A distance constraint based distributed dynamic positioning method

Abstract

The application provides a distributed dynamic positioning method based on distance constraint, uses local information and target constraint, constructs an estimator based on local consensus on each sensor; combines real-time information under distance constraint, adopts an alternating multiplier method to realize real-time single-target tracking under only distance constraint, and realizes fast and accurate single-target tracking.

Description

Technical Field

[0001] This invention belongs to the field of wireless sensor positioning technology, and particularly relates to a distributed dynamic positioning method based on distance constraints. Background Technology

[0002] In today's 5G era, with rapid technological advancements and continuous social progress, our lives are gradually entering an era of intelligence. Spatial location and information are closely related to our lives; therefore, services based on location information are becoming a hot topic. Positioning technologies mainly include outdoor and indoor positioning. In outdoor positioning, GNSS has the capability to provide precise three-dimensional positioning, timing, and velocity measurement globally, 24 / 7, meeting most outdoor positioning needs, and its technology system is relatively mature. Unlike the open outdoor environment, indoor environments are relatively small and contain structured environments such as corridors and passageways. This leads to higher accuracy requirements for indoor positioning systems compared to outdoor positioning. Indoors, satellite positioning signals based on microwave transmission are subject to blockage, resulting in weaker signals that cannot cover or penetrate buildings. Lower signal power and multipath attenuation further complicate the accuracy requirements of indoor scenarios, leading to significant positioning errors or even complete failure to locate. Due to the complex and varied structure of indoor environments and the significant differences between different locations, and the lack of a unified framework for technical standards, positioning representations, and positioning costs for indoor positioning, research on high-precision indoor positioning systems has become a hot topic.

[0003] Ultra-wideband (UWB) technology is a novel communication technology approved by the U.S. Federal Communications Commission (FCC) in 2002 for operation in public frequency bands. This technology requires strict adherence to the 3.1 GHz to 10.6 GHz communication frequency band. It does not rely on carrier waves as in traditional communication systems, but instead uses extremely narrow nanosecond-level pulses to transmit data, thus possessing excellent GHz-level bandwidth. Due to its strong penetration, low power consumption, excellent multipath resistance, high resolution, and simplified system complexity, UWB is poised to further expand its application areas and has become a research focus in the field of wireless communications. Compared to other radio signal technologies, UWB technology effectively utilizes limited spectrum resources, avoiding spectrum congestion. Furthermore, UWB technology has a low average transmit power, meaning that its use in indoor positioning systems will not interfere with other wireless communication systems, which is particularly important for indoor positioning applications. These characteristics give UWB technology significant advantages in indoor positioning and make it a hot research topic for the future. Because obtaining distance information is relatively simple, many scholars are researching positioning problems based on distance measurements. However, determining the accurate location of a target node under what wireless sensor network topology conditions is a key issue in localization research.

[0004] For the localization of mobile intelligent agents, distributed estimators have attracted increasing attention due to their scalability and robustness, and have been widely used in single-target coordination and target tracking. Currently, many studies attempt to solve these problems using the commonly employed Kalman filtering method. However, when facing distributed localization problems with distance constraints, distributed Kalman filters with nonlinear equality constraints still require further development. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a distance-constrained distributed dynamic localization method that can effectively handle the target tracking problem of intelligent agents.

[0006] A distance-constrained distributed dynamic localization method includes the following steps:

[0007] A distance measurement matrix relative to the ground vehicle is constructed for each sensor, wherein each sensor is deployed at the same height and the ground vehicle is moving in a circle around a fixed axis;

[0008] The optimization objective function is to minimize the Euclidean norm between the theoretical state of the ground vehicle and the posterior estimated state obtained by combining measurement information. The distance between the position of the ground vehicle at each time and the fixed axis is used as a constant value as the distance constraint condition for the optimization objective function to construct a local consensus estimator based on the distance measurement matrix for each sensor. The state of the ground vehicle includes the vehicle's x-axis coordinate, y-axis coordinate and vehicle orientation θ.

[0009] The ground vehicle positions in the local consensus estimator are obtained based on the scaling form of the ADMM iterative method, and the ground vehicles are tracked and located.

[0010] Furthermore, the local consensus estimator is:

[0011]

[0012]

[0013] z k,i =x k,i

[0014] Where, x k,i Let be the theoretical state of the ground vehicle obtained by the i-th sensor at time k. Let be the posterior estimated state of the ground vehicle obtained by the i-th sensor at time k by combining measurement information. Let be the posterior covariance matrix of the i-th sensor at time k. The inverse matrix, ||| 2 Let b be the Euclidean norm, b be the position coordinate of the fixed axis, and d be the Euclidean coordinate. k Let z be the known predetermined distance between the ground vehicle and the fixed axle at time k. k,i Let B be the distance measurement matrix of the i-th sensor at time k; i = 1, 2, ..., N, where N is the number of sensors; matrix B is represented as

[0015]

[0016] Distance measurement matrix z k,i The method for obtaining it is as follows:

[0017]

[0018] in, Let x be the theoretical state of the ground vehicle acquired by the i-th sensor at time k. k,i The vehicle's x-axis coordinates in the image. Let x be the theoretical state of the ground vehicle acquired by the i-th sensor at time k. k,i The vehicle's y-axis coordinate, l i(1) Let l be the x-axis coordinate of the i-th sensor. i(2) Let be the y-coordinate of the i-th sensor, h be the height of the sensor, and v be the y-coordinate of the i-th sensor. k,i The noise is Gaussian white noise for the i-th sensor at time k.

[0019] Posterior estimated state The method for obtaining it is as follows:

[0020]

[0021] in, Let K be the predicted state of the ground vehicle obtained by the i-th sensor at time k using the unconstrained EKF algorithm. k,i Let H be the measurement information matrix of the i-th sensor at time k. k-1,i Let be the partial derivative matrix of the measurement information matrix of the i-th sensor at time k-1.

[0022] Furthermore, the measurement information matrix K k,i The method for obtaining it is as follows:

[0023]

[0024] in, Let be the predicted value of the covariance matrix of the i-th sensor at time k. for The inverse matrix, H k,i Let R be the partial derivative matrix of the i-th sensor at time k with respect to the measurement information matrix. k,i Let T represent the Gaussian white measurement noise of the i-th sensor at time k, and let T denote the transpose.

[0025] Furthermore, the predicted values ​​of the covariance matrix The method for obtaining it is as follows:

[0026]

[0027] Among them, A k-1,i Let be the partial derivative of the process function of the i-th sensor at time k. Let Q be the estimated state of the ground vehicle obtained by the i-th sensor at time k-1 based on the scaled ADMM iterative method. k-1,i Let be the variance of the process noise of the i-th sensor at time k.

[0028] Furthermore, the ground vehicle positions in the local consensus estimator are solved based on the scaled ADMM iterative method, and the tracking and localization of ground vehicles are specifically achieved as follows:

[0029] Using the rotation direction method Assign to Where r represents the r-th round of the rotation direction method. Let be the posterior covariance matrix of the i-th sensor at time k. The inverse matrix of , where ρ is the augmented Lagrange parameter, and I is the identity matrix. Let be the distance measurement matrix of the i-th sensor in the r-th round at time k. Constraints in the r-th round The corresponding scaling dual variable, Let be the theoretical state of the ground vehicle obtained by the i-th sensor at time k in the r-th round. Let be the posterior estimated state of the ground vehicle obtained by the i-th sensor in the r-th round at time k by combining measurement information;

[0030] Will Assign to in, The constraints are Let x be the distance measurement matrix of the i-th sensor in the (r+1)-th round at time k. k,i r+1 Let b be the theoretical state of the ground vehicle acquired by the i-th sensor at time k in the (r+1)-th round, and d be the position coordinates of the fixed axis. k The known predetermined distance between the ground vehicle and the fixed axle at time k;

[0031] Will Assign to The ADMM iteration steps to obtain the scaled form are as follows:

[0032]

[0033]

[0034]

[0035]

[0036] Define auxiliary variables Update based on the following questions:

[0037]

[0038]

[0039] Performing eigenvalue decomposition on matrix B, we have B = UΛU T Where U is the matrix composed of the eigenvectors of matrix B, Λ is the diagonal matrix composed of the eigenvalues, and let... The above optimization problem can then be updated as follows:

[0040]

[0041]

[0042] Solving the above optimization problem using the Lagrange multiplier method yields:

[0043]

[0044]

[0045] Where, λ l Let l be the l-th eigenvalue of matrix B. Constraints in the r-th round The corresponding unscaled dual variable, To and The relevant nonlinear equations;

[0046] Solve the nonlinear equation using the equal division method. get After the value, Substitution get The value, and then the relation get The value;

[0047] Will As Substitute into the following equation:

[0048]

[0049]

[0050] Where i = 1, 2, ..., N, and N is the number of sensors. Let be the posterior covariance matrix of the i-th sensor at time k. This represents the final estimated state of the ground vehicle at time k obtained by the i-th sensor based on the scaled ADMM iterative method. This is the covariance of the i-th sensor at time k, obtained by the scaling form of the ADMM iterative method.

[0051] Beneficial effects:

[0052] This invention provides a distance-constrained distributed dynamic positioning method. It utilizes local information and target constraints to construct an estimator based on local consensus on each sensor. Combining real-time information under distance constraints, it employs the alternating multiplier method to achieve real-time single-target tracking under distance constraints only, thus realizing fast and accurate single-target tracking. Attached Figure Description

[0053] Figure 1 A flowchart of a distance-constrained distributed dynamic positioning method provided by the present invention;

[0054] Figure 2 A schematic diagram of vehicle motion with state constraints, sensor network and its communication topology provided for this invention;

[0055] Figure 3This invention provides schematic diagrams of the actual and estimated trajectories of the vehicle.

[0056] Figure 4 This diagram illustrates a comparison of the MSE values ​​of a distance-constrained distributed dynamic localization method provided by this invention with those of the CKF, DEKF, and DUKF methods. Detailed Implementation

[0057] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0058] The present invention provides a distance-constrained distributed dynamic localization method. Its core idea is to construct a distributed estimator based on the basic ideas of extended Kalman filtering and consensus iteration; and to redefine the constraints by using the alternating direction multiplier method. This method ensures that each constrained subproblem can be effectively solved.

[0059] like Figure 1 As shown, the present invention provides a distributed dynamic positioning method based on distance constraints, which specifically includes the following steps:

[0060] S1: Construct distance measurement matrices relative to the ground vehicle for each sensor, wherein each sensor is deployed at the same height and the ground vehicle is moving in a circle around a fixed axis.

[0061] It should be noted that each ground vehicle is equipped with a beacon for ranging with the sensors; the position of the ground vehicle is indicated by x. p =(x,y) T Let θ represent the direction, and let the state vector be x = (x, y, θ). T Associated with each vehicle; the vehicle's velocity and angular velocity are represented by v and ω, respectively; the control input is u = (v, ω). T Includes noise perturbation w = (w v ,w ω ) T They follow the covariance matrix Q g Given a zero-mean normal distribution, the vehicle motion model at each sampling time with a sampling time of Δt is given below:

[0062]

[0063]

[0064]

[0065]

[0066] Where k and k+1 represent time k and time k+1, respectively. and These are the measured velocity and the measured angular velocity, respectively.

[0067] For example, in a single-target node tracking simulation, the number of sensors in the vehicle tracking system is set to N=3, which needs to track M=1 ground vehicles; the fixed axis can be a lighthouse, then the ground vehicles move in a circle around the lighthouse, and their trajectory is related to the sensor network and its communication topology as follows. Figure 2 As shown; the experimental parameters were selected as follows: velocity noise perturbation w v =0, rotational angular velocity noise perturbation w ω =0, Gaussian white measurement noise R k =1; the lighthouse's position vector is b = [0, 3, 0]. T The initial position of the vehicle is x0 = [0,0,0]. T and initial position covariance

[0068] S2: The optimization objective function is to minimize the Euclidean norm between the theoretical state of the ground vehicle and the posterior estimated state obtained by combining measurement information, and the distance between the position of the ground vehicle at each time and the fixed axis is used as a constant value as the distance constraint condition of the optimization objective function to construct a local consensus estimator based on the distance measurement matrix for each sensor; wherein, the state of the ground vehicle includes the vehicle x-axis coordinate, y-axis coordinate and vehicle direction θ;

[0069] Specifically, the local consensus estimator is:

[0070]

[0071]

[0072] z k,i =x k,i

[0073] Where, x k,i Let be the theoretical state of the ground vehicle obtained by the i-th sensor at time k. Let be the posterior estimated state of the ground vehicle obtained by the i-th sensor at time k by combining measurement information. Let be the posterior covariance matrix of the i-th sensor at time k. The inverse matrix, ||| 2 Let b be the Euclidean norm, b be the position coordinate of the fixed axis, and d be the Euclidean coordinate. k Let z be the known predetermined distance between the ground vehicle and the fixed axle at time k. k,iLet B be the distance measurement matrix of the i-th sensor at time k; i = 1, 2, ..., N, where N is the number of sensors; matrix B is represented as

[0074]

[0075] Distance measurement matrix z k,i The method for obtaining it is as follows:

[0076]

[0077] in, Let x be the theoretical state of the ground vehicle acquired by the i-th sensor at time k. k,i The vehicle's x-axis coordinates in the image. Let x be the theoretical state of the ground vehicle acquired by the i-th sensor at time k. k,i The vehicle's y-axis coordinate, l i(1) Let l be the x-axis coordinate of the i-th sensor. i(2) Let be the y-coordinate of the i-th sensor, h be the height of the sensor, and v be the y-coordinate of the i-th sensor. k,i The noise is Gaussian white noise for the i-th sensor at time k.

[0078] Posterior estimated state The method for obtaining it is as follows:

[0079]

[0080] in, Let be the predicted state of the ground vehicle obtained by the i-th sensor at time k using the unconstrained EKF algorithm, i.e. i = 1, 2, 3, K k,i Let H be the measurement information matrix of the i-th sensor at time k. k-1,i Let be the partial derivative matrix of the measurement information matrix of the i-th sensor at time k-1.

[0081] Measurement Information Matrix K k,i The method for obtaining it is as follows:

[0082]

[0083] in, Let be the predicted value of the covariance matrix of the i-th sensor at time k. for The inverse matrix, H k,i Let R be the partial derivative matrix of the i-th sensor at time k with respect to the measurement information matrix. k,i Let T represent the Gaussian white measurement noise of the i-th sensor at time k, and let T denote the transpose.

[0084] Covariance matrix predicted values The method for obtaining it is as follows:

[0085]

[0086] Among them, A k-1,i Let be the partial derivative of the process function of the i-th sensor at time k. Let Q be the estimated state of the ground vehicle obtained by the i-th sensor at time k-1 based on the scaled ADMM iterative method. k-1,i Let be the variance of the process noise of the i-th sensor at time k.

[0087] S3: The ground vehicle positions in the local consensus estimator are obtained based on the scaling form of the ADMM iterative method, and the tracking and localization of ground vehicles are realized. Specifically, the following steps are included:

[0088] Using the rotation direction method Assign to Where r represents the r-th round of the rotation direction method. Let be the posterior covariance matrix of the i-th sensor at time k. The inverse matrix of , where ρ is the augmented Lagrange parameter, and I is the identity matrix. Let be the distance measurement matrix of the i-th sensor in the r-th round at time k. Constraints in the r-th round The corresponding scaling dual variable, Let be the theoretical state of the ground vehicle obtained by the i-th sensor at time k in the r-th round. Let be the posterior estimated state of the ground vehicle obtained by the i-th sensor in the r-th round at time k by combining measurement information;

[0089] Will Assign to in, The constraints are Let be the distance measurement matrix of the i-th sensor in the (r+1)-th round at time k. Let b be the theoretical state of the ground vehicle acquired by the i-th sensor at time k in the (r+1)-th round, and d be the position coordinates of the fixed axis. k The known predetermined distance between the ground vehicle and the fixed axle at time k;

[0090] Will Assign to The ADMM iteration steps to obtain the scaled form are as follows:

[0091]

[0092]

[0093]

[0094]

[0095] in, This represents the first block in the rotation direction method, and is an auxiliary variable. Form the second block;

[0096] Define auxiliary variables Update based on the following questions:

[0097]

[0098]

[0099] Performing eigenvalue decomposition on matrix B, we have B = UΛU T Where U is the matrix composed of the eigenvectors of matrix B, Λ is the diagonal matrix composed of the eigenvalues, and let... The above optimization problem can then be updated as follows:

[0100]

[0101]

[0102] Solving the above optimization problem using the Lagrange multiplier method yields:

[0103]

[0104]

[0105] Where, λ l Let l be the l-th eigenvalue of matrix B. Constraints in the r-th round The corresponding unscaled dual variable, To and The relevant nonlinear equations;

[0106] Solve the nonlinear equation using the equal division method. get After the value, Substitution get The value, and then the relation get The value;

[0107] Will As Substitute into the following equation:

[0108]

[0109]

[0110] Where i = 1, 2, ..., N, and N is the number of sensors. Let be the posterior covariance matrix of the i-th sensor at time k. This represents the final estimated state of the ground vehicle at time k obtained by the i-th sensor based on the scaled ADMM iterative method. This is the covariance of the i-th sensor at time k, obtained by the scaling form of the ADMM iterative method.

[0111] It should be noted that the parameters in the distance-constrained distributed dynamic positioning method proposed in this invention are set to a maximum number of iterations of 35 and ρ = 1; in the simulation below, the Position Mean Square Error (MSE) is set to quantitatively analyze the positioning performance of different positioning algorithms, and the MSE of each sensor is quantitatively determined by N. m =100 Monte Carlo experiment calculation is as follows:

[0112]

[0113] After applying the positioning algorithm presented in this chapter, the estimated trajectories and actual trajectories of each sensor are as follows: Figure 3 As shown, the red line represents the actual target trajectory, while the green, blue, and pink lines represent the MSE data trajectory of each sensor after more than 100 Monte Carlo simulation runs. The simulation numerical results are... Where T = 100 represents the sample size.

[0114] Table 1 shows a comparison of the MSE value and running time between the distance-constrained distributed dynamic localization method proposed in this invention and the CKF, DEKF, and DUKF methods.

[0115] Table 1

[0116]

[0117] Furthermore, to demonstrate the superiority of the DFSC algorithm proposed in this invention, its localization performance is compared below with that of the Centralized Kalman Filter (CKF), Distributed Extended Kalman Filter (DEKF), and Distributed Unscented Kalman Filter (DUKF) methods, all of which use precisely known global observation information (without considering any constraints). Simulation results are as follows: Figure 4 As shown in the figure, the curves displayed represent the MSE data trajectories after more than 100 Monte Carlo simulations using the four methods described above. For example, the MSE value at time k is... Table 1 compares the running time and MSE values ​​of the four algorithms in 1000 Monte Carlo simulations. Simulation results show that all four algorithms have good stability. However, the DFSC algorithm proposed in this paper outperforms DEKF and DUKF in both convergence speed and estimation performance. The DFSC algorithm effectively integrates constraint information, enabling it to converge quickly to the performance achieved by centralized algorithms. Therefore, compared with DEKF and DUKF, the DFSC algorithm exhibits better estimation ability.

[0118] In summary, the distance-constrained distributed dynamic positioning method provided by this invention can be summarized as follows:

[0119] Step 1: Construct a single-objective dynamic distributed estimator based on the basic ideas of extended Kalman filtering and consensus iteration.

[0120] The design of the single-objective distributed estimator is carried out in two steps. Let... Let be the predicted state of the ground vehicle by sensor i at sampling time k. To apply the extended Kalman filter to estimate the covariance posteriorly at time k, firstly, each node runs the unconstrained EKF algorithm to obtain measurement update information. Then, based on the local constraints of node i, the single-objective distance constraint problem is formulated as follows:

[0121]

[0122] Where b represents the location of the lighthouse, d k This represents the known distance between a single target and the lighthouse.

[0123] To address this issue, auxiliary variables are introduced, and the expression is reformulated into a consensus form.

[0124]

[0125] The scaling form of the consensus mechanism for the single-objective distance-constrained problem, ADMM, has the following iterative steps:

[0126]

[0127]

[0128]

[0129]

[0130] This involves using the rotation direction method. The first block is represented as shown in equation (3), with auxiliary variables... The second block is formed, as shown in equations (4) and (5). Representing constraints The corresponding scaling dual variable, with the superscript r representing the r-th round of the rotation direction method.

[0131] definition The update encountered the following issues:

[0132]

[0133] Performing eigenvalue decomposition on matrix B, we have B = UΛU T Where U is the matrix composed of the eigenvectors of matrix B, Λ is the diagonal matrix composed of the eigenvalues, and let... The above optimization problem can then be updated as follows:

[0134]

[0135] Step 2: Solve the optimization problem (8).

[0136] The optimization problem (8) will be solved using the Lagrange multiplier method. Dual variables will be defined. The augmented Lagrange quantity of equation (8) can be expressed as:

[0137]

[0138] Therefore, for all μ k,i Inequality 1+μ k,i The condition that ≥0 holds is a necessary condition for the existence of an optimal solution to optimization problem (8). Therefore, we can obtain φ(μ) k,i The solution is monotonic within the feasible region of the solution, and any locally feasible solution is unique.

[0139] After finding the solution to problem (8), the solution to equation (9) can be obtained using the method of equal division, and then the solution can be obtained. The value of .

[0140] Will As Substitute into the following equation:

[0141]

[0142]

[0143] This allows us to determine the location of the ground vehicles and thus achieve their positioning.

[0144] In summary, this invention addresses the distributed localization problem in single-target tracking where only distance constraints exist. It designs a distributed nonlinear estimator based on second-order constraints, enabling state estimation to meet both real-time and global constraint requirements. First, a distributed estimator is constructed based on the fundamental ideas of extended Kalman filtering and consensus iteration. Then, the constraints are redefined using the alternating direction multiplier method, ensuring that each constrained subproblem can be effectively solved. Finally, tracking simulations under distance constraints verify the effectiveness of the proposed algorithm and demonstrate its improved localization accuracy.

[0145] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A distributed dynamic positioning method based on distance constraints, characterized in that, Includes the following steps: A distance measurement matrix relative to the ground vehicle is constructed for each sensor, wherein each sensor is deployed at the same height and the ground vehicle is moving in a circle around a fixed axis; The optimization objective function is to minimize the Euclidean norm between the theoretical state of the ground vehicle and the posterior estimated state obtained by combining measurement information. A local consensus estimator based on the distance measurement matrix is ​​constructed for each sensor using the distance between the ground vehicle's position at each time point and the fixed axis as a constant value. The state of the ground vehicle includes the vehicle's position... x Axis coordinates y Axis coordinates and vehicle direction ; The ground vehicle position in the local consensus estimator is solved based on the scaling form of the ADMM iterative method, and the ground vehicle is tracked and located. The local consensus estimator is: in, For the first i The sensor at the first k The theoretical state of ground vehicles acquired at all times. For the first i The sensor at the first k The posterior estimated state of ground vehicles is obtained by combining measurement information at all times. For the first i The sensor at the first k The posterior covariance matrix at time t The inverse matrix, It is a Euclidean norm. Let be the position coordinates of the fixed axis. For ground vehicles in the k The known set distance between the time and the fixed axis For the first i The sensor at the first k Distance measurement matrix at time; i =1,2,…,N, where N is the number of sensors; matrix B is represented as Distance measurement matrix The method for obtaining it is as follows: in, For the first i The sensor at the first k Theoretical state of ground vehicles acquired at all times Vehicles in x Axis coordinates For the first i The sensor at the first k Theoretical state of ground vehicles acquired at all times Vehicles in y Axis coordinates For the first i One sensor x Axis coordinates For the first i One sensor y Axis coordinates For the height of the sensor, For the first i The sensor at the first k Gaussian white noise at any given time; Posterior estimated state The method for obtaining it is as follows: in, For the first i The sensor at the first k The predicted state of ground vehicles is obtained at any time based on the unconstrained EKF algorithm. For the first i The sensor at the first k Measurement information matrix at time, For the first i The sensor at the first k The partial derivative matrix of the measurement information matrix at time -1.

2. The distributed dynamic positioning method based on distance constraints as described in claim 1, characterized in that, Measurement Information Matrix The method for obtaining it is as follows: in, For the first i The sensor at the first k The predicted value of the covariance matrix at time t. for The inverse matrix, For the first i The sensor at the first k The partial derivative matrix of the measurement information matrix at time step. For the first i The sensor at the first k Gaussian white measurement noise at time t, where T represents transpose.

3. The distributed dynamic positioning method based on distance constraints as described in claim 2, characterized in that, Covariance matrix predicted values The method for obtaining it is as follows: in, For the first i The sensor at the first k The partial derivative of the process function at time t. For the first i The sensor at the first k The estimated state of the ground vehicle at time -1, obtained using the scaled ADMM iterative method. For the first i The sensor at the first k The variance of process noise at any given time.

4. The distributed dynamic positioning method based on distance constraints as described in claim 1, characterized in that, The ground vehicle positions in the local consensus estimator are obtained based on the scaled ADMM iterative method. The specific implementation of ground vehicle tracking and localization is as follows: Using the rotation direction method Assign to ,in, r The first method of rotation direction r wheel, For the first i The sensor at the first k The posterior covariance matrix at time t The inverse matrix, To augment the Lagrange parameters, It is the identity matrix. For the first r Wheel of Life i The sensor at the first k Distance measurement matrix at time, For the first r Wheel constraint The corresponding scaling dual variable, For the first r Wheel of Life i The sensor at the first k The theoretical state of ground vehicles acquired at all times. For the first r Wheel of Life i The sensor at the first k The posterior estimated state of ground vehicles obtained by combining measurement information at all times; Will Assign to ,in, The constraints are , For the first r +1 round i The sensor at the first k Distance measurement matrix at time, For the first r +1 round i The sensor at the first k The theoretical state of ground vehicles acquired at all times. Let be the position coordinates of the fixed axis. For ground vehicles in the k The known predetermined distance between the fixed axis and the time point; Will Assign to The scaling form of ADMM is obtained through the following iteration steps: Define auxiliary variables , Update based on the following questions: Performing eigenvalue decomposition on matrix B, we have: ,in It is a matrix composed of the eigenvectors of matrix B. It is a diagonal matrix composed of eigenvalues, and let... The above optimization problem is then updated to: Solving the above optimization problem using the Lagrange multiplier method yields: in, For matrix B, the first... l 1 eigenvalue, For the first r Wheel constraint The corresponding unscaled dual variable, To and The relevant nonlinear equations; Solve the nonlinear equation using the equal division method. ,get After the value, Substitution ,get The value, and then the relation get The value; Will As Substitute into the following equation: in, i =1,2,…,N, where N is the number of sensors. For the first i The sensor at the first k The posterior covariance matrix at time t. The solution obtained by the scaling form ADMM iterative method is the first... i The sensor at the first k The final estimated state of ground vehicles at any given time. The solution obtained by the scaling form ADMM iterative method is the first... i The sensor at the first k Covariance at time.

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