A vehicle positioning method based on pareto and lyapunov

Abstract

The application discloses a kind of vehicle positioning methods based on Pareto and Lyapunov, by obtaining multiple sensor data of vehicle, and according to multiple sensor data constructs positioning model, according to speed and direction constructs vehicle's dead reckoning model, and the position estimation of the dead reckoning model is fused and estimated to obtain vehicle state information, error state constraint Pareto algorithm is used to optimize and analyze vehicle state to determine constraint optimization problem, and according to Pareto front algorithm, the optimal solution of constraint optimization problem is determined, according to optimal solution, the state space model of fusion estimation process is constructed, and Lyapunov and state space model are used to analyze the stability of vehicle positioning to obtain stability evaluation result, the stability of fusion estimation is analyzed using state space model, realizes robust fusion estimation process, and enhances the ability of vehicle positioning in dynamic environment and the ability of reliable operation under changing conditions.

Description

Technical Field

[0001] This invention belongs to the field of vehicle positioning technology, and particularly relates to a vehicle positioning method based on Pareto and Lyapunov. Background Technology

[0002] With the development of sensing technology, the safety and operational efficiency of automated driving systems in typical urban environments have been greatly improved. In-depth research into the development of various automotive technologies demands enhanced traffic system safety, reduced travel time, and improved energy efficiency. Accurate, real-time, and reliable positioning is one of the most critical functions in assisted driving operations and forms the foundation for many other core applications, including target tracking, trajectory prediction, motion planning, and control. Unlike traditional single-objective optimization methods that focus on maximizing accuracy, Pareto optimization allows for simultaneous trade-offs among multiple competing objectives, such as accuracy, computational efficiency, and robustness to environmental disturbances. In the context of positioning, Pareto optimization has demonstrated its ability to reduce the mean and variance of positioning errors. Therefore, a more balanced and adaptable solution is suitable for a wider range of operating conditions and can be implemented effectively.

[0003] In complex and dynamic scenarios, real-time optimization of multiple criteria, including sensor accuracy, computational load, and robustness to environmental changes, is necessary. This is particularly useful in autonomous driving in complex urban environments, where multiple dynamic considerations must be taken into account in real time to provide reliable positioning estimates. However, in autonomous vehicle navigation, demonstrating the stability of the estimation process is crucial to ensuring that positioning remains accurate and reliable over time. Stability analysis studies the growth of small perturbations or estimation errors and determines whether they decrease over time, remain bounded, or grow infinitely. Therefore, there is an urgent need to provide a Pareto and Lyapunov-based vehicle localization method to address the aforementioned technical problems. Summary of the Invention

[0004] In view of this, the present invention provides a vehicle localization method based on Pareto and Lyapunov, which uses a state-space model to analyze the stability of the fusion estimation and realizes a robust fusion estimation process. While providing stable localization estimation, it enhances the vehicle's ability to localize in dynamic environments and its ability to operate reliably under changing conditions. Specifically, the following technical solutions are adopted to achieve this.

[0005] This invention provides a vehicle localization method based on Pareto and Lyapunov principles, comprising the following steps: Acquire data from multiple sensors of the vehicle and construct a positioning model based on the multiple sensor data, wherein the positioning model includes the estimated position, speed and direction of the vehicle; A dead reckoning model for the vehicle is constructed based on the speed and direction, and the estimated position and the position estimate of the dead reckoning model are fused to obtain vehicle state information, which includes wheel speed, yaw rate and position information. The Pareto algorithm with error state constraints is used to optimize the vehicle state to determine the constrained optimization problem, and the optimal solution of the constrained optimization problem is determined according to the Pareto front algorithm. Based on the optimal solution, a state-space model of the fusion estimation process is constructed, and the stability of vehicle positioning is analyzed using Lyapunov and the state-space model to obtain the stability assessment results.

[0006] This invention provides a vehicle localization method based on Pareto and Lyapunov principles. It acquires data from multiple vehicle sensors and constructs a localization model based on this data. A dead reckoning model is then built based on speed and direction. The estimated position and the position estimate from the dead reckoning model are fused to obtain vehicle state information. An error-constrained Pareto algorithm is used to optimize the vehicle state and determine the constrained optimization problem. The optimal solution to the constrained optimization problem is determined using the Pareto front algorithm. A state-space model for the fusion estimation process is constructed based on the optimal solution. The stability of the vehicle localization is analyzed using the Lyapunov and state-space model to obtain a stability evaluation result. By analyzing the stability of the fusion estimation using the state-space model, a robust fusion estimation process is achieved. This method provides stable localization estimates while enhancing the vehicle's ability to locate itself in dynamic environments and its reliable operation under changing conditions. Attached Figure Description

[0007] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 A flowchart of the vehicle positioning method based on Pareto and Lyapunov provided for this invention. Detailed Implementation

[0009] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0010] See Figure 1This invention provides a vehicle localization method based on Pareto and Lyapunov principles, comprising the following steps: S1: Acquire multiple sensor data of the vehicle and construct a positioning model based on the multiple sensor data, wherein the positioning model includes the estimated position, speed and direction of the vehicle; S2: Construct a dead reckoning model for the vehicle based on the speed and direction, and fuse the estimated position and the position estimate of the dead reckoning model to obtain vehicle state information, wherein the vehicle state information includes wheel speed and yaw rate; S3: The Pareto algorithm with error state constraints is used to perform optimization analysis on the vehicle state to determine the constraint optimization problem, and the optimal solution of the constraint optimization problem is determined according to the Pareto front algorithm. S4: Construct a state-space model of the fusion estimation process based on the optimal solution, and use Lyapunov and the state-space model to perform stability analysis on vehicle positioning to obtain stability assessment results.

[0011] In this embodiment, the latest development in localization methods utilizes Pareto-based multi-objective optimization. Unlike traditional single-objective optimization methods, Pareto optimization focuses on maximizing accuracy, allowing for the simultaneous consideration of multiple competing objectives, such as accuracy, computational efficiency, and robustness to environmental disturbances. In localization problems, Pareto optimization algorithms have demonstrated excellent performance in reducing the mean and variance of localization errors. Therefore, a more balanced and adaptive solution is applicable to a wider range of operating conditions and can function effectively. These multi-objective methods are particularly advantageous in urban scenarios, as these scenarios are complex and dynamic, requiring real-time optimization of multiple criteria, including sensor accuracy, computational load, and robustness to environmental changes. This is especially useful for autonomous driving in complex urban scenarios, where multiple dynamic factors need to be considered in real-time to provide reliable localization estimates.

[0012] It is important to note that in the context of autonomous vehicle navigation, accurate and reliable positioning is crucial. Most traditional positioning methods combine various sensor input data to continuously estimate the vehicle's position and orientation. The most widely used is the dead reckoning model, which utilizes onboard sensors to measure wheel speed and yaw rate. This model calculates the position and heading in navigation coordinates and provides a basic reference for data from other sensors (such as LiDAR). By acquiring data from multiple vehicle sensors and constructing a positioning model based on this data, a dead reckoning model is built based on speed and orientation. The estimated position and the position estimate from the dead reckoning model are fused to obtain vehicle state information. An error-constrained Pareto algorithm is used to optimize the vehicle state to determine the constrained optimization problem. The optimal solution to the constrained optimization problem is determined using the Pareto front algorithm. A state-space model of the fusion estimation process is constructed based on the optimal solution. A Lyapunov and state-space model are used to perform stability analysis on the vehicle positioning to obtain stability evaluation results. By analyzing the stability of the fusion estimation using the state-space model, a robust fusion estimation process is achieved, enhancing the vehicle's positioning capability in dynamic environments and its reliable operation under changing conditions.

[0013] Optionally, acquiring multiple sensor data from the vehicle and constructing a positioning model based on the multiple sensor data includes: Set the plane where the driving vehicle is located as , ,in, , For discrete-time exponents, the estimated location is based on a set of reference points or distance measurements at known locations. , and ,in The time distance between the location node and each reference point is represented as: Observation distance yes Noise measurement value, distance measurement value , Subjected to additive zero-mean Gaussian noise The destruction is represented by the following expression: (1) Among them, the variance of noise Related to distance, it is modeled as follows: (2) in, and It is a known constant. It is distance The baseline variance of the noise is zero. An initial level for the noise variance is set, and the minimum noise variance is represented. It is a constant and is used to control the noise variance as a function of distance. Increased with the increase; Represents the set of planar coordinates of the first position node. Let i represent the set of planar coordinates of the second position node, where i and j represent the reference point and the position node at the known position, respectively.

[0014] In this embodiment, the vehicle state is obtained by fusing the estimated position and the position estimate from the dead reckoning model, including: Vehicle in time The position is estimated by fusing two estimates: one obtained from range measurements using a weighted least squares algorithm, and the other obtained from dead reckoning using velocity and heading measurements. The fused estimate is denoted as . The corresponding expression is: (3) (4) The estimation problem is solved by updating the distance measurement using readings of speed and direction to estimate the vehicle's position. Location in time, of which, estimation The position is determined by fusing the outputs of two estimators: a range-based estimator and a dead reckoning estimator. The expression for the position estimate is: (5) in, This represents the set of position coordinates of the first position node at time k+1. This represents the set of position coordinates of the second position node at time k+1. It is a position estimate derived from range measurement. It is a dead reckoning position estimate. and It is to satisfy The sensor fusion parameters are estimated based on the fusion of ranging measurements and dead reckoning. And in The time frame provides the eastern and northern locations, and the corresponding expressions are: (6) (7) in, Indicates in The estimated eastern location in terms of time. Indicates in The estimated northern location in terms of time, Indicates in Sensor fusion parameters for eastern location estimation using temporal ranging measurements. Indicates in Sensor fusion parameters for eastern position estimation using dead reckoning over time. Indicates in Sensor fusion parameters for northward location estimation based on temporal ranging measurements. Indicates in Sensor fusion parameters for northbound position estimation using dead reckoning over time, where the sensor fusion parameters are part of vehicle state information.

[0015] It should be noted that the control noise variance and how the variance increases with distance are defined. The variance increases more rapidly with increasing distance, and the measurement noise also increases significantly with the distance between the master and slave nodes. The vehicle's position in time is estimated by fusing two estimates: one using weighted least squares (WLS) for distance measurement, and the other using velocity and direction measurements for dead reckoning. The estimation problem is equivalent to updating the distance measurement using velocity and direction readings to estimate the vehicle's position in time. This is accomplished within a loosely coupled sensor fusion framework, where the estimation is determined by fusing the outputs of two estimators: a distance-based estimator and a dead reckoning estimator.

[0016] Optionally, a dead reckoning model is constructed by estimating the vehicle's position based on its current position, speed, and direction, including: The vehicle's position in navigation coordinates is calculated using wheel speed and yaw rate from onboard sensors, as well as its heading between LiDAR coordinates and navigation coordinates. hour along The expression for dead reckoning of axis position is: (8) in, for Time position estimate, The time interval between two measurements. for Observe the speed at all times. yes Observe the azimuth angle at all times. The true location at any moment Represented as: (9) in, for The true speed of a moment for The true azimuth angle at any given moment, measured from the wheel speed sensor. and direction , It is the vehicle's heading angle. It is the heading angle. It is the vehicle's sideslip angle. The expression is: (10) in, It is the yaw rate, the measured value is... and Given the corresponding noise term and The damage is such that the measured values ​​follow a variance of . and The zero-mean Gaussian distribution; Based on the given dead reckoning data and observed speed and direction The expressions for calculating the eastward and northward velocities are as follows: (11) (12) in, It is the speed being measured. Indicates the direction being measured.

[0017] In this embodiment, the dead reckoning model estimates the vehicle's position based on its previous position, speed, and orientation. The model utilizes wheel speed and yaw rate data provided by onboard sensors (similar to an inertial navigation system) to calculate the vehicle's position in navigation coordinates and its heading between LiDAR and navigation coordinates. Since the vehicle's lateral excitation is small, meaning the sideslip angle is small, the yaw rate can be neglected and approximated by the heading angle. Noisy measurements can affect speed estimation; these measurements from external sensors are fused together to improve the accuracy of position and speed estimation, thereby better modeling the vehicle's state in navigation coordinates.

[0018] Optionally, the Pareto algorithm with error state constraints is used to perform optimization analysis on the vehicle state to determine the constrained optimization problem, including: The ideal sensor fusion parameters are determined using the error state-constrained Pareto algorithm. and And achieve a balance between minimizing estimated position and heading errors and managing noise variance; Error state vector The individual errors in position, speed, and heading for the east and north can be represented in the following expressions: (13) in, and It is the actual eastern and northern location. and The true speed of the East and North This represents the actual course and includes a corresponding estimate. , , , and The error state covariance matrix is ​​defined as: (14) The total error is represented as a weighted sum Q of the individual errors using a weighted matrix: (15) in, To determine the diagonal matrix representing the relative importance of each error component, (16) The noise covariance matrix related to the measurement noise vector affecting dead reckoning and distance measurement is expressed as: (17) Among them, the variance of the heading noise of the distance measurement noise, velocity noise, and heading noise is respectively represented by... , and express.

[0019] In this embodiment, the goal of the error state constraint Pareto method is to estimate the position and heading errors in the dead reckoning model and obtain the error measurements of the northeast position, speed and heading. This method optimizes the fusion parameters to ensure that the error state constraints are met while minimizing the estimation error and noise variance, and maintains a balance between the two competing objectives.

[0020] Optionally, the error state-constrained Pareto algorithm estimates the position and heading errors in the dead reckoning model and obtains the error measurements of position, speed, and heading for the east and north. The estimated errors of position, speed, and heading for the east and north are represented in matrix form as follows: (18) in, Representing the error state vector, the Pareto optimization problem is to minimize the estimation error and noise variance, while being influenced by the sensor fusion parameters. and Given the constraints, the corresponding objective function is expressed as: Make obedience and (19) Where Q is the weighting matrix of the error components, and R is the noise covariance matrix related to the sensor noise. It is a regularization parameter that controls the trade-off between minimizing estimation error and management noise variance. This represents the maximum permissible error to ensure that the constraints are met; the sensor fusion parameters are selected using an optimization framework. and This reduces positioning and heading errors while controlling the overall noise variance.

[0021] In this embodiment, the optimization framework is used to select fusion parameters, which reduces positioning and heading errors while controlling the overall noise variance. Error constraints ensure that the estimation error does not exceed a certain maximum value, while constraints on the sum ensure that the total weights of sensor fusion do not exceed 1. A balance is achieved between reducing the mean square error (MSE) of the estimation and minimizing the uncertainty caused by sensor noise, thereby ensuring the robust positioning of the assisted driving vehicle.

[0022] Optionally, the constrained optimization problem of the error-state-constrained Pareto algorithm is estimated to balance the estimation error and sensor noise, including: Initial estimate: The estimated value is determined based on the dead reckoning model and distance measurement. , , , and The initial estimate will provide a baseline for calculating errors and determining fusion parameters; Error propagation: Estimation error is propagated using formula (18). Estimate the actual state The difference between the initial estimate and the actual value Propagate the difference and calculate the covariance matrix in formula (14). To quantify errors from different sources; Noise analysis: The noise covariance matrix is ​​calculated by analyzing the sensor characteristics using formula (17). ; Optimization analysis: Solve the Pareto optimization problem in formula (18) to determine the fusion parameters. and Minimize the weighted sum of estimation error and noise variance, and maintain and It is pointed out that Lagrange multipliers help manage equality constraints in nonlinear optimization problems. ; Updated estimation: After obtaining the optimal fusion parameters and Then, update the location. estimation, speed and heading The revised optimal estimate includes distance and dead reckoning data; The Pareto front is used to graphically represent the solution of the Pareto optimization problem in formula (19). The points on the curve correspond to different methods of balancing the minimization of estimation error and the management of noise variance. The points on the Pareto front are the optimal solutions and correspond to the minimum overall error, satisfying the constraints on estimation accuracy and noise variance.

[0023] In this embodiment, a state-space model of the fusion estimation process is constructed based on the optimal solution, and a stability assessment result is obtained by performing stability analysis on vehicle positioning using Lyapunov and the state-space model, including: A state-space model is used to analyze the stability of the fusion estimation process. State vector at time step Represented as: (20) Discrete-time linear systems can be used to model the evolution of this state vector: (twenty one) in, It is the state transition matrix, which defines the state transition from time to time. arrive The evolution, It is to control input The input matrix mapped to the state. The process noise is assumed to be a zero-mean Gaussian random vector with a covariance matrix. The measurement model associates the state vector with the observed measurements, and the corresponding expression is: (twenty two) in, For the measurement matrix, To measure noise, a preset Given a zero-mean Gaussian distribution with covariance, the state transition matrix is ​​analyzed. Use the eigenvalues ​​of the eigenvalues ​​to test; If all eigenvalues ​​are inside the unit circle, then the system is stable; If any feature value is outside the radius of the unit circle, the positioning process is unstable; Based on the state transition matrix The stability of the eigenvalue analysis estimation process, when The system is stable when all its eigenvalues ​​lie on the unit circle in the complex plane, and the corresponding expression is: (twenty three) If any eigenvalue is greater than 1, the system is unstable.

[0024] It is important to note that in navigation for assisted driving vehicles, demonstrating the stability of the estimation process is crucial for ensuring that positioning remains accurate and reliable over time. Stability analysis examines the growth of small disturbances or estimation errors and determines whether they decrease over time, remain bounded, or grow infinitely. Stability can be tested by analyzing the eigenvalues ​​of the state transition matrix; if all eigenvalues ​​are within the unit circle, the system is stable, essentially meaning that any estimation error will decay over time. On the other hand, if any eigenvalue is outside the radius of the unit circle, the disturbance will be amplified and may lead to instability in the localization process. Furthermore, analyzing the covariance matrix is ​​useful as it provides insights into process noise and measurement noise regarding the stability of the state estimation. A robust fusion estimation process was implemented, enhancing the vehicle's ability to locate in dynamic environments and operate reliably under changing conditions while providing stable positioning estimates.

[0025] Optionally, a Lyapunov function can be used. Stability analysis is performed using the state vector, which is defined as follows: (twenty four) Where P is a positive definite matrix, and the decrease of the Lyapunov function over time indicates the stability of the system, with the corresponding expression being: (25) Substituting the state-space equations into the Lyapunov function yields: (26) in, If the value is a negative constant, then: (27) Formula (27) is the Lyapunov stability criterion. If there exists a positive definite matrix that satisfies Formula (27), then stability exists.

[0026] In this embodiment, the stability analysis process of the Lyapunov function includes: If there exists a positive definite matrix Make the Lyapunov function If the value decreases along the system trajectory, then the state-space equations apply. The discrete-time linear system represented by the matrix is ​​asymptotically stable, or if the matrix represents the asymptotically stable system. The system is stable when it satisfies the Lyapunov function, where, It is a positive definite matrix: (28) Lyapunov function from state Become The expression is: (29) State space equations Substitute the Lyapunov function: (30) The change of the Lyapunov function is as follows: (31) Based on the necessary condition for establishing the stability of the Lyapunov function, the expression for calculating the Lyapunov function is as follows: (32) Among them, according to the positive definite matrix and each non-zero state vector binomial Always positive, any of All are negative: (33) Lyapunov function The system is asymptotically stable based on the fact that all non-zero state vectors decrease over time. The negative increment value with Increase, Status Converging toward zero, according to the matrix Obtains a positive definite matrix The Lyapunov function proves that the system is asymptotically stable. when hour, Approaching zero, state Converging to the origin; when For positive definiteness, Lyapunov functions are used to ensure the system state transition matrix. All eigenvalues ​​lie within the unit circle of the complex plane.

[0027] It should be noted that the combination of eigenvalue analysis and the Lyapunov method can provide sufficient basis for stability analysis in fusion estimation. When determining the long-term stability of the estimation process, it can be guaranteed that the eigenvalues ​​of the state transition matrix lie within the unit circle, and the existence of an appropriate Lyapunov function can be verified. The latter is the foundation of the reliability of assisted driving vehicle navigation. Because the Lyapunov function decreases with time for all non-zero state vectors, the system is asymptotically stable. The negative increment of ... When the state approaches zero, it means that the state converges to the origin, which guarantees the existence of a positive definite matrix satisfying the Lyapunov equation, ensuring that the system state does not grow unbounded over time. It converges to zero, thus ensuring the asymptotic stability of the system.

[0028] If the eigenvalues ​​of the state transition matrix happen to be positive definite, then the Lyapunov method is used to guarantee the stability of the system. This ensures that all eigenvalues ​​of the system's state transition matrix lie within the unit circle of the complex plane, thus guaranteeing stability. In the calculation of matrix P, this process begins with a solution to the Lyapunov equation, where is the state transition matrix; should be the positive definite matrix to be determined. It is a pre-selected positive definite matrix. The choice can be arbitrary, because it can only be affirmative to guarantee... The uniqueness and certainty of. satisfy First, it must be positive definite, and then MATLAB must be used to process the obtained LMI. Numerical solutions are derived from this LMI, which provides the matrix. Satisfying the stability condition, the solution to LMI gives the following matrix. for All non-zero states mean that the system is asymptotically stable.

[0029] Specifically, multiple data acquisition systems were employed to capture point cloud data for high-precision mapping and positioning. The HDL-32E 3D LiDAR sensor mounted on the vehicle provided the required high-frequency point cloud data at 20 Hz, while algorithms developed by ROS processed this data in real time on an industrial-grade PC. Vehicle attitude updates were performed in response to positioning at 5 Hz, while ground truth was determined by an integrated GNSS and IMU system, and a planar LVX. For large-scale data collection, the RIEGL VMX-2HA mobile laser scanning system was used, providing highly accurate 3D data with an accuracy of 8 mm and 5 mm, acquiring up to 1.1 million measurement data points per second due to its dual-scan mechanism. Fixed GPS stations were also used to establish control points to enhance georeferencing, ensuring precise alignment of the data with real-world coordinates. The MLS system operated at speeds up to 60 km / h, achieving a point density of approximately 7500-8500 points per square meter. This extremely high point density allowed even the finest details to be represented in the data, providing the granularity required for mapping and subsequent analysis. Four different independent MLS datasets were used and provided in LAS file format. Dataset 1 is a 30-meter-long urban road corridor segment with 1,827,963 points, achieving a density of 8,500 points / m². Dataset 2 consists of other road segments with a length of 176.5 m, each containing 9,850,578 points. These datasets span different segments of highways, each presenting unique localization and mapping challenges. The high point density in these datasets allows for thorough detail scanning of road markings, curbs, and even building facades, easily capturing details and providing robust analytics for applications in autonomous navigation.

[0030] Specifically, real-time performance is the most critical issue in autonomous vehicle localization. The rotation rate of the Velodyne LiDAR and the update frequency of the algorithm ensure that the vehicle's attitude is generated at a frequency of 5 Hz, thereby achieving continuous and responsive localization. The computational burden of processing large datasets in real time using an industrial PC is mitigated, ensuring both the accuracy and speed of the algorithm. A powerful data acquisition and localization system is proposed, integrating a high-performance LiDAR, a precision GNSS / IMU, and a robust data processing platform. These datasets are invaluable for further validating and continuously improving the localization algorithm in challenging real-world scenarios.

[0031] Testing was conducted on a loop of approximately 2.7 km, with a 0.5 km section specifically selected for analysis due to its complex environment, including highly intricate architecture and diverse vegetation. The performance of the brightness map was assessed by identifying five invariant features across 1D, 2D, and 3D structures. Regions 1 and 2, containing buildings and vegetation, were considered, and the impact of the environment on algorithm accuracy was analyzed in detail. These tests were conducted under conditions common in the region, including heavy rain and fog. These adverse conditions introduced significant variability into the LiDAR point cloud, primarily due to the scattering effect of raindrops and reduced visibility under fog conditions. Raindrop density and the light diffusion effect in fog necessitate frequent map updates and adaptations for accurate real-time localization. Indeed, the ability to consider and adapt to such environmental changes is a crucial factor in evaluating the algorithm.

[0032] To simulate real-world driving conditions, a shuttle bus traveled along a circular road under normal acceleration, deceleration, and steering patterns. During testing, the longitudinal speed was maintained between 0 and 25 km / h by adhering to the speed limits of the circular road. Therefore, the test focused on the robustness of the map matching algorithm under adverse weather conditions, particularly rain, which affects the data acquisition from the LiDAR sensors and the processing required for accurate vehicle localization. The algorithm was initially executed in clear weather to provide a baseline for its practical localization performance, and this result has been used as a reference for further evaluation. Subsequent experiments were conducted to test the combination of rainfall with LiDAR scanning and feature extraction. The test also explored how weather affects the ability to distinguish between static features (such as buildings) and dynamic environmental features (such as vegetation). Considering their appearance properties in rain, this part of the evaluation is crucial for determining whether cost-effective navigation can be relied upon in variable weather conditions, especially in areas where heavy rainfall is expected.

[0033] The proposed brightness map generation was tested under adverse weather conditions, specifically during a period of clear skies followed by heavy rain. Two types of point cloud maps were created: a dense map incorporating data from all available LiDAR frames, and a lighting map that retained only invariant features such as buildings and roads, while filtering out transient objects like vegetation. The dense map contained all the information from the LiDAR points and provided a complete representation of the environment. Notably, the lighting map retained less point density because weather-sensitive points were removed. Compared to the dense map, vegetation, characterized by regions 1 and 2, showed a greater reduction in point density in the brightness map. This was particularly beneficial during heavy rain, as this often worsens LiDAR data due to scattering and reflection effects. The brightness map, by removing these weather-sensitive points, presents less artifacts and provides a clearer view of the campus infrastructure.

[0034] Therefore, the size of the point cloud map decreased from 118 MB for the dense map to 48.3 MB for the lightweight map, representing a 59% reduction in density. Furthermore, although vegetation changes necessitate seasonal updates to the dense map, the coarse localization map generated based on a low-cost GNSS receiver exhibits good robustness to seasonal and weather changes. This allows for the filtering out of different vegetation points, resulting in a denser map and reduced update frequency, making the map matching algorithm more efficient, reliable, and robust even under very severe weather conditions such as heavy rain.

[0035] Specifically, processing dense LiDAR frames effectively filters out vegetation points, thereby reducing point cloud density. This filtering step is crucial because the ability of LiDAR to capture accurate data is severely impacted during heavy rain. LiDAR scans obtained under heavy rain conditions appear relatively sparse and darker, and the presence of noise points increases compared to LiDAR scans collected in clear weather. Notably, these noise points are primarily generated by raindrops reflecting off the laser beam, accounting for only 1.22% of the total points received per scan—a negligible number. Under heavy rain conditions, the number of measurement points decreases, intensity values ​​drop, and some noise points randomly exist in the scan due to laser reflection from raindrops. Table 1 summarizes the statistics for three other rainfall scenarios in the environment, showing that, on average, 23% of points are lost per scan cycle. However, even after losing these points, the impact of noise points generated by reflected raindrops is very small, further reinforcing the strength of the filtering method under weather conditions.

[0036] Table 1 Rainfall Impact Assessment

[0037] The reduction in the number of receiver points not only affects the quantity and quality of features relevant to good localization that can be extracted, but also the cumulative ground reflectance features from approximately 200 scans during the localization test. In contrast, some areas showed no ground reflectance features during rainfall, while others remained unchanged. This is because of the varying permeability of surface materials; this is why some areas, such as roadside grass, easily allow groundwater to seep into the soil and show less change in reflectance during rainfall. Table 2 shows the corresponding number of features for each scenario, with the number of observable features decreasing significantly as rainfall intensity increases. However, features less affected by rainfall show minimal change; while falling raindrops may absorb some lidar points, they are unlikely to absorb all points impacting the surface.

[0038] Table 2. Characteristic observations under different weather conditions

[0039] After preprocessing, an ensemble localization algorithm was implemented using lightweight and dense maps generated under heavy rain conditions. Lightweight frames and lightweight maps are denoted as LL, lightweight frames and dense maps as LD, and dense frames and dense maps as DD. Lightweight frame images can be accurately registered on both lightweight and dense maps, similar to dense frame image registration on a dense map. When responding to the current fair weather conditions, the LL method has the shortest processing time, averaging 107.5 ms, while the LD and DD methods have higher processing times, at 136.1 ms and 243.8 ms, respectively. The processing time of all methods increases from light to heavy rain, with the DD method reaching a critical peak of 284.7 ms during heavy rain. This behavior changes beneficially when using the ensemble Pareto method: efficiency is significantly improved across various methods and conditions. When the DD method is considered for heavy rain, the processing time for heavy rain decreases from 284.7 ms to 104.4 ms. The optimization emphasizes the efficiency of the Pareto method in finding a proper balance between computational efficiency and accuracy; therefore, it may be suitable for real-time map matching under adverse weather conditions.

[0040] Table 3 summarizes the comparison of processing times under different environmental conditions and map matching methods, while highlighting the efficiency of individual and combined Pareto methods. The data shows that the Lightweight Frame and Lightweight Map (LL) method has the shortest processing time under good weather conditions, averaging 107.5 ms with a root mean square (RMS) of 32.1 ms. In contrast, the Lightweight Frame and Dense Map (LD) method has an average processing time of 136.1 ms and an RMS of 47.4 ms, while the Dense Frame and Dense Map (DD) method has the longest processing time, averaging 243.8 ms with an RMS of 65.3 ms. The processing time increases for each method as the weather worsens. During heavy rain, the LL method averages 125.2 ms with a standard deviation of 37.39 ms. On the other hand, the average times for the LD and DD methods under the same weather conditions are 155.5 ms and 284.7 ms, respectively, with root mean square values ​​of 54.3 ms and 76.2 ms, respectively. This increase is due to the increased complexity and noise caused by severe weather, which will ultimately affect frame quality and map matching accuracy.

[0041] The integrated Pareto method reduced processing time under all conditions and methods. Specifically, under heavy rain conditions, the average time for the LL method decreased from 125.2 ms to 70.8 ms, the LD method from 155.5 ms to 81.5 ms, and the DD method from 284.7 ms to 104.4 ms. This pattern remained consistent regardless of weather changes. For example, under favorable weather conditions, the LL method reduced time to 60.8 ms, the LD method to 71.5 ms, and the DD method to 89.3 ms. This not only demonstrates accuracy but also proves the high processing efficiency of the method employed in this paper. In summary, the data above shows that lightweight frames reduce computation time by more than 43.4%, and it also indicates a slight reduction in the root mean square value for both the LL and LD methods. While the use of lightweight maps did not significantly reduce processing time, it did effectively reduce map size. Currently, the integrated Pareto method effectively optimizes real-time map matching systems, especially under challenging conditions, because it balances computational performance and accuracy.

[0042] Table 3 Comparison of Processing Times

[0043] Table 4 shows a comparison of the positioning estimation errors of different settings in the map matching algorithm under different weather conditions, using three different methods: (1) Lightweight Frame and Lightweight Map (LL), (2) Lightweight Frame and Dense Map (LD), and (3) Dense Frame and Dense Map (DD). For this comparison, error metrics will include AME and RMSE. Since positioning performance is evaluated as balanced under different environmental conditions, an integrated Pareto method is applied to optimize the trade-off between these error metrics.

[0044] Table 4 Comparison of Positioning Estimation Errors

[0045] The above comprehensive analysis of the error performance of various sensor fusion methods reveals clear patterns in error distribution across ranging, dead reckoning, and the proposed Pareto sensor fusion method. In the LL scenario, the proposed Pareto sensor fusion exhibits a lower cumulative error distribution compared to ranging and dead reckoning, indicating its superior performance in minimizing absolute position errors. For the LD scenario, although the error level is higher than in LL, the error level in the empirical cumulative distribution function (CDF) of the simulated error data is also more favorable for the proposed Pareto sensor fusion. With further reductions in the error rate, the DD method extends the advantages of the proposed Pareto sensor fusion, achieving the lowest cumulative error among all methods. These observations are further confirmed by the root mean square error (RMSE) values, as the proposed Pareto sensor fusion produces the minimum RMSE value in each case, confirming its ability to generate accurate and reliable position estimates. These results further enhance the strength of the proposed Pareto sensor fusion, effectively improving error performance across different orders of magnitude and complexities of error in sensor data.

[0046] Under favorable weather conditions, lightweight frames with lightweight maps exhibit the lowest positioning errors, thus providing a fair baseline for location accuracy: it balances computational efficiency with reduced frame and map density to avoid overfitting. However, under favorable conditions, denser settings that provide detailed environmental features do not offer significant accuracy improvements. Positioning performance deteriorates across all configurations as weather conditions worsen. Moderate and heavy rain cause substantial increases in positioning errors, with more pronounced increases observed in denser configurations (lightweight frames with dense maps and dense frames with dense maps). This is likely because the LiDAR sensor interacts more with the rain; transient environmental features such as raindrops and wet surfaces introduce noise.

[0047] Lightweight frames with lightweight map configurations remain fairly stable with low positioning errors even in light rain; however, they suffer some accuracy loss even in moderate and heavy rain. Nevertheless, they still outperform denser, more noise-resistant positioning methods. While dense maps may offer benefits under ideal conditions, lighter approaches (especially lightweight frames with lightweight maps) may provide stronger positioning performance in adverse weather conditions such as heavy rain, as noise can compromise the integrity of dense point clouds.

[0048] The east and north position errors of the three selected frame and map density configurations: Light frame with Light map (LL), Light frame with Dense map (LD) and Dense frame with Dense map (DD). The results show all four different weather conditions: sunny, light rain, moderate rain and heavy rain. The variation of the east position error of the configuration over time reflects the fluctuation of positioning accuracy under environmental changes. (1) LL (Light Frame with Light Map) configuration, in which the LL (Light Frame with Light Map) configuration performs stably under good weather conditions, with the east position error generally less than 0.5 meters. Its performance is roughly the same under light rain. However, under light rain and heavy rain conditions, its east position error begins to deteriorate, sometimes exceeding 0.75 meters. Although the LL configuration is robust under good conditions, its sparse mapping cannot capture and compensate for dynamic environmental changes (such as raindrops and wet surfaces), resulting in a large position accuracy deviation. (2) LD (Light Frame with Dense Map) configuration, in which the LD configuration has a slightly higher error under severe weather conditions. The performance is relatively stable in sunny weather, with a position error of around -0.25 to 0.25 m. Light rain and heavy rain cause large fluctuations in power and position error. In most heavy rain conditions, the positioning error exceeds 0.5 m. The increased map density captures transient features such as raindrops and reflections that the positioning algorithm cannot filter out uniformly, thus reducing accuracy. (3) DD (Dense Frame with Dense Map) configuration, where the maximum position error value under different weather conditions is the DD configuration. In good weather, the error is very close to the values ​​of the other two configurations, mostly less than 0.5 m. However, as the rain begins to intensify, these position errors become unstable, mostly exceeding 0.75 m, and approaching 1 m in heavy rain. The combination of dense frame and dense map greatly amplifies environmental noise and captures too many transient or irrelevant features, such as artifacts caused by rain. This will lead to overfitting and a serious loss of positioning accuracy.

[0049] Comparative analysis shows that the LL configuration exhibits the most stable performance, as the location error remains constant and lower compared to other configurations, regardless of whether it's sunny or in light rain. This means that the frame and map density in LL optimally balances environmental representation, thus resisting noise and making it the most reliable for general use, especially under adverse conditions. Conversely, LD and DD configurations provide finer environmental representation details but are more susceptible to environmental noise, particularly during heavy rain. Dense configurations introduce redundant data points, significantly increasing noise and reducing positioning accuracy. This means that excessive detail in the environmental model is detrimental under dynamic and noisy conditions, as the positioning system cannot filter out useful information from the noise. Therefore, LL performs best under all weather conditions, especially under highly disturbed conditions such as heavy rain. While higher-density LD and DD can capture more detail, they are also more susceptible to noise, leading to significant errors during weather degradation. Appropriate selection of frame and map density is crucial for achieving optimal positioning accuracy, at least in noisy environments, especially in highly dynamic and challenging outdoor conditions.

[0050] By comparing different analyses, it can be observed that rainfall significantly increases positioning errors across all configurations, with the severity of these errors increasing with rainfall intensity. However, the most consistent performance is provided by the LL configuration, as the error deviation is smaller in both sunny and rainy conditions. The lightweight frame and map settings are more effective in handling noisy and dynamic environments without capturing irrelevant details that interfere with positioning accuracy. However, in heavy rain, the LD setting is more sensitive to rain, while the dense map provides more environmental detail. It may be useful under ideal conditions, but in severe weather, it introduces more noise, leading to greater positioning errors. This results in the highest positional error across all weather types in the DD configuration, which uses both dense frames and a dense map. Such a configuration, especially in rainy conditions, captures too much noise, making it difficult for the system to maintain good positioning, thus making it the least suitable configuration for use in challenging environments. Therefore, the LL configuration is the most robust and reliable in positioning performance under various weather conditions, especially in rainy conditions. Denseer configurations, whether involving dense maps or frames, or both, are more prone to noise and positional errors, especially in rainy conditions. These results bring us back to the question of optimizing a positioning system by balancing environmental detail and noise immunity. Therefore, lightweight frames and map settings may perform better when dealing with dynamic and challenging outdoor conditions, which are often accompanied by rain or other types of environmental disturbances.

[0051] It is worth noting that these results provide important insights into the performance and optimization possibilities of sensor fusion methods in handling time and location estimation errors. Removing vegetation from LiDAR point clouds to reduce point cloud density and improve computational efficiency is a highly effective strategy. This reduction, especially for lightweight frame configurations, significantly reduces the processing load required by the mapping matching algorithm. Although vegetation removes some low-quality features, it does not significantly affect localization accuracy because structural features (such as buildings) dominate the map matching process. These features are more stable and invariant, thus providing a more reliable reference for localization.

[0052] Calculations show that using lightweight maps alone offers limited benefits in terms of increased processing time, while combining them with lightweight frame generation reduces computational requirements and significantly further reduces computational burden under adverse weather conditions. This is evident from the examples already demonstrated using moderate and heavy rain, where processing times were significantly lower than using dense frames and maps. As assisted driving systems further develop, computational complexity will increase. Optimizing each subsystem will become even more critical as sensor fusion systems begin to integrate numerous features and functions. By simplifying maps to reduce computational load, this invention, in addition to enhancing real-time processing capabilities, opens new avenues for deploying complex localization and map-matching algorithms in challenging dynamic environments.

[0053] Considering the variations in sensor data caused by rain, localization in rain-affected environments is one of the most challenging tasks for any autonomous driving localization system. LiDAR point cloud data exhibits high variability under rainfall conditions because each beam scatters and attenuates the signal. These effects reduce the accuracy of map matching algorithms, especially those relying on dense point clouds representing transient environmental features such as vegetation. These features, like vegetation, are highly sensitive to rain, thus increasing the variability of point-to-point localization performance during moderate to heavy rain. The proposed Pareto sensor fusion method achieves optimal map generation by intelligently excluding these rain-sensitive features. Therefore, the reference map will be highly stable and reliable because it filters out points associated with vegetation, which tend to fluctuate with weather conditions and seasons. This reduction in point cloud density improves the efficiency of the process and reduces the adverse effects of rainfall on LiDAR-based map matching.

[0054] Integrating lightweight frames and lightweight maps enhances the system's robustness in rain-affected environments. This setup strikes a good balance during light to moderate rainfall, minimizing computational load without compromising positioning accuracy. When rain is heavy, the additional contribution of instantaneous point cloud removal becomes more critical. While dense point clouds can offer higher spatial resolution, increased LiDAR signal distortion makes them more susceptible to noise and errors under heavy rainfall conditions. The resulting lightweight map is better suited to these conditions, focusing on preserving more stable and rain-resistant features such as building and road boundaries, which serve as reliable markers for positioning.

[0055] Therefore, rain-affected environments need to be further processed in a more automated and adaptive manner. In practice, this would involve manually removing rain-sensitive features, such as vegetation, by combining them with coarse GNSS data using tools like navigation maps. Automating this process using machine learning and computer vision would significantly improve accuracy and efficiency. For example, deep learning models can be used to identify and exclude rain-affected elements in LiDAR point clouds in real time. This would provide more consistent LiDAR performance under different weather conditions without human intervention. Such adaptive filtering can also further enhance the system's ability to maintain high positioning accuracy under heavy rainfall conditions, thereby improving the reliability of assisted driving navigation in rain-affected environments. Furthermore, integrating data from weather forecasts or rainfall sensors into the positioning framework (model) allows for dynamic adjustment of the point cloud filtering process based on real-time weather conditions. While proposed Pareto sensor fusion methods have significantly improved positioning performance under rain-affected conditions, considerable room for optimization remains. Automating the removal of rain-sensitive features and using adaptive filtering techniques with real-time environmental data hold great promise for further enhancing the robustness and accuracy of future autonomous positioning systems.

[0056] The system would be even stronger if GNSS data were also considered in map matching under good signal conditions to provide large-scale resilience to cope with increasingly larger dead reckoning errors over time. This hybrid approach, which integrates GNSS with lidar and inertial sensors within a consensus framework, has the potential to further expand the system's operational range by improving its adaptability to real-world conditions. The Pareto-optimized positioning framework optimally balances accuracy and computational efficiency under different conditions. This multi-objective approach excels at providing high adaptability and accuracy, especially in complex urban environments. Combining Pareto optimization with lightweight map and sensor fusion enhances the system's resilience and accuracy, making it suitable for real-time, weather-variable positioning in autonomous vehicle applications. The Pareto-optimized positioning method achieves significant improvements across all metrics, with a 40-45% reduction in RMSE (from 0.0965 m to 0.0566 m in heavy rain), thus significantly improving the positioning flexibility and accuracy of traditional methods. By using a brightness map that retains only fundamentally invariant features, the method reduces point cloud density by 59%, thereby reducing computational load and improving performance under adverse weather conditions. Meanwhile, the Pareto optimized lightweight frame and lightweight map (LL) method reduces the processing time from 107.5 ms to 60.8 ms under clear weather conditions and from 284.7 ms to 104.4 ms under heavy rain conditions, demonstrating the efficiency and accuracy of the method. The Pareto method is effective for real-time applications in dynamic and climate change environments, while pursuing higher positioning accuracy and higher processing efficiency.

[0057] In all examples shown and described herein, any specific values ​​should be interpreted as merely exemplary and not as limitations; therefore, other examples of exemplary embodiments may have different values.

[0058] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0059] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A vehicle positioning method based on Pareto and Lyapunov principles, characterized in that, Includes the following steps: Acquire data from multiple sensors of the vehicle and construct a positioning model based on the multiple sensor data, wherein the positioning model includes the estimated position, speed and direction of the vehicle; A dead reckoning model for the vehicle is constructed based on the speed and direction, and the estimated position and the position estimate of the dead reckoning model are fused to obtain vehicle state information, which includes wheel speed and yaw rate. The Pareto algorithm with error state constraints is used to optimize the vehicle state to determine the constrained optimization problem, and the optimal solution of the constrained optimization problem is determined according to the Pareto front algorithm. Based on the optimal solution, a state-space model of the fusion estimation process is constructed, and the stability of vehicle positioning is analyzed using Lyapunov and the state-space model to obtain the stability assessment results.

2. The vehicle positioning method based on Pareto and Lyapunov as described in claim 1, characterized in that, Acquire data from multiple vehicle sensors and construct a positioning model based on the data, including: Set the estimated position of the driving vehicle on the plane as , ,in, , For discrete-time exponents, the estimated location is based on distance measurements of a set of reference points at known locations. , and ,in The time distance between the location node and each reference point is represented as: Observation distance yes Noise measurement value, distance measurement value , Subjected to additive zero-mean Gaussian noise The destruction is represented by the following expression: （1） Among them, the variance of noise Related to distance, it is modeled as follows: （2） in, and It is a known constant. It is distance The baseline variance of the noise is zero. An initial level for the noise variance is set, and the minimum noise variance is represented. It is a constant and is used to control the noise variance as a function of distance. Increased with the increase; Represents the set of planar coordinates of the first position node. Let i represent the set of planar coordinates of the second position node, where i and j represent the reference point and the position node at the known position, respectively.

3. The vehicle positioning method based on Pareto and Lyapunov as described in claim 2, characterized in that, The vehicle state is obtained by fusing the estimated position and the position estimate from the dead reckoning model, including: Vehicle in time The position is estimated by fusing two estimates: one obtained from range measurements using a weighted least squares algorithm, and the other obtained from dead reckoning using velocity and heading measurements. The fused estimate is denoted as . The corresponding expression is: （3） （4） The estimation problem is solved by updating the distance measurement using readings of speed and direction to estimate the vehicle's position. Location in time, of which, estimation The position is determined by fusing the outputs of two estimators: a range-based estimator and a dead reckoning estimator. The expression for the position estimate is: （5） in, This represents the set of position coordinates of the first position node at time k+1. This represents the set of position coordinates of the second position node at time k+1. It is a position estimate derived from range measurement. It is a dead reckoning position estimate. and It is to satisfy The sensor fusion parameters are estimated based on the fusion of ranging measurements and dead reckoning. And in The time frame provides the eastern and northern locations, and the corresponding expressions are: （6） （7） in, Indicates in The estimated eastern location in terms of time. Indicates in The estimated northern location in terms of time, Indicates in Sensor fusion parameters for eastern location estimation using temporal ranging measurements. Indicates in Sensor fusion parameters for eastern position estimation using dead reckoning over time. Indicates in Sensor fusion parameters for northward location estimation based on temporal ranging measurements. Indicates in Sensor fusion parameters for northbound position estimation using dead reckoning over time, where the sensor fusion parameters are part of vehicle state information.

4. The vehicle positioning method based on Pareto and Lyapunov as described in claim 3, characterized in that, Based on the vehicle's current position, speed, and direction, a dead reckoning model is constructed to estimate the vehicle's position, including: The vehicle's position in navigation coordinates is calculated using wheel speed and yaw rate from onboard sensors, as well as its heading between LiDAR coordinates and navigation coordinates. hour along The expression for dead reckoning of axis position is: （8） in, for Time position estimate, The time interval between two measurements. for Observe the speed at all times. yes Observe the azimuth angle at all times. The true location at any moment Represented as: （9） in, for The true speed of a moment for The true azimuth angle at any given moment, measured from the wheel speed sensor. and direction , It is the vehicle's heading angle. It is the heading angle. It is the vehicle's sideslip angle. The expression is: （10） in, It is the yaw rate, the measured value is... and Given the corresponding noise term and The damage is such that the measured values ​​follow a variance of . and The zero-mean Gaussian distribution; Based on the given dead reckoning data and observed speed and direction The expressions for calculating the eastward and northward velocities are as follows: （11） （12） in, It is the speed being measured. Indicates the direction being measured.

5. The vehicle positioning method based on Pareto and Lyapunov as described in claim 1, characterized in that, The Pareto algorithm with error state constraints is used to analyze the vehicle state and determine the constrained optimization problem, including: The ideal sensor fusion parameters are determined using the error state-constrained Pareto algorithm. and And achieve a balance between minimizing estimated position and heading errors and managing noise variance; Error state vector The individual errors in position, speed, and heading for the east and north can be represented in the following expressions: （13） in, and It is the actual eastern and northern location. and The true speed of the East and North This represents the actual course and includes a corresponding estimate. , , , and The error state covariance matrix is ​​defined as: （14） The total error is represented as a weighted sum Q of the individual errors using a weighted matrix: （15） in, To determine the diagonal matrix representing the relative importance of each error component, ) （16） The noise covariance matrix related to the measurement noise vector affecting dead reckoning and distance measurement is expressed as: ) （17） Among them, the variance of the heading noise of the distance measurement noise, velocity noise, and heading noise is respectively represented by... , and express.

6. The vehicle positioning method based on Pareto and Lyapunov as described in claim 5, characterized in that, The error-state-constrained Pareto algorithm estimates the position and heading errors in the dead reckoning model and obtains the error measurements of position, speed, and heading for the east and north. The estimated errors of position, speed, and heading for the east and north are represented in matrix form as follows: （18） in, Representing the error state vector, the Pareto optimization problem is to minimize the estimation error and noise variance, while being influenced by the sensor fusion parameters. and Given the constraints, the corresponding objective function is expressed as: Make obedience and (19) Where Q is the weighting matrix of the error components, and R is the noise covariance matrix related to the sensor noise. It is a regularization parameter that controls the trade-off between minimizing estimation error and management noise variance. This represents the maximum permissible error to ensure that the constraints are met; the sensor fusion parameters are selected using an optimization framework. and This reduces positioning and heading errors while controlling the overall noise variance.

7. The vehicle positioning method based on Pareto and Lyapunov as described in claim 6, characterized in that, Estimating the constrained optimization problem of the error-state-constrained Pareto algorithm to balance estimation error and sensor noise includes: Initial estimate: The estimated value is determined based on the dead reckoning model and distance measurement. , , , and The initial estimate will provide a baseline for calculating errors and determining fusion parameters; Error propagation: Estimation error is propagated using formula (18). Estimate the actual state The difference between the initial estimate and the actual value Propagate the difference and calculate the covariance matrix in formula (14). To quantify errors from different sources; Noise analysis: The noise covariance matrix is ​​calculated by analyzing the sensor characteristics using formula (17). ; Optimization analysis: Solve the Pareto optimization problem in formula (18) to determine the fusion parameters. and Minimize the weighted sum of estimation error and noise variance, and maintain and It is pointed out that Lagrange multipliers help manage equality constraints in nonlinear optimization problems. ; Updated estimation: After obtaining the optimal fusion parameters and Then, update the location. estimation, speed and heading The revised optimal estimate includes distance and dead reckoning data; The Pareto front is used to graphically represent the solution of the Pareto optimization problem in formula (19). The points on the curve correspond to different methods of balancing the minimization of estimation error and the management of noise variance. The points on the Pareto front are the optimal solutions and correspond to the minimum overall error, satisfying the constraints on estimation accuracy and noise variance.

8. The vehicle positioning method based on Pareto and Lyapunov as described in claim 1, characterized in that, A state-space model of the fusion estimation process is constructed based on the optimal solution, and the stability assessment results are obtained by performing stability analysis on vehicle positioning using Lyapunov and the state-space model, including: A state-space model is used to analyze the stability of the fusion estimation process. State vector at time step Represented as: （20） Discrete-time linear systems can be used to model the evolution of this state vector: （21） in, It is the state transition matrix, which defines the state transition from time to time. arrive The evolution, It is to control input The input matrix mapped to the state. The process noise is assumed to be a zero-mean Gaussian random vector with a covariance matrix. The measurement model associates the state vector with the observed measurements, and the corresponding expression is: （22） in, For the measurement matrix, To measure noise, a preset Given a zero-mean Gaussian distribution with covariance, the state transition matrix is ​​analyzed. Use the eigenvalues ​​of the eigenvalues ​​to test; If all eigenvalues ​​are inside the unit circle, then the system is stable; If any feature value is outside the radius of the unit circle, the positioning process is unstable; Based on the state transition matrix The stability of the eigenvalue analysis estimation process, when The system is stable when all its eigenvalues ​​lie on the unit circle in the complex plane, and the corresponding expression is: （23） If any eigenvalue is greater than 1, the system is unstable.

9. The vehicle positioning method based on Pareto and Lyapunov as described in claim 8, characterized in that, Using Lyapunov functions Stability analysis is performed using the state vector, which is defined as follows: （24） Where P is a positive definite matrix, and the decrease of the Lyapunov function over time indicates the stability of the system, with the corresponding expression being: （25） Substituting the state-space equations into the Lyapunov function yields: （26） in, If the value is a negative constant, then: （27） Formula (27) is the Lyapunov stability criterion. If there exists a positive definite matrix that satisfies Formula (27), then stability exists.

10. The vehicle positioning method based on Pareto and Lyapunov as described in claim 9, characterized in that, The stability analysis process of Lyapunov functions includes: If there exists a positive definite matrix Make the Lyapunov function If the value decreases along the system trajectory, then the state-space equations apply. The discrete-time linear system represented by the matrix is ​​asymptotically stable, or if the matrix represents the asymptotically stable system. The system is stable when it satisfies the Lyapunov function, where, It is a positive definite matrix: （28） Lyapunov function from state Become The expression is: （29） State space equations Substitute the Lyapunov function: （30） The change of the Lyapunov function is as follows: （31） Based on the necessary condition for establishing the stability of the Lyapunov function, the expression for calculating the Lyapunov function is as follows: （32） Among them, according to the positive definite matrix and each non-zero state vector binomial Always positive, any of All are negative: （33） Lyapunov function The system is asymptotically stable based on the fact that all non-zero state vectors decrease over time. The negative increment value with Increase, Status Converging toward zero, according to the matrix Obtains a positive definite matrix The Lyapunov function proves that the system is asymptotically stable. when hour, Approaching zero, state Converging to the origin; when For positive definiteness, Lyapunov functions are used to ensure the system state transition matrix. All eigenvalues ​​lie within the unit circle of the complex plane.

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