Mobile agent closed-loop dynamic positioning optimization method based on digital twinning

Abstract

The invention discloses a mobile agent closed-loop dynamic positioning optimization method based on digital twinning. The method is suitable for dynamic positioning of unmanned vehicles, mobile robots and the like in complex and high-noise environments. The method comprises the following steps of: simulating signal multi-path propagation characteristics through a digital twin system, extracting characteristic coefficients such as path propagation time delay, attenuation and frequency shift, calculating a dynamic difference degree of a virtual signal and an actually measured signal, and establishing a joint posterior probability model in combination with a node motion state, so as to realize dynamic position estimation based on Bayesian reasoning. According to computing resource conditions, the method supports three optimization modes of convex optimization relaxation, a nonlinear Levenberg-Marquardt algorithm and a Kalman filtering fusion mechanism, real-time high-precision positioning is realized, recursive correction is performed on a prediction state and an observation error, and time sequence continuity and positioning precision are improved. According to the method, the problem of poor indoor static positioning precision caused by multi-path interference and non-line-of-sight propagation in a complex industrial environment is solved, and the anti-fluctuation capability and the estimation stability of the system are remarkably improved.

Description

Technical Field

[0001] This invention relates to a closed-loop optimization dynamic positioning method for mobile intelligent agents based on digital twins, applicable to the dynamic positioning needs of unmanned vehicles and mobile robots in complex, high-noise environments. It aims to improve the dynamic positioning accuracy of traditional positioning methods in complex industrial environments, especially indoor environments. Furthermore, the system integrates a Kalman filter fusion mechanism, utilizing convex optimization and nonlinear optimization methods, and continuously corrects the virtual node positions by combining historical states and observation errors, forming a closed-loop, time-continuous, real-time updated multi-dimensional dynamic positioning system. Background Technology

[0002] Currently, mobile intelligent agents such as drones, autonomous vehicles, and service robots are widely used in fields such as inspection, logistics, and intelligent manufacturing. However, their positioning performance in dynamic scenarios has become a core bottleneck for technology implementation. Complex environments (such as indoor GPS signal failure or outdoor building obstruction) and the high-speed movement of the intelligent agents themselves can easily cause positioning drift and signal interruption, directly restricting autonomous decision-making and operational safety. Accurate dynamic positioning is a prerequisite for mobile intelligent agents to achieve path planning, obstacle avoidance, and multi-agent collaboration. It can not only ensure the efficient execution of tasks such as drone power line inspection and obstacle avoidance and robot indoor delivery navigation, but also break through the technical bottlenecks of unmanned systems, promote the development of intelligent Internet of Things and industrial automation, and provide key technical support for the large-scale implementation of smart cities, unmanned transportation, and other fields.

[0003] In existing research, the main research directions for the dynamic localization problem of mobile intelligent agents include filter-based state estimation, environmental perception and map building, and collaborative localization through multi-source information fusion.

[0004] Dynamic localization based on filtering is one of the most widely used techniques. Typical examples include the Kalman Filter (KF), Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF). These methods achieve dynamic tracking of the target trajectory by recursively estimating the motion states (position, velocity, acceleration, etc.) of nodes. Particle filtering, as an implementation of Monte Carlo simulation, can effectively handle nonlinear and non-Gaussian systems and is widely used in the localization and tracking of moving targets in complex industrial environments.

[0005] Simultaneous Localization and Mapping (SLAM) has become a core technology in the fields of mobile robotics and autonomous driving in recent years. SLAM methods fuse data from multiple sensors, such as LiDAR, cameras, and inertial measurement units (IMUs), to simultaneously estimate the user's position and the surrounding map in unknown environments. Branches of SLAM, including visual SLAM, LiDAR SLAM, and fusion SLAM, have achieved significant results in scenarios such as autonomous vehicles, industrial robots, and drones.

[0006] Furthermore, collaborative localization based on multi-source information fusion is also a current research hotspot. This type of method integrates data from various heterogeneous sensors, such as wireless signals (e.g., UWB, WiFi, Bluetooth), vision, radar, and IMU, and utilizes Bayesian inference, graph optimization, and deep learning to improve the robustness and accuracy of localization. For example, multi-node collaborative localization systems for the Industrial Internet of Things (IIoT) can achieve globally consistent dynamic position estimation based on mutual distance and angle measurement between nodes, using structures such as factor graphs and graph neural networks.

[0007] In complex industrial scenarios, the electromagnetic reflection from metal components, signal obstruction from thick walls, and multi-source reflection in enclosed spaces intertwine, significantly exacerbating the multi-path propagation (MPCs) and non-line-of-sight (NLOS) effects of positioning signals. This leads to signal phase distortion and amplitude fluctuations. Existing single-mode or traditional multi-mode fusion methods struggle to fundamentally eliminate multi-path interference at the signal modeling level, directly hindering positioning accuracy and stability. To address this issue, existing research has introduced digital twin technology based on multi-domain channel characteristics (such as time, frequency, and spatial characteristics) into static positioning studies. By constructing a mapping model between the physical environment and channel characteristics, accurate simulation of the multi-path propagation process is achieved, and this model is integrated into a multi-dimensional joint closed-loop optimization positioning framework, mitigating the impact of multi-path propagation on static positioning to some extent. However, upon closer examination, the current digital twin-driven static positioning closed-loop optimization method still has significant limitations: its optimization logic focuses on spatial domain feature matching and fails to fully consider the dynamic correlation of time-series signals during the positioning process. In particular, for parameters with time-series dependence such as Received Signal Strength Indicator (RSSI), it cannot effectively mine the correlation information between consecutive frames, resulting in the lack of a positioning error compensation mechanism in the time-series dimension.

[0008] To address the complex problems that the aforementioned static methods cannot solve, this invention proposes a closed-loop optimization dynamic positioning method for mobile intelligent agents based on digital twins. Building upon traditional static difference modeling, it introduces transmitter trajectory and time variables to construct a dynamic position estimation model. By combining velocity and time intervals to calculate the trajectory and position of the virtual transmitter node in real time, it achieves temporally continuous predictive modeling. The system utilizes a digital twin platform to generate signal propagation waveforms at the predicted location and constructs a likelihood function model by calculating dynamic difference. Summary of the Invention

[0009] The present invention provides a closed-loop optimization dynamic positioning method for mobile intelligent agents based on digital twins, comprising the following steps:

[0010] Step 1: Calculation of dynamic dissimilarity based on feature coefficient vector

[0011] This invention analyzes the propagation characteristics of multipath signals and, for each path, comprehensively considers its propagation parameters, including propagation delay, path attenuation, and frequency offset, constructs a dynamic modeling formula for multipath received signals. Based on this, a dynamic digital twin system modeling method is designed to recreate the propagation behavior of signals in complex structural environments in physical space and generate corresponding virtual simulation waveforms at predicted locations.

[0012] The system describes the coupling relationship between each signal path and the transmitter-receiver positions. By introducing variable nodes (such as signal observations from each base station), it achieves joint modeling and message passing inference of the multi-path propagation process. Within this structure, a feature coefficient vector of the signal is defined, representing the propagation characteristics of each path at a specific location. Subsequently, the feature coefficients of the actually received signal and the feature coefficients of the predicted signal generated in the digital twin system are extracted, and their multidimensional difference is calculated as a matching index for the virtual location. Finally, a joint likelihood function is constructed using the difference information of all base stations and embedded into a Bayesian inference-based positioning framework for dynamically estimating the optimal location of the node to be located. Compared to traditional indirect matching methods based on wavelet coefficients, this method employs a structural modeling and physical feature parameter difference fusion comparison approach, adapting to the real-time, high-precision dynamic positioning requirements in complex industrial environments such as dynamic transmitting nodes, multi-path propagation, and strong interference.

[0013] Step 2: Construction of a joint positioning model based on dynamic position estimation

[0014] This invention aims to establish a joint positioning mathematical model for dynamic transmitting nodes. This model utilizes dynamic dissimilarity to construct a likelihood function, employs a posterior probability model to obtain the optimal solution location information, and combines temporal prediction and feature dissimilarity feedback mechanisms to achieve dynamic closed-loop optimization of the positioning system in complex multipath environments and estimate the precise location of the target node. Based on the current velocity of the transmitting node and the position estimation result of the previous moment, its possible location at the current time point is predicted. This prediction process considers the continuous motion characteristics and trajectory change trends of the node and introduces a certain amount of state noise to describe the uncertainty of the location prediction. Based on the predicted location, a signal propagation scenario is constructed using a digital twin system, generating a virtual signal waveform that matches the actual environment. This waveform contains propagation information from multiple paths, and key physical features of each path are extracted, including propagation delay, path attenuation, and frequency offset, forming a path-level feature coefficient vector. The actual signal acquired by the receiving base station is also parsed into corresponding feature coefficients. By comparing the difference between the actual coefficients and the virtual coefficients, the signal error metric for each base station can be calculated. The system uses the difference information from multiple base stations as input to construct a joint likelihood function. Based on this, and combined with the prior location information of the transmitting node, a complete posterior estimation model is built. This model not only considers the degree of matching between the currently observed signal and the predicted waveform, but also incorporates historical knowledge of the node's movement trend, effectively improving the temporal continuity and accuracy of the positioning estimation.

[0015] Step 3: Position estimation based on convex optimization relaxation method

[0016] In real-time positioning systems with multiple nodes and base stations, convex functions guarantee that the objective function converges to the global optimum, yielding the globally optimal solution. This invention proposes a global optimum solution method based on convex optimization relaxation. First, it determines whether the objective function satisfies the convexity condition. If it does, the solution is directly obtained using the properties of convex functions. If it does not, the maximum a posteriori probability function is transformed into an analytical objective function form. By taking the negative logarithm and removing the constant term, the objective function becomes a standard convex optimization problem consisting of an observation error term and a prior regularization term, which is then optimized and solved. In this structure, the observation error term characterizes the multidimensional difference between the digital twin generated waveform and the actual received signal, while the prior term reflects the continuity constraint of node motion. The combination of these two ensures the differentiability and convexity of the objective function, thus allowing a unique globally optimal solution to be obtained analytically.

[0017] Furthermore, this invention constructs a Jacobian matrix of the observation error of each base station relative to the node position by linearizing the posterior probability objective function, and embeds it into a standard quadratic programming framework. By incorporating the signal variance of each base station into the weight matrix form, the confidence levels of different signal channels can be weighted and adjusted to improve the robustness of the global solution. Subsequently, the Lagrange multiplier method is introduced to perform convex optimization relaxation on the objective, constructing the Lagrange function and solving the partial derivative conditions to ensure that the optimal solution satisfies the first-order necessary condition. If the Hessian matrix of the objective is positive definite, the strict convexity of the problem can be guaranteed, thereby obtaining a globally convergent solution.

[0018] Step 4: Position estimation method based on LM nonlinear algorithm

[0019] To address the highly nonlinear characteristics of signal propagation in complex industrial scenarios, and considering that some non-convex functions in step three cannot be precisely converted into convex forms, this invention further proposes a position estimation method based on the Levenberg-Marquardt (LM) nonlinear optimization algorithm. This method combines the advantages of the Gauss-Newton method and gradient descent, enabling high-precision position determination in non-convex, multi-constraint, and multi-peak problems.

[0020] In this step, the system first constructs a nonlinear residual function based on the difference between the observed signal at the current moment and the predicted waveform from the digital twin. The residual consists of two parts: the observation residual reflects the error between the actual received signal and the virtual waveform, while the prior residual reflects the continuity constraint of historical position prediction. Subsequently, the system calculates the Jacobian matrix of the residual vector and establishes an LM optimization equation with a damped term. By adjusting the damping coefficient λ, the system dynamically switches between Gaussian-Newton and gradient descent modes: when λ approaches 0, the algorithm converges rapidly in a quadratic approximation form; when λ increases, the algorithm degenerates into a step-size controlled gradient descent form to ensure convergence stability. During the iteration process, the system adaptively adjusts the value of λ according to the decreasing trend of the residual sum of squares. When the objective function decreases significantly, λ is decreased to accelerate convergence; otherwise, λ is increased to prevent divergence. Through multiple iterations, the system obtains the optimal position estimate that minimizes the residual sum of squares.

[0021] Step 5: Maximum A posteriori location estimation method based on Kalman filter fusion

[0022] To further improve the system's estimation accuracy and temporal continuity of the transmitter node's location, and to reduce the computational complexity of large-scale solutions, this invention proposes a dynamic positioning method that combines a Kalman filter fusion mechanism with a maximum a posteriori estimation criterion.

[0023] At each time step, the system predicts the current position of the transmitting node and its corresponding signal propagation characteristics based on the state estimate and velocity information from the previous time step, and generates virtual waveform features at that predicted position. Subsequently, the system obtains the observation error by comparing the predicted waveform with the actual received physical signal at the feature level. To suppress prediction bias caused by noise interference and modeling errors, a Kalman filter mechanism is introduced to fuse the predicted and observed states. In this process, the system uses the predicted position state as a priori input and combines it with the actual waveform observation difference as measurement information to dynamically update the state estimate result of the current frame, achieving recursive correction of the transmitting node's trajectory. Based on the fused waveform error information, the system constructs a joint posterior probability model and uses it as the objective function to perform maximum a posteriori position estimation. To meet the real-time and accuracy requirements of different computing scenarios, the system supports two optimization modes. On low-resource platforms, a fast-converging local iterative algorithm is used for position optimization; while in environments with high computing power, a global search strategy traverses a preset position space, selecting the estimated point with the highest posterior probability as the current positioning result.

[0024] This invention innovatively introduces a Kalman filtering mechanism to achieve fusion and updating between the virtual predicted waveform and the actual received waveform. By recursively fusing the predicted signal with the current observation result, Kalman filtering effectively reduces the impact of environmental noise and modeling errors, and dynamically corrects historical states in each frame of positioning. This method not only improves the temporal continuity of the positioning system but also enhances its stability in dynamic and complex environments.

[0025] Compared with the prior art, the advantages of the present invention are:

[0026] 1. Compared to static intelligent agent positioning of a stationary or semi-stationary transmitter source, this invention introduces a motion state modeling mechanism for the transmitter node for the first time based on digital twin closed-loop positioning. It combines velocity and time step to dynamically predict the node trajectory position, forming a continuous virtual position evolution path between frames, which significantly improves the response capability and temporal stability of the positioning system in highly dynamic scenarios.

[0027] 2. Compared with the indirect matching method of traditional multi-domain wavelet coefficient difference, this invention directly extracts explicit physical quantities such as path delay, frequency shift, and attenuation from the propagation model as feature coefficients. By measuring the difference of these real interpretable parameters, the interpretability and accuracy of the model are improved.

[0028] 3. This invention achieves dynamic switching from global approximate optimum to local high-precision optimum through a hybrid solution mechanism combining convex optimization relaxation, nonlinear LM algorithm, and maximum a posteriori position estimation method based on Kalman filtering fusion and dynamic optimization. The convex optimization relaxation method ensures the uniqueness and stability of the solution, while the LM algorithm further optimizes local accuracy in complex nonlinear scenarios, achieving a balance between global and local accuracy. Kalman filtering recursively fuses the predicted state and observation error, using Kalman filtering to update the predicted position state and real-time observation error information. This effectively suppresses the interference of environmental noise and modeling errors on positioning estimation, improves the system's resistance to fluctuations and estimation stability, and is suitable for high-frequency, low-latency real-time positioning scenarios. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the implementation of the closed-loop dynamic positioning optimization method for mobile intelligent agents based on digital twins, as described in this invention. Detailed Implementation

[0030] This invention provides a closed-loop optimization dynamic positioning method for mobile intelligent agents based on digital twins, applicable to high-precision positioning of dynamic multi-agent nodes in complex industrial environments. Based on the multipath propagation characteristics of signals, this method extracts characteristic coefficients such as propagation delay, attenuation, and phase for each path and constructs a model to express the conditional dependence between path features and node positions. The system generates simulated waveforms at the predicted position and compares them with the received signal, calculating the path difference as the basis for position evaluation. Combining node motion states and historical estimation results, a joint posterior probability model is established, fusing difference information from multiple base stations and the prior position distribution of nodes. Convex optimization relaxation and nonlinear algorithms are used to solve for the optimal position information. Furthermore, the system introduces a Kalman filter mechanism to fuse and update the predicted state of the previous frame with the observation error of the current frame, enhancing the continuity and stability of state estimation. Maximum a posteriori position estimation is achieved through dynamic optimization. The system can flexibly switch between rapid iteration and global search based on computational resource conditions, achieving a balance between positioning accuracy and efficiency.

[0031] Step 1: Calculation of dynamic dissimilarity based on feature coefficient vector

[0032] In complex electromagnetic signal propagation environments, the propagation path of a signal from the node to be located to the base station may include direct paths, reflected paths, and scattered paths. These multipath propagation causes complex changes in the signal characteristics at the receiving end. Each path results in signal propagation delay, intensity attenuation, and phase changes. Furthermore, electromagnetic signals transmitted at different times may overlap during reception due to the different paths taken; therefore, the received signal is the sum of signals from multiple paths. In scenarios where the transmitting node moves and the receiving base station is fixed, the signal received by the receiver at any time t is a superposition of signals from multiple paths. Therefore, for the i-th base station R... i The received signal can be represented as:

[0033]

[0034] Where, φ i (t) is the base station R i The signal received at time t, s(t) is the continuously transmitted signal, N is the number of paths, and a n θ is the attenuation factor for each path, representing the signal strength variation along the path. n It is the initial phase information, ω n The Doppler rate component is used to capture the target's velocity information, τ. n (t) is the time delay of each path signal from the node to be located to the base station through that path, while τ n (t) satisfies M n It is the number of reflections along the nth path. It is the position of the m-th relay point (reflection / refraction point) on the n-th path. It is the receiver's terminal path point. This represents the position of the transmitting node at time t. Where T(t) is the position of the transmitting node at time t. For base station R i The point of reflection or endpoint where the signal from path n is received, where c is the speed of light.

[0035] In actual motion, the positions of the signal transmitter and the node to be located can be simulated in a digital twin. By comparing the difference between the received signals from the simulated transmitter at different locations and the signal strengths received by the sensors, a difference of 0 or a minimum threshold indicates that the location is the transmitter's position, i.e., the position of the mobile agent. Therefore, the node to be located in the physical world, T, can be positioned relative to the known locations of base stations R1, R2, ..., R... n The transmitted signals are denoted as φ1(t), φ2(t), ..., φ1(t), respectively. n (t). For each path, its propagation characteristics are extracted to form a path feature coefficient vector:

[0036]

[0037] In the twin world, a virtual predicted location T is set. * The system can simulate and generate corresponding virtual signal waveforms and extract their characteristic coefficient vectors.

[0038]

[0039] This invention decomposes a complex multipath propagation model, transforming it into the computation of multiple factor nodes and variable nodes. Each node has a signal dissimilarity level, which follows a Gaussian distribution. When a base station or agent simultaneously receives signals from multiple distances, the joint likelihood function of these signals is obtained as follows:

[0040]

[0041] in, φ is the variance of the observation error of the i-th base station in the model. i (T * ) represents the waveform received by the i-th base station in the twin world, used to control the convergence rate of the difference in the probability space.

[0042] Assuming the dissimilarity follows a Gaussian distribution, substituting the formula for dissimilarity yields the following formula:

[0043]

[0044] Where N is the number of multipath signals received by the base station, σ i τ is the standard deviation of the overall characteristic error of the i-th signal. n ,a n ,ω n ,θ n Let be the measured time delay, amplitude, azimuth, and elevation angle of the nth path. τ represents the predicted value of the virtual signal. n a n ω n θ n This represents the actual value of the received signal; the dynamic difference reflects the predicted position T. * The difference in signal propagation characteristics between the actual location and the real location.

[0045] When the system consists of M receiving base stations, assuming that the observation errors of each base station are independent, the joint likelihood function can be expressed as the product of the likelihood functions of multiple base stations:

[0046]

[0047] Simplified, we get:

[0048]

[0049] Among them, T * For the current predicted position, φ i (t) represents the received signal, and Φ represents the set of signals received by all base stations. i (T * The value represents the feature coefficient difference. This formula indicates the overall degree of fitting of the signal characteristics of the predicted location to each base station; a larger value indicates a better match.

[0050] Then, a conditional dependency model between node location and path features is established. Each path feature is treated as a variable node, and the dissimilarity is treated as a factor node. The dissimilarity ensemble composed of M base stations is as follows:

[0051]

[0052] Expanding, we get:

[0053]

[0054] Update results in:

[0055]

[0056] Where M is the number of receiving base stations, and N i The number of multipaths corresponding to the i-th base station, σ i It is the standard deviation of the overall feature error of the i-th signal. This formula represents the difference between the received signal and the virtual base station signal at each base station, calculating the sum of squared errors ε(T) between the predicted and actual signal features. * The smaller the value, the closer the location of the node to be located in the twin world is to the actual location of the node to be located.

[0057] Step 2: Construction of a joint positioning model based on dynamic position estimation

[0058] Given the signal characteristic difference degree received by a single base station, assume the difference degree error term ε i (T * The probability density function approximates a Gaussian distribution, with an exponentially decaying probability density. This means that the smaller the difference, the higher the matching degree and the greater the corresponding probability; conversely, the greater the difference, the lower the matching degree and the smaller the corresponding probability. The matching degree between the virtual feature signal observed by each base station and the real signal can be modeled using the following likelihood function.

[0059] Furthermore, to reflect the uncertainty of node position, the predicted position and movement trend of the transmitting node in the previous moment are considered. To avoid large deviations or jumps in position estimation, the system introduces a Gaussian distribution prior model as a prediction constraint:

[0060]

[0061] Among them, T * For the current predicted position, μ T It is the mean of the predicted positions at the previous moment, v T Δt is the displacement obtained by extrapolating the velocity, μ T +v T Δt is the prior mean, V t It is the location state prediction covariance matrix, where d is the spatial dimension.

[0062] Based on the Bayesian criterion, a joint posterior probability distribution is constructed by combining the likelihood function based on dissimilarity with the prior distribution of location:

[0063] p(T * |Φ)∝p(Φ(T * )|Φ)·p(T * |μ T ,v T (12)

[0064] Substituting the terms into the above equation, we obtain the final posterior probability function:

[0065]

[0066] Among them, T * Let Φ be the current predicted location, Φ be the set of signals received by all base stations, and μ be the value of μ. T It is the mean of the predicted positions at the previous moment, v T Δt is the displacement obtained by extrapolating the velocity, μ T +v T Δt is the prior mean, V t It is the position state prediction covariance matrix.

[0067] To obtain the optimal estimated position of the transmitting node at the current moment, the system constructs an objective optimization function (outputting the optimal position of the maximum a posteriori estimate) by maximizing the aforementioned posterior probability, i.e., minimizing its negative logarithmic form:

[0068]

[0069] Step 3: Position estimation based on convex optimization relaxation method

[0070] For scenarios involving fast solutions in large-scale multi-agent networks, this invention uses convex optimization relaxation techniques to solve the global optimal problem of position estimation. The objective function in formula (14) can be transformed into a convex optimization problem, which is treated as a convex function to find the global optimal solution.

[0071] If we want the joint localization maximum a posteriori estimation of mobile intelligent agents to achieve the global optimal solution, we need to ensure that the negative logarithmic posterior probability function is a convex function and the feasible region is a convex set.

[0072] First, determine whether formula (14) satisfies the convexity condition. If it satisfies the convexity condition, then directly use the properties of convex functions to solve it. If formula (14) does not satisfy the convexity condition, that is, it satisfies the non-convexity property, then perform convex optimization relaxation and use the Lagrange multiplier method to optimize and solve it.

[0073] Rewriting the posterior probability function formula (13) as a convex objective function, taking the negative logarithm and removing the constant, yields the result to be minimized.

[0074]

[0075] The first term is the observation error, and the second term is the velocity prior regularity.

[0076] The prior term is a standard quadratic form.

[0077] Strictly convex, in the observation error term, each difference degree is essentially the sum of squares of the differences between two sets of features. If these features and positions are linear or linearized affine functions, then each difference degree itself is a quadratic convex function, and the weighted sum of convex functions is still a convex function. Therefore, formula (14) is a convex optimization problem with no constraints or with convex constraints, and the existence of a minimum value is necessarily unique and global.

[0078] Secondly, it is necessary to determine that the feasible region is a convex set. Equation (14) is transformed into a standard quadratic programming form. Under a first-order linearized approximation, the Jacobian matrix H of all base stations and the residual r constitute:

[0079]

[0080] The Jacobian matrix represents a linear approximation of the observation error with respect to the position.

[0081] Expanding the squared terms yields the positive definite matrix as follows:

[0082]

[0083] Where W is the weight matrix of the observation error, used to weight the Gaussian variance σ of each base station. 2 Write it into a quadratic form and transform the likelihood term into a standard L2 squared form. Q is the Hessian matrix, and r is the difference vector between the observed values ​​and the model predictions, which measures the deviation between the features generated by the digital twin model at the current candidate location and the features actually measured by the sensor. V t It is the position state prediction covariance matrix. μ t It is the prior mean. μ predIt estimates the center of mass, which is the sum of the old position and velocity-time.

[0084] The Lagrange multiplier method is used to perform convex optimization relaxation on the objective, and the Lagrange function is constructed as follows:

[0085]

[0086] Where λ is the Lagrange multiplier, y is the actual observed signal, and A and b are the matrix constraints and constraint vectors.

[0087] Taking the partial derivative of the Lagrange function, we get:

[0088]

[0089] Without constraints, we have:

[0090]

[0091] If Q is positive definite, then the objective is strictly convex, meaning the feasible region is also a convex set, and the global optimal solution, i.e., the convergence position T, can be obtained. *opt :

[0092] T *opt =Q -1 (qA T (AQ -1 A T ) -1 (AQ -1 qb)) (22)

[0093] Step 4: Position estimation method based on LM nonlinear algorithm

[0094] When the objective function of formula (14) is highly nonlinear and cannot be precisely linearized, and cannot be transformed into a convex function, traditional convex optimization methods are often difficult to apply directly to highly nonlinear and nonconvex real-world scenarios, and have high requirements for model accuracy and prior knowledge. The classic nonlinear optimization method (Levenberg-Marquardt) has the advantages of strong adaptability and the ability to handle nonconvex and nonlinear problems. It also combines the advantages of Gauss-Newton method and gradient descent method: when λ(k)→0, it is close to the Gauss-Newton method with fast convergence speed; when λ(k)→∞, it degenerates into gradient descent with step size control to ensure stability.

[0095] Therefore, when dealing with complex, nonlinear, multi-peak, and multi-constraint dynamic positioning problems, we adopt classical nonlinear optimization methods for position estimation.

[0096] When the target is nonlinear and not necessarily convex globally, the global optimal position can be solved using classical nonlinear methods:

[0097]

[0098] Observation residual row vector:

[0099]

[0100] Prior residual row vectors:

[0101] r pri (T * ) = V t -12 [T * -(μ t +v t Δt)] (25) Residual vector:

[0102]

[0103] Where W is the weighting matrix, y is the measured eigenvector, and f(T) * ) is the virtual feature vector generated by the digital twin model, r obs (T * ) represents the observation residual, r pri (T * ) is the prior residual, J(T) * ) is the Jacobian matrix of the residual vector.

[0104] The Levenberg-Marquardt (LM) algorithm was chosen as the nonlinear optimization method. This method has a fast local convergence speed and a robust gradient method, which always ensures that the target decreases monotonically and is not prone to divergence.

[0105] First take

[0106]

[0107] Then calculate the residual.

[0108] r (k) =r(T) *(k) (28) Find the Jacobian matrix.

[0109]

[0110] The Jacobian matrix of the observed residual block is given for the i-th base station.

[0111]

[0112] The observation residuals have a weight matrix W 12 ,therefore

[0113] J obs =-W 12 J f(31) Jacobian matrix of prior residual block

[0114]

[0115] Stacked into a total Jacobian matrix:

[0116]

[0117] It can be deduced that the linear equation for LM is used at the k-th iteration point:

[0118] (J T J+λ (k) I)Δ (k) =-J T r (k) (34)

[0119] Solve the linear system of equations in formula (21) when λ (k) When →0, return to the Gauss–Newton(GN) step:

[0120]

[0121] When λ (k) As the value approaches infinity, it degenerates into gradient descent with step size control:

[0122]

[0123] Generate trial solutions:

[0124]

[0125] If there is If the update is accepted, λ is decreased; otherwise, λ is increased and the calculation is recalculated.

[0126] Finally, determine convergence if ||Δ (k) ||<ε x or ||r (k) ||<ε r or Then it converges, and the global optimal solution T at the convergence position is obtained. *opt :

[0127]

[0128] ||r(T * )|| 2 This term is the sum of squared residuals, used to measure the discrepancy between the model and the observations. It reflects the degree of agreement between the current location estimate and the actual observed data. This term is typically used in optimizing the objective function, minimizing it to approximate the global optimum.

[0129] Step 5: Maximum A posteriori location estimation method based on Kalman filter fusion

[0130] Classical nonlinear optimization methods suffer from high computational complexity, requiring the calculation of Jacobian and Hessian matrices, and are still prone to getting trapped in local optima. Their convergence speed is heavily influenced by the initial values ​​and the choice of parameter λ, making them unsuitable for large-scale problems. This approach is applicable to systems with significant and complex nonlinearity, particularly those involving multipath propagation, and when more accurate solutions are required. Addressing real-time state estimation in highly dynamic environments, especially when nodes are continuously moving and signal characteristics are rapidly changing, the transmitting nodes move continuously within a given timeframe, and their positional states change over time, resulting in strong temporal correlations in the signal waveforms received by each base station. To ensure high accuracy and continuity of the positioning system under multipath and NLOS interference, this paper proposes a virtual waveform generation mechanism based on predicted trajectories, a dynamic difference reconstruction method, and a waveform-level fusion method, building upon Kalman filtering and posterior estimation to form a closed-loop estimation structure that fuses spatial and waveform layers.

[0131] During each frame localization process, the system first bases its localization on the state estimate from the previous time step. Predict the node position of the current frame using a state transition model:

[0132]

[0133] in, It is the predicted value at the current position, F is the state transition matrix, and μ k For controlling input.

[0134] Subsequently, the predicted location is input into the digital twin system to construct a virtual signal propagation model at the current location and generate a corresponding virtual waveform:

[0135]

[0136] in, To predict the propagation delay of the nth path from the location to the receiving point, These are the estimated values ​​of the path's characteristic parameters.

[0137] Based on the signal received by the base station, formula (1) is used to calculate the temporal difference within a given time window [t0, t1] to measure the degree of fit between the predicted location waveform and the actual signal:

[0138]

[0139] To enhance estimation stability and incorporate waveform fitting error information, the system employs an extended Kalman filter (EKF) structure for state updates. The waveform difference is used as the measured observation value z. kThe following nonlinear measurement model is established:

[0140]

[0141] in, Indicates the position Mapped to the difference between the virtual signal and the observation, v k To observe noise.

[0142] In the Kalman filter prediction stage, after predicting the node positions of the current frame, the state covariance matrix P is then... k The prediction yields the following formula:

[0143]

[0144] Kalman filter update phase:

[0145]

[0146] in, It is the predicted covariance, K k It is the Kalman filter gain. Let Jacobian matrix be the nonlinear measurement function with respect to position. This is the filtered and updated position estimate, P. k This is the updated covariance matrix, where Q and R are the process and observation noise covariances, respectively.

[0147] Through this mechanism, the system not only integrates position prediction and trajectory history, but also integrates the differences between digital twin prediction signals and real signals at the waveform level, enabling fine-grained updates of the state for each frame.

[0148] After filtering and updating, based on the joint posterior probability model constructed in step two, maximum a posteriori estimation (MAP) is performed to obtain the optimal position of the virtual node to be located. This location is selected as the final location result for the node to be located:

[0149]

Claims

1. A closed-loop dynamic positioning optimization method for mobile intelligent agents based on digital twins, characterized in that, Includes the following steps: Step 1: Calculation of dynamic dissimilarity based on feature coefficient vector This invention analyzes the propagation characteristics of multipath signals and, for each path, comprehensively considers its propagation parameters, including propagation delay, path attenuation, and frequency offset, constructs a dynamic modeling formula for multipath received signals. Based on this, a dynamic digital twin system modeling method is designed to recreate the propagation behavior of signals in complex structural environments in physical space and generate corresponding virtual simulation waveforms at predicted locations. The system describes the coupling relationship between each signal path and the transmitter-receiver positions. By introducing variable nodes (such as signal observations from each base station), it achieves joint modeling and message passing inference of the multi-path propagation process. Within this structure, a feature coefficient vector of the signal is defined, representing the propagation characteristics of each path at a specific location. Subsequently, the feature coefficients of the actually received signal and the feature coefficients of the predicted signal generated in the digital twin system are extracted, and their multidimensional difference is calculated as a matching index for the virtual location. Finally, a joint likelihood function is constructed using the difference information of all base stations and embedded into a Bayesian inference-based positioning framework for dynamically estimating the optimal location of the node to be located. Compared to traditional indirect matching methods based on wavelet coefficients, this method employs a structural modeling and physical feature parameter difference fusion comparison approach, adapting to the real-time high-precision dynamic positioning requirements in complex industrial environments such as dynamic transmitting nodes, multi-path propagation, and strong interference. Step 2: Construction of a joint positioning model based on dynamic position estimation This invention aims to establish a joint positioning mathematical model for dynamic transmitting nodes. This model utilizes dynamic dissimilarity to construct a likelihood function, employs a posterior probability model to obtain the optimal solution location information, and combines temporal prediction and feature dissimilarity feedback mechanisms to achieve dynamic closed-loop optimization of the positioning system in complex multipath environments and estimate the precise location of the target node. Based on the current velocity of the transmitting node and the position estimation result of the previous moment, its possible location at the current time point is predicted. This prediction process considers the continuous motion characteristics and trajectory change trends of the node and introduces a certain amount of state noise to describe the uncertainty of the location prediction. Based on the predicted location, a signal propagation scenario is constructed using a digital twin system, generating a virtual signal waveform that matches the actual environment. This waveform contains propagation information from multiple paths, and key physical features of each path are extracted, including propagation delay, path attenuation, and frequency offset, forming a path-level feature coefficient vector. The actual signal acquired by the receiving base station is also parsed into corresponding feature coefficients. By comparing the difference between the actual coefficients and the virtual coefficients, the signal error metric for each base station can be calculated. The system uses the difference information of multiple base stations as input to construct a joint likelihood function, and then combines this with the prior location information of the transmitting node to construct a complete posterior estimation model. This model not only considers the matching degree between the current observed signal and the predicted waveform, but also incorporates historical knowledge of the node's movement trend, effectively improving the temporal continuity and accuracy of the positioning estimation. Step 3: Position estimation based on convex optimization relaxation method In real-time positioning systems with multiple nodes and base stations, convex functions guarantee that the objective function converges to the global optimum, yielding the globally optimal solution. This invention proposes a global optimum solution method based on convex optimization relaxation. First, it determines whether the objective function satisfies the convexity condition. If it does, the solution is directly obtained using the properties of convex functions. If it does not, the maximum a posteriori probability function is transformed into an analytical objective function form. By taking the negative logarithm and removing the constant term, the objective function becomes a standard convex optimization problem consisting of an observation error term and a prior regularization term. In this structure, the observation error term characterizes the multidimensional difference between the digital twin generated waveform and the actual received signal, while the prior term reflects the continuity constraint of node motion. The combination of these two ensures the differentiability and convexity of the objective function, thus allowing a unique globally optimal solution to be obtained analytically. Furthermore, this invention constructs a Jacobian matrix of the observation error of each base station relative to the node position by linearizing the posterior probability objective function, and embeds it into a standard quadratic programming framework. By incorporating the signal variance of each base station into the weight matrix form, the confidence levels of different signal channels can be weighted and adjusted to improve the robustness of the global solution. Subsequently, the Lagrange multiplier method is introduced to perform convex optimization relaxation on the objective, constructing the Lagrange function and solving the partial derivative conditions to ensure that the optimal solution satisfies the first-order necessary condition. If the Hessian matrix of the objective is positive definite, the strict convexity of the problem can be guaranteed, thereby obtaining a globally convergent solution. Step 4: Position estimation method based on LM nonlinear algorithm To address the highly nonlinear characteristics of signal propagation in complex industrial scenarios, and considering that some non-convex functions in step three cannot be precisely converted into convex forms, this invention further proposes a position estimation method based on the Levenberg-Marquardt (LM) nonlinear optimization algorithm. This method combines the advantages of the Gauss-Newton method and gradient descent, enabling high-precision position determination in non-convex, multi-constraint, and multi-peak problems. In this step, the system first constructs a nonlinear residual function based on the difference between the observed signal at the current moment and the predicted waveform from the digital twin. The residual consists of two parts: the observation residual reflects the error between the actual received signal and the virtual waveform, while the prior residual reflects the continuity constraint of historical position prediction. Subsequently, the system calculates the Jacobian matrix of the residual vector and establishes an LM optimization equation with a damped term. By adjusting the damping coefficient λ, the system dynamically switches between Gaussian-Newton and gradient descent modes: when λ approaches 0, the algorithm converges rapidly in a quadratic approximation form; when λ increases, the algorithm degenerates into a step-size controlled gradient descent form to ensure convergence stability. During the iteration process, the system adaptively adjusts the value of λ according to the decreasing trend of the residual sum of squares. When the objective function decreases significantly, λ is decreased to accelerate convergence; otherwise, λ is increased to prevent divergence. Through multiple iterations, the system obtains the optimal position estimate that minimizes the residual sum of squares. Step 5: Maximum A posteriori location estimation method based on Kalman filter fusion To further improve the system's estimation accuracy and temporal continuity of the transmitter node's location, and to reduce the computational complexity of large-scale solutions, this invention proposes a dynamic positioning method that combines a Kalman filter fusion mechanism with a maximum a posteriori estimation criterion. At each time step, the system predicts the current position of the transmitting node and its corresponding signal propagation characteristics based on the state estimate and velocity information from the previous time step, and generates virtual waveform features at that predicted position. Subsequently, the system obtains the observation error by comparing the predicted waveform with the actual received physical signal at the feature level. To suppress prediction bias caused by noise interference and modeling errors, a Kalman filter mechanism is introduced to fuse the predicted and observed states. In this process, the system uses the predicted position state as a priori input and combines it with the actual waveform observation difference as measurement information to dynamically update the state estimate result of the current frame, achieving recursive correction of the transmitting node's trajectory. Based on the fused waveform error information, the system constructs a joint posterior probability model and uses it as the objective function to perform maximum a posteriori position estimation. To meet the real-time and accuracy requirements of different computing scenarios, the system supports two optimization modes. On low-resource platforms, a fast-converging local iterative algorithm is used for position optimization; while in environments with high computing power, a global search strategy traverses a preset position space, selecting the estimated point with the highest posterior probability as the current positioning result.

2. The method according to claim 1, characterized in that, In step one, the signal propagation path from the node to be located to the base station may include direct path, reflection path, and scattering path. These multipath propagation causes complex changes in the signal characteristics at the receiving end. Each path results in signal propagation delay, intensity attenuation, and phase change. Furthermore, electromagnetic signals transmitted at different times may overlap during reception due to different paths; therefore, the received signal is the sum of signals from multiple paths. In a scenario where the transmitting node moves and the receiving base station is fixed, the signal received by the receiver at any time t is the sum of signals from multiple paths. Therefore, for the i-th base station R... i The received signal can be represented as: Where, φ i (t) is the base station R i The signal received at time t, s(t) is the continuously transmitted signal, N is the number of paths, and a n θ is the attenuation factor for each path, representing the signal strength variation along the path. n It is the initial phase information, ω n The Doppler rate component is used to capture the target's velocity information, τ. n (t) is the time delay of each path signal from the node to be located to the base station through that path, while τ n (t) satisfies M n It is the number of reflections along the nth path. It is the position of the m-th relay point (reflection / refraction point) on the n-th path. It is the receiver's terminal path point. This represents the position of the transmitting node at time t. Where T(t) is the position of the transmitting node at time t. For base station R i The point of reflection or endpoint where the signal from path n is received, where c is the speed of light. In the twin world, a virtual predicted location T is set. * The system can simulate and generate corresponding virtual signal waveforms and extract their characteristic coefficient vectors. This invention decomposes a complex multipath propagation model, transforming it into the computation of multiple factor nodes and variable nodes. Each node has a signal dissimilarity level, which follows a Gaussian distribution. When a base station or agent simultaneously receives signals from multiple distances, the joint likelihood function of these signals is obtained as follows: in, φ is the variance of the observation error of the i-th base station in the model. i (T * ) represents the waveform received by the i-th base station in the twin world, used to control the convergence rate of the difference in the probability space. Assuming the dissimilarity follows a Gaussian distribution, substituting the formula for dissimilarity yields the following formula: Where N is the number of multipath signals received by the base station, σ i τ is the standard deviation of the overall characteristic error of the i-th signal. n ,a n ,ω n ,θ n Let be the measured time delay, amplitude, azimuth, and elevation angle of the nth path. τ represents the predicted value of the virtual signal. n a n ω n θ n This represents the actual value of the received signal; the dynamic difference reflects the predicted position T. * The difference in signal propagation characteristics between the actual location and the real location. When the system consists of M receiving base stations, each path feature is treated as a variable node, and the difference is treated as a factor node. The difference of the M base stations is integrated as follows:

3. The method according to claim 1, characterized in that, In step two, the signal characteristic difference degree received by a single base station is assumed to be based on the difference error term ε. i (T * The probability density function approximates a Gaussian distribution, with an exponentially decaying probability density. This means that the smaller the difference, the higher the matching degree and the greater the corresponding probability; conversely, the greater the difference, the lower the matching degree and the smaller the corresponding probability. The matching degree between the virtual feature signal observed by each base station and the real signal can be modeled using the following likelihood function. Furthermore, to reflect the uncertainty of node position, the predicted position and movement trend of the transmitting node in the previous moment are considered. To avoid large deviations or jumps in position estimation, the system introduces a Gaussian distribution prior model as a prediction constraint: Among them, T * For the current predicted position, μ T It is the mean of the predicted positions at the previous moment, v T Δt is the displacement obtained by extrapolating the velocity, μ T +v T Δt is the prior mean, V t It is the location state prediction covariance matrix, where d is the spatial dimension. Based on the Bayesian criterion, a joint posterior probability distribution is constructed by combining the likelihood function based on dissimilarity with the prior distribution of location: p(T * |Φ)∝p(Φ(T * )|Φ)·p(T * |m T ,v T ) Substituting the terms into the above equation, we obtain the final posterior probability function: Among them, T * Let Φ be the current predicted location, Φ be the set of signals received by all base stations, and μ be the value of μ. T It is the mean of the predicted positions at the previous moment, v T Δt is the displacement obtained by extrapolating the velocity, μ T +v T Δt is the prior mean, V t It is the position state prediction covariance matrix. To obtain the optimal estimated position of the transmitting node at the current moment, the system constructs an objective optimization function (outputting the optimal position of the maximum a posteriori estimate) by maximizing the aforementioned posterior probability, i.e., minimizing its negative logarithmic form:

4. The method according to claim 1, characterized in that, In step three, position estimation is based on the convex optimization relaxation method. For scenarios requiring fast solutions in large-scale multi-agent networks, this invention uses convex optimization relaxation techniques to solve the global optimum problem of position estimation. The objective function can be transformed into a convex optimization problem, which is then converted into a standard quadratic programming form, treated as a convex function to find the global optimum. If we want the joint localization maximum a posteriori estimation of mobile intelligent agents to achieve the global optimal solution, we need to ensure that the negative logarithmic posterior probability function is a convex function and the feasible region is a convex set. First, determine whether the objective function satisfies the convexity condition. If it does, solve it directly using the properties of convex functions. If the objective function does not satisfy the convexity condition, i.e., it satisfies the non-convexity property, then perform convex optimization relaxation and use the Lagrange multiplier method for optimization. Under a first-order linearized approximation, the Jacobian matrix H of all base stations is formed by the residual r: The Jacobian matrix represents a linear approximation of the observation error with respect to the position. Expanding the squared terms yields the positive definite matrix as follows: Where W is the weight matrix of the observation error, used to weight the Gaussian variance σ of each base station. 2 Write it into a quadratic form and transform the likelihood term into a standard L2 norm square. Q V is the Hessian matrix, and r is the difference vector between the observed values ​​and the model predictions. It measures the deviation between the features generated by the digital twin model at the current candidate location and the features actually measured by the sensor. t It is the position state prediction covariance matrix. μ t It is the prior mean. μ pred It estimates the center of mass, which is the sum of the old position and velocity-time. We use the Lagrange multiplier method to perform convex optimization relaxation on the objective, construct a Lagrange function, and take the partial derivative of the Lagrange function. If Q is positive definite, then the objective is strictly convex, meaning the feasible region is also a convex set, and thus the global optimum, i.e., the convergence position T, can be obtained. *opt : T *opt =Q -1 (q-A T (AQ -1 A T ) -1 (AQ -1 q-b))。 5. The method according to claim 1, characterized in that, In step four, a position estimation method based on the LM nonlinear algorithm is used. For complex, nonlinear, nonconvex, multi-peak, and multi-constraint dynamic positioning problems, we employ a classical nonlinear optimization method for position estimation. When the target is nonlinear and not necessarily convex globally, the global optimal position can be solved using classical nonlinear methods: Observation residual row vector: Prior residual row vectors: r pri (T * )=V t -12 [T * -(μ t +v t Δt)] Residual vector: Where W is the weighting matrix, y is the measured eigenvector, and f(T) * ) is the virtual feature vector generated by the digital twin model, r obs (T * ) represents the observation residual, r pri (T * ) is the prior residual, J(T) * ) is the Jacobian matrix of the residual vector. The Levenberg-Marquardt (LM) algorithm was chosen as the nonlinear optimization method. This method has a fast local convergence speed and a robust gradient method, which always ensures that the target decreases monotonically and is not prone to divergence. First take Then calculate the residual. r (k) ＝r(T *(k) ) Find the Jacobian matrix The Jacobian matrix of the observation residual block is given for the i-th base station. Total Jacobian matrix: Finally, determine convergence if ||Δ (k) ||<ε x or ||r (k) ||<ε r or Then it converges, and the global optimal solution T at the convergence position is obtained. *opt : ||r(T * )|| 2 This term is the sum of squared residuals, used to measure the discrepancy between the model and the observations. It reflects the degree of agreement between the current location estimate and the actual observed data. This term is typically used in optimizing the objective function, minimizing it to approximate the global optimum.

6. The method according to claim 1, characterized in that, In step five, position estimation is performed based on Kalman filtering and maximum a posteriori estimation. However, classical nonlinear optimization methods are computationally too complex, requiring the calculation of the Jacobian and Hessian matrices, and may still get trapped in local optima. Furthermore, their convergence speed is greatly affected by the initial values ​​and the choice of parameter λ, making them unsuitable for large-scale problems. To ensure the positioning system maintains high accuracy and continuity under multipath and NLOS interference, a virtual waveform generation mechanism based on predicted trajectories, a dynamic difference degree reconstruction method, and a waveform-level fusion method are proposed, building upon Kalman filtering and a posteriori estimation to form a closed-loop estimation structure that integrates spatial and waveform layers. During each frame localization process, the system first bases its localization on the state estimate from the previous time step. Predict the node position of the current frame using a state transition model: in, It is the predicted value at the current position, F is the state transition matrix, and μ k To control the input. Subsequently, the predicted location is input into the digital twin system to construct a virtual signal propagation model at the current location and generate a corresponding virtual waveform: In the Kalman filter prediction stage, after predicting the node positions of the current frame, the state covariance matrix P is then... k The prediction yielded the following: Kalman filter update phase: in, It is the predicted covariance, K k It is the Kalman filter gain. Let Jacobian matrix be the nonlinear measurement function with respect to position. This is the filtered and updated position estimate, P. k This is the updated covariance matrix, where Q and R are the process and observation noise covariances, respectively. Through this mechanism, the system not only integrates position prediction and trajectory history, but also integrates the differences between digital twin prediction signals and real signals at the waveform level, enabling fine-grained updates of the state for each frame. After filtering and updating, based on the joint posterior probability model constructed in step two, maximum a posteriori estimation (MAP) is performed to obtain the optimal position of the virtual node to be located. This location is selected as the final location result for the node to be located: By using Kalman filtering to fuse and update the predicted location status with real-time observation error information, the interference of environmental noise and modeling errors on the positioning estimation is effectively suppressed, improving the system's resistance to fluctuations and estimation stability. It is suitable for high-frequency, low-latency real-time positioning scenarios.

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