced to avoid the influence of unmodeled noise in the process.
[0155] Secondly, the variables are updated through measurement, starting with the calculation of measurement residuals:
[0156] Y(k|k)=Z(k|k)-H k X(k|k)
[0157] Where Z(k|k) is the observed value at time t, Y(k|k) represents the difference between the observed value and the predicted value, and H... k The observation matrix describes the mapping of the state vector in the observation space, and then its covariance and residuals are calculated:
[0158] Where R represents the observation noise, the Kalman gain can be calculated from the covariance residual as follows:
[0159]
[0160] State update is represented as:
[0161]
[0162] The covariance update function is expressed as:
[0163] P(k+1|k)=(IK k H k )·P(k|k)
[0164] By updating the state values and covariance function, the next round of predictions can be made, and then corrections can be made based on the observations to achieve stable tracking results.
[0165] Figure 2 It is the original image; Figure 3 In diagram (a), the target contour is extracted using the contour method; (b), Monte Carlo extraction of auxiliary positioning particles is performed on the contour edge points; (c), a schematic diagram shows the auxiliary particles after horizontal and vertical segmentation; and (d), a schematic diagram shows the auxiliary particles after vertical and horizontal segmentation. (Reference) Figure 4 For image tracking methods using particle filtering alone, the localization bounding box drifts over time when occlusion exists. Figure 5 The method shown is a tracking method of the present invention, which exhibits good tracking ability under occlusion conditions.
[0166] This invention provides an image tracking method based on a filtering algorithm. First, video images are processed to obtain frame-by-frame image information. The target object is determined based on the images of relevant frames. A particle filter algorithm is used for coarse tracking of the target to achieve preliminary localization. Then, the KCF_DCF target tracking algorithm is used to calculate the position and scale response of the particle filter in each segmented region. The region response results are compared and judged, and a threshold is determined using a weighted response coefficient L to finally obtain the target localization structure. The coarse localization using particle filtering achieves an efficient and effective localization method. Occlusion detection using contour region particles improves the accuracy of target tracking after occlusion and prevents target loss.
[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.
Claims
1. An image tracking method based on a filtering algorithm, characterized in that, Includes the following steps: S1. Process the video images to obtain frame-by-frame image information; S2. Read image frame information, set an initial search window from relevant frame images, determine the target object to be tracked, use the contour method to obtain the edge information of the target object to be tracked, and use the Monte Carlo method to extract edge points for auxiliary particle filtering; The target features of the selected edge point region are extracted using the Histogram of Oriented Gradients (HOG) method. S3. Use the particle filter algorithm to perform coarse tracking of the target and obtain the preliminary positioning of the target. S4. Use the KCF_DCF target tracking algorithm to obtain the position and scale response of the particle filter in each divided region; S5. Compare and evaluate the regional response results using weighted response coefficients. Perform a threshold judgment. If the threshold is greater than the set threshold, proceed to step S6; if the threshold is less than the threshold, proceed to step S7. S6. If the result is greater than the threshold, output the location result directly as the final result; S7. If the value is less than the threshold, it is determined to be an occluded area, and Kalman filtering is performed on the particles in the unoccluded area for prediction. The prediction result is used as the target localization result.
2. The image tracking method based on a filtering algorithm as described in claim 1, characterized in that, The S2 step specifically includes: Select the target area by drawing a box. The rectangle represents the target region at time k. This rectangle serves as the search window. As the target moves and changes, the target lock and size are adjusted. Target analysis is performed within the rectangular region, and the contour method is used to obtain the target edge. The Canny edge detection algorithm is used to extract the target edges; the region image is then smoothed using a two-dimensional Gaussian function, as shown below: The gradient vector is represented as: Finite difference finite difference is used to obtain the gradient magnitude and gradient direction of the data array. , represent x and Array of partial derivatives in the y-direction: Pixel gradient magnitude and gradient direction It is expressed as follows: Non-maximum suppression refines the gradient magnitude: is a sector region of the pixel neighborhood center along the gradient direction, and is also the execution region of non-maximum suppression; Subgraph of nonmaximum suppression By high and low thresholds , After segmentation, the result is , ,in Without false edges, the Monte Carlo method is used to... Auxiliary positioning points are extracted from them.
3. The image tracking method based on filtering algorithm as claimed in claim 1, wherein, The S3 step specifically includes: To initialize the particle set, first, for the initial N particles, use prior probabilities... That is, the sampling particles are generated based on the probability distribution of the moving target in the initial state. ; As the video frames advance, for Moment State Generate sampling particles from importance probability density Then the particle weights are calculated. Then normalize it; Furthermore, the recursive method for particle weights is as follows: Resampling of particle set The resampled particle set is: After performing k iterations on the above results, the state estimate at time k is obtained: 。 4. The image tracking method based on filtering algorithm as claimed in claim 1, wherein, The S4 step specifically includes: The target region is divided into left and right, and top and bottom regions. Taking the left region as an example, the samples include: This represents the number of particles in the corresponding region, multiplied by left. A cyclic matrix can be used to represent displacements, thus yielding a cyclic matrix, which is the set of all displacements. : The set of all circular matrices can be represented diagonally by the Discrete Fourier Transform (DFT): where F is a constant matrix independent of x, y, and z, is the Fourier transform of The training objective of KCF algorithm is to find a function such that the square error of regression target is minimized, i.e.: The regularization parameter w, obtained by the regression method, is expressed as follows: Mapping the input of a linear problem to a nonlinear feature space will... Represented as a linear combination of samples: where As weight, For kernel functions, it can be represented as The weights are obtained through fast kernel regression using a circular matrix: in, For the kernel matrix The first row, in the next frame, the same position image z is cyclically shifted to generate a cyclic matrix, then the kernel matrix is defined as: where represents , the core of z is related, and the regression function can be calculated as: wherein is a vector comprising all the cyclically shifted outputs, i.e. the complete detection response, Performing a discrete Fourier transform on it and calculating the result yields: 。 5. The image tracking method based on a filtering algorithm as described in claim 1, characterized in that, The S5 step specifically includes: Divide the area into two parts each, left and right, and top and bottom. By extracting the auxiliary positioning particles, the particle response factors in each divided region are solved respectively 、 、 、 are solved respectively; The larger the response factor value, the better the matching and tracking of the particles on the target; the smaller the response factor, the more likely the particles on the target are not being tracked or are being occluded. Given a threshold, if the response factor ρ is less than the threshold, it indicates that the target particles in the region are not being tracked well, indicating that occlusion has occurred; if the response factor ρ is greater than the threshold, it indicates that occlusion has not occurred in the region.
6. The image tracking method based on filtering algorithm as claimed in claim 1, wherein, The specific steps in S7 include: Extract the region where the response factor is greater than the threshold, where the particle's corresponding state is ,here If the response factor is greater than the threshold, then the calculation is performed using Kalman filtering. First, the prediction includes state prediction and covariance prediction, which are represented as follows: in It is the estimated value of the state vector at time t. A is the estimated value at time step 1, A represents the state transition matrix, describing the system's state from the previous time step to the current time step, and B is the input matrix, which takes external factors into account in the state prediction. This controls the input vector. It is the predicted value of the covariance matrix of the state estimate. This represents the process noise covariance matrix. Introducing this value can avoid the influence of unmodeled noise during the process. Secondly, the variables are updated through measurement, starting with the calculation of measurement residuals: in, It is the observed value at time [time]. This represents the difference between observed and predicted values. The observation matrix describes the mapping of the state vector in the observation space, and then its covariance and residuals are calculated: Where R represents the observation noise, the Kalman gain can be calculated from the covariance residual as follows: State update is represented as: The covariance update function is expressed as: By updating the state values and covariance function, the next round of predictions can be made, and then corrections can be made based on the observations to achieve stable tracking results.