Beidou positioning adaptive filtering method

Abstract

The invention discloses a Beidou positioning adaptive filtering method, which comprises the steps of establishing a dynamic state equation and an observation equation of a Beidou positioning system based on a motion state of a carrier and a geometric physical principle between a satellite and a receiver; abnormal value detection is carried out on observation data of the Beidou positioning system, and a layered robust control architecture is constructed; calculating a multi-level adaptive factor based on hierarchical robust control, and performing hierarchical adaptive adjustment on the observation noise covariance matrix and the process noise covariance matrix according to the adaptive factor; and on the basis of the covariance matrix after hierarchical robust processing and self-adaptive adjustment, Kalman filtering prediction and update recursion are executed, and a positioning result is obtained. The method improves the positioning precision, achieves the unification of the robust capability and the filtering stability, and remarkably improves the stability and reliability of the filter in a complex environment.

Description

Technical Field

[0001] This invention relates to the technical field of satellite navigation and positioning, and in particular to an adaptive filtering method for BeiDou positioning. Background Technology

[0002] As my country's independently developed global satellite navigation system, the BeiDou Navigation Satellite System faces challenges in practical applications due to the complexity and diversity of observation environments. Particularly in environments with severe multipath interference, such as urban canyons, forest cover, and areas with high levels of interference, observation data often contains various types of outliers and gross errors. These include, but are not limited to, observation biases caused by multipath effects, increased observation noise due to signal blockage, unmodeled errors from ionospheric and tropospheric delays, systematic errors caused by receiver hardware failures, and anomalous observations resulting from human interference or natural phenomena. These anomalous observations severely impact positioning accuracy and reliability. Traditional Kalman filtering methods are extremely sensitive to anomalous observations, easily leading to filter divergence and ultimately positioning failure.

[0003] While existing robust filtering methods can handle outlier observations to some extent, they still suffer from the following key technical problems: Fixed weight functions lack environmental adaptability, and outlier detection thresholds lack statistical theoretical basis: Existing methods often use fixed weight functions (such as IGG weight functions), and their parameter thresholds are usually based on empirical settings or assumptions of normal distribution, making it difficult to adaptively adjust them according to the statistical characteristics of different observation environments. Traditional methods' outlier detection thresholds are mostly based on the assumption of normal distribution, lacking in-depth analysis of the actual statistical distribution characteristics of the observed data, resulting in low detection accuracy in non-normally distributed observation environments. Insufficient hierarchical coordination capability of adaptive filtering: Existing robust filtering methods often focus on single-level robustness processing, lacking coordinated optimization across multiple levels such as observation quality control, state estimation stability, and parameter adaptive adjustment, making it impossible to finely adjust for quality issues at different levels. These problems severely restrict the application effectiveness of the BeiDou positioning system in complex environments, necessitating a hierarchical coordinated adaptive filtering method with stronger environmental adaptability and higher robustness. Summary of the Invention

[0004] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a BeiDou positioning adaptive filtering method to solve the problems existing in the background technology.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, embodiments of the present invention provide a BeiDou positioning adaptive filtering method, comprising: Based on the motion state of the carrier and the geometric and physical principles between the satellite and the receiver, the dynamic state equation and observation equation of the BeiDou positioning system are established. Anomaly detection was performed on the observation data of the BeiDou positioning system, and a hierarchical robust control architecture was constructed. Based on the hierarchical robust control, a multi-level adaptive factor is calculated, and the observation noise covariance matrix and the process noise covariance matrix are adjusted hierarchically and adaptively according to the adaptive factor. Based on the hierarchical robust processing and the adaptively adjusted covariance matrix, Kalman filtering prediction and update recursion are performed to obtain the localization result.

[0006] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the outlier detection of the observation data of the BeiDou positioning system includes: calculating the observation residual vector and performing standardization processing, and calculating the first quartile, the third quartile, the interquartile range and the median after arranging the standardized residual absolute value sequence in ascending order. The outlier detection threshold is determined according to the outlier detection threshold calculation formula, wherein the outlier detection threshold is equal to the sum of the products of the third quartile, the outlier detection adjustment coefficient, and the interquartile range; The outlier detection adjustment coefficient is dynamically adjusted according to the environmental complexity index. Specifically, the outlier detection adjustment coefficient is equal to the sum of the product of the baseline coefficient, the adjustment range, and the environmental complexity index function value. The environmental complexity index is calculated based on a weighted combination of the normalized geometric accuracy factor, the normalized multipath index, and the carrier-to-noise ratio variation coefficient.

[0007] The beneficial effects of this preferred technical solution are that the dynamic adjustment mechanism enables outlier detection to adaptively optimize according to real-time changes in the observation environment, adopting a more stringent detection strategy in complex environments and relaxing detection standards in favorable environments, thus achieving a balance between detection accuracy and stability.

[0008] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the construction of a hierarchical robust control architecture includes: the hierarchical robust control architecture includes observation layer robust processing, state layer stability control, and cross-layer coupling adjustment; The robustness processing of the observation layer is achieved through an improved equivalent weight function based on the quartile method statistics. The first threshold of the weight function is equal to the sum of the product of the median, the first adjustment parameter, and the interquartile range. The second threshold is equal to the sum of the product of the third quartile, the second adjustment parameter, and the interquartile range. The first and second adjustment parameters are dynamically adjusted according to the observation environment. State-level stability control is achieved by monitoring the condition number of the covariance matrix, which is equal to the ratio of the largest eigenvalue to the smallest eigenvalue of the covariance matrix. When the condition number exceeds a preset threshold, stabilization processing is initiated.

[0009] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the cross-layer coupling adjustment includes: calculating the coupling strength index, wherein the coupling strength index is equal to the absolute value of the correlation coefficient between the observation layer adaptive factor and the state layer adaptive factor; When the coupling strength index exceeds the threshold, the process noise covariance matrix and the observation noise covariance matrix are coupled and adjusted. The adjusted final process noise covariance matrix is ​​equal to the original adaptive process noise covariance matrix multiplied by a coupling gain factor greater than 1; the adjusted final observation noise covariance matrix is ​​equal to the original restricted observation noise covariance matrix multiplied by the same coupling gain factor greater than 1; wherein, the coupling gain factor is equal to 1 plus the sum of the products of the coupling adjustment coefficient and the coupling strength index.

[0010] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, it further includes: updating the historical quartile statistics through a dynamic learning rate, wherein the dynamic learning rate is equal to the base learning rate multiplied by 1 minus the negative exponential function of the ratio of observation time to learning time constant; Based on historical statistics, the weight function threshold is optimized. The adaptive first threshold is equal to the sum of the products of the historical median, the historical first adjustment parameter, and the historical interquartile range. The adaptive second threshold is equal to the sum of the products of the historical third quartile, the historical second adjustment parameter, and the historical interquartile range. The first and second historical adjustment parameters are dynamically adjusted based on the environmental stability index.

[0011] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the calculation of multi-level adaptive factors based on hierarchical robust control includes: The observation layer adaptive factor is equal to the ratio of the observation layer baseline variance to the observation layer estimated variance; The state layer adaptive factor is equal to the ratio of the state layer baseline variance to the state layer estimated variance; The overall adaptive factor is equal to the product of the observation layer weights and the observation layer adaptive factor, plus the product of the state layer weights and the state layer adaptive factor.

[0012] The beneficial effects of this preferred technical solution are that the multi-level adaptive factor design allows for targeted handling of quality issues at different levels. The observation-level adaptive factor mainly reflects the quality changes of the observation data, while the state-level adaptive factor reflects the reliability of the state estimation. Through a reasonable fusion strategy, comprehensive quality control is achieved.

[0013] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, it further includes: calculating the observation layer quality score, the state layer stability score, and the cross-layer coordination score; A comprehensive filtering quality index is constructed, which is equal to the product of the first weighting coefficient and the observation layer quality score, the product of the second weighting coefficient and the state layer stability score, and the product of the third weighting coefficient and the cross-layer coordination score. Based on the comprehensive filtering quality index, at least one of the outlier detection adjustment coefficient, weight function adjustment parameter, and fusion weight is adaptively adjusted.

[0014] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the hierarchical adaptive adjustment of the observation noise covariance matrix and the process noise covariance matrix according to the adaptive factor includes: the adjusted observation noise covariance matrix is ​​the product of the diagonal weight matrix, the basic observation noise covariance matrix, and the constrained observation layer adaptive factor, wherein the diagonal elements of the diagonal weight matrix are the reciprocals of the final weights. The adjusted process noise covariance matrix is ​​the product of the constrained state layer adaptive factor, the basic process noise covariance matrix, and the stability correction factor; wherein the stability correction factor is a negative exponential function of the ratio of the maximum value of the difference between the condition number and the condition number threshold to the condition number threshold.

[0015] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the following steps are performed: based on the hierarchical robust processing and the adaptively adjusted covariance matrix, Kalman filtering prediction and update recursion are executed to obtain the positioning result, including: using the optimal state estimate of the previous epoch and the system's state transition matrix to predict the state of the current epoch. Predict the covariance matrix of the current epoch state estimate; calculate the innovation vector and Kalman gain; By using the difference between the actual and predicted observations at the current epoch, and combining it with the Kalman gain, the predicted state is corrected to obtain the optimal state estimate for the current epoch, which is then output as the positioning result.

[0016] As a preferred embodiment of the BeiDou positioning adaptive filtering method described in this invention, the dynamic state equation and observation equation of the BeiDou positioning system are established based on the motion state of the carrier and the geometric and physical principles between the satellite and the receiver, including: The dynamic state equation is expressed as: in, Indicates the first The process noise vector of an epoch. Here is the state transition matrix. Indicates the first The state vector of an epoch; The observation equation is expressed as: in, Indicates the first Observation vector of an epoch, Indicates the first Observation matrix of an epoch, Indicates the first The observation noise vector of an epoch.

[0017] Compared with existing technologies, the beneficial effects of this invention are as follows: By introducing the quartile method, this invention overcomes the limitations of traditional outlier detection methods that rely on the assumption of normal distribution. It performs adaptive outlier detection based on the actual data distribution characteristics, which significantly improves the detection accuracy and positioning precision compared with traditional methods. Through the hierarchical robust control method, a three-layer robust control architecture consisting of the observation layer, the state layer, and cross-layer coupling achieves a balance between robustness and filtering stability, significantly improving the stability and reliability of the filter in complex environments. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart illustrating a BeiDou positioning adaptive filtering method according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the overall process of a BeiDou positioning adaptive filtering method according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the outlier detection principle of a BeiDou positioning adaptive filtering method according to an embodiment of the present invention. Figure 4 This is a flowchart illustrating the hierarchical robust control architecture design of a BeiDou positioning adaptive filtering method according to an embodiment of the present invention. Figure 5 This is a flowchart of a robust adaptive Kalman filter recursive algorithm for a BeiDou positioning adaptive filtering method according to an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0020] Example 1, referring to Figures 1-5 As one embodiment of the present invention, this embodiment provides a BeiDou positioning adaptive filtering method, such as... Figure 1 As shown, it includes: S100: Based on the motion state of the carrier and the geometric and physical principles between the satellite and the receiver, the dynamic state equation and observation equation of the BeiDou positioning system are established. S200: Perform outlier detection on the observation data of the BeiDou positioning system and construct a hierarchical robust control architecture; S300: Calculates multi-level adaptive factors based on hierarchical robust control, and performs hierarchical adaptive adjustment of the observation noise covariance matrix and process noise covariance matrix according to the adaptive factors; S400: Based on the hierarchical robust processing and the adaptively adjusted covariance matrix, Kalman filtering is performed for prediction and update recursion to obtain the localization result.

[0021] It should be noted that while existing robust filtering methods can handle outlier observations to some extent, they still suffer from the following key technical problems: Fixed weight functions lack environmental adaptability, and outlier detection thresholds lack statistical theoretical basis: Existing methods often use fixed weight functions (such as IGG weight functions), and their parameter thresholds are usually determined based on empirical settings or the assumption of a normal distribution, making it difficult to adaptively adjust according to the statistical characteristics of different observation environments. Traditional methods often base outlier detection thresholds on the assumption of a normal distribution, lacking in-depth analysis of the actual statistical distribution characteristics of the observation data, resulting in low detection accuracy in non-normally distributed observation environments. Furthermore, the hierarchical coordination capability of adaptive filtering is insufficient: Existing robust filtering methods often focus on robust processing at a single level, lacking coordinated optimization across multiple levels such as observation quality control, state estimation stability, and adaptive parameter adjustment, making it impossible to finely adjust for quality issues at different levels. This invention provides a BeiDou positioning adaptive filtering method based on quartile statistical theory and hierarchical robust control, suitable for high-precision real-time positioning systems in complex observation environments such as urban canyons, forest obstruction, and severe multipath effects. By introducing the quartile method, this invention overcomes the limitations of traditional outlier detection methods that rely on the assumption of a normal distribution. It performs adaptive outlier detection based on actual data distribution characteristics, significantly improving detection accuracy and positioning precision compared to traditional methods. Furthermore, through a hierarchical robust control method—a three-layer robust control architecture involving observation, state, and cross-layer coupling—it achieves a balance between robustness and filtering stability, significantly improving the filter's stability and reliability in complex environments. This invention specifically discloses the technical implementation of a hierarchical robust control-based adaptive filtering method for BeiDou positioning in static high-precision measurement applications.

[0022] Reference Figure 2In this embodiment of the invention, step S100, based on the motion state of the carrier and the geometric and physical principles between the satellite and the receiver, establishes the dynamic state equation and observation equation of the BeiDou positioning system, including: In static positioning applications, the carrier's velocity is zero, and the state vector is: in, Indicates the first X-coordinate of the epoch (unit: meters); Indicates the first Y-coordinate of the epoch (unit: meters); Indicates the first Z-coordinate of the epoch (unit: meters); Indicates the first Receiver clock error at an epoch (unit: nanosecond); Indicates the first Frequency offset of an epoch (unit: Hz).

[0023] The dynamic state equation is expressed as: in, Indicates the first The process noise vector of an epoch. Here is the state transition matrix. Indicates the first The state vector of an epoch, with covariance matrix as follows: .

[0024] The state transition matrix is: in, Indicates the time interval between adjacent epochs (unit: seconds); Represents a 3×3 identity matrix; Represents a 3×1 dimensional zero vector; It represents a 1×3 dimensional zero vector.

[0025] The observation equation is expressed as: in, Indicates the first The observation vector for each epoch includes pseudorange and carrier phase observations from visible satellites (in meters). Indicates the first The observation matrix of an epoch establishes the geometric relationship between the state vector and the observed values; Indicates the first The observation noise vector of an epoch, with a covariance matrix of: .

[0026] It should be noted that the establishment of the dynamic state equation and observation equation provides the mathematical foundation for the entire adaptive filtering algorithm. The design of the state transition matrix fully considers the stationarity of the position state and the time-varying characteristics of the clock error in static applications, ensuring the accuracy of the model.

[0027] In this embodiment of the invention, step S200 for outlier detection of the observation data of the BeiDou positioning system includes: calculating the observation residual vector and performing standardization processing; arranging the standardized residual absolute value sequence in ascending order and then calculating the first quartile, the third quartile, the interquartile range, and the median. The outlier detection threshold is determined according to the outlier detection threshold calculation formula. The outlier detection threshold is equal to the sum of the products of the third quartile, the outlier detection adjustment coefficient, and the interquartile range. The outlier detection adjustment coefficient is dynamically adjusted according to the environmental complexity index. Specifically, the outlier detection adjustment coefficient is equal to the sum of the product of the baseline coefficient, the adjustment range, and the environmental complexity index function value. The environmental complexity index is calculated based on a weighted combination of the normalized geometric precision factor, the normalized multipath index, and the carrier-to-noise ratio variation coefficient.

[0028] Reference Figure 3 In one optional embodiment, the basic principle of quartile outlier detection is to determine the outlier detection threshold by calculating the quartile statistics of the data. First, the quartile statistic is calculated... Observation residual vector of an epoch: in, Indicates the first The observation residual vector of an epoch; Indicates based on the previous epochal information for the first Predicted values ​​for epoch states.

[0029] Standardize the observation residuals: in, Indicates the first Era 1 Standardized residuals of each observation; Indicates the first Era 1 The original residuals of each observation; Indicates the first Era 1 The standard deviation of each observation. Represents the observation noise covariance matrix The One diagonal element.

[0030] Calculate the first quartile after sorting the standardized residual absolute value series in ascending order. Third and quartiles Interquartile range and median : First quartile: in This represents the first quartile (25th percentile); This represents the 25th percentile of the standardized residual absolute value sequence; This represents the total number of observed data; This indicates a round-down operation.

[0031] Third quartile: in This represents the third quartile (75th percentile). This represents the 75th percentile of the standardized residual absolute value sequence.

[0032] Interquartile range: in This represents the interquartile range, reflecting the degree of dispersion of the data.

[0033] Median: in This represents the median (50th percentile). It represents the 50th percentile of the standardized residual absolute value sequence.

[0034] Furthermore, the outlier detection threshold is determined based on the outlier detection threshold formula: in, This indicates the outlier detection threshold; This represents the outlier detection adjustment coefficient, used to control the sensitivity of the detection.

[0035] It should be noted that the core advantage of the quartile method in statistical theory lies in its reliance on the actual distribution characteristics of the data, rather than the assumption of a normal distribution. By calculating the quantile characteristics of the data, it can adaptively reflect the statistical properties of the observed data, providing a more robust outlier detection capability.

[0036] Furthermore, the outlier detection adjustment coefficient Dynamically adjusted based on the environmental complexity index: in, Indicates the first Outlier detection adjustment coefficient for each epoch; This represents the baseline coefficient, reflecting the basic detection capability under normal conditions. This indicates the adjustment range, controlling the degree to which environmental changes affect the detection coefficient; A nonlinear mapping function representing the environmental complexity index; This represents the environmental complexity index calculated based on a weighted combination of the normalized geometric precision factor, the normalized multipath index, and the carrier-to-noise ratio variation coefficient.

[0037] It should be noted that the dynamic adjustment mechanism enables outlier detection to adaptively optimize based on real-time changes in the observation environment. It adopts stricter detection strategies in complex environments and relaxes detection standards in favorable environments, thus achieving a balance between detection accuracy and stability.

[0038] In this embodiment of the invention, the construction of the hierarchical robust control architecture in step S200 includes: the hierarchical robust control architecture includes observation layer robustness processing, state layer stability control, and cross-layer coupling adjustment; The robustness processing of the observation layer is achieved through an improved equivalent weight function based on the quartile method statistics. The first threshold of the weight function is equal to the sum of the product of the median, the first adjustment parameter, and the interquartile range. The second threshold is equal to the sum of the product of the third quartile, the second adjustment parameter, and the interquartile range. The first and second adjustment parameters are dynamically adjusted according to the observation environment. State-level stability control is achieved by monitoring the condition number of the covariance matrix. The condition number is equal to the ratio of the largest eigenvalue to the smallest eigenvalue of the covariance matrix. When the condition number exceeds a preset threshold, stabilization processing is initiated.

[0039] Furthermore, the improved IGG weight function in the robustness processing of the observation layer is as follows: when the absolute value of the standardized residual is less than or equal to the first threshold, the weight is equal to 1; when the absolute value of the standardized residual is greater than the first threshold and less than or equal to the second threshold, the weight is equal to the ratio of the first threshold to the absolute value of the standardized residual, multiplied by the ratio of the difference between the second threshold and the absolute value of the standardized residual to the difference between the second threshold and the first threshold; when the absolute value of the standardized residual is greater than the second threshold, the weight is equal to 0.

[0040] Furthermore, it also includes a progressive weight adjustment strategy: progressive weight adjustment is performed according to the smoothing weight calculation formula. The smoothing weight is equal to the product of the smoothing coefficient and the smoothing weight of the previous epoch, plus 1 minus the smoothing coefficient, and the product of the new weight of the current epoch.

[0041] Furthermore, in the state-level stability control, when the stability index exceeds the threshold, a stabilization process is performed: the stabilization process is to add the product of the regularization parameter and the identity matrix to the original covariance matrix. The regularization parameter is the larger of one-thousandth of the trace of the covariance matrix and the minimum regularization coefficient.

[0042] Reference Figure 4 In an optional embodiment, robustness processing of the observation layer is achieved through an improved IGG weighting function based on quartile statistics. The first threshold of the weighting function is... The second threshold is .

[0043] in, This represents the first threshold of the improved IGG weight function, used to distinguish between normal and suspicious observations; This represents the second threshold of the improved IGG weight function, used to distinguish between suspicious and outlier observations; This represents the first adjustment parameter, which controls the offset of the first threshold relative to the median; This represents the second adjustment parameter, which controls the offset of the second threshold relative to the third quartile. and Adjust dynamically according to the observation environment.

[0044] The improved IGG weight function is as follows: when At that time, weight ; when At that time, weight ; when At that time, weight .

[0045] in, Indicates the first The weights of each observation are used to adjust the contribution of that observation in the filtering process; Indicates the first The absolute value of the standardized residuals of each observation.

[0046] It should be noted that the improved IGG weight function replaces the traditional fixed threshold with an adaptive threshold based on quartile statistics, enabling the weight function to be dynamically adjusted according to the actual distribution characteristics of the data, which significantly improves the robustness in non-normal distribution environments.

[0047] Furthermore, a weighted gradual adjustment strategy is adopted: in, Indicates the first Era 1 Smoothed weights of each observation; This represents the smoothing coefficient, which controls the time stability of the weights (value range is 0 to 10). Indicates the first Era 1 Smoothed weights of each observation; Indicates the first Era 1 The new calculated weights for each observation.

[0048] It should be noted that the gradual weight adjustment strategy avoids filtering oscillations that may be caused by sudden changes in weights through smoothing of the time series, thus maintaining the stability of the system while ensuring a rapid response to outliers.

[0049] Furthermore, state-level stability control is achieved by monitoring the condition number of the covariance matrix: in, Indicates the first The stability index (condition number) of an epoch; Represents the covariance matrix The largest eigenvalue; Represents the covariance matrix The smallest eigenvalue; Indicates the first The state covariance matrix after epoch filtering update.

[0050] when Exceeding the preset threshold Stabilization process is initiated at the appropriate time: in, This represents the covariance matrix after stabilization. This represents the stability threshold, used to determine whether stabilization processing is required. Represents the regularization parameter; This represents the minimum regularization coefficient, ensuring the lowest possible effect of regularization. Represents the identity matrix; Represents the covariance matrix The trace (the sum of the diagonal elements).

[0051] It should be noted that by monitoring the condition number of the covariance matrix, the numerical stability of the filter can be evaluated in real time. When the condition number is too large, it indicates that the covariance matrix is ​​close to singular. In this case, regularization is used to increase the diagonal elements, thereby improving the condition number of the matrix and preventing numerical calculation failure.

[0052] In this embodiment of the invention, the cross-layer coupling adjustment in step S200 includes: calculating the coupling strength index, which is equal to the absolute value of the correlation coefficient between the observation layer adaptive factor and the state layer adaptive factor; When the coupling strength index exceeds the threshold, the process noise covariance matrix and the observation noise covariance matrix are coupled and adjusted. The adjusted final process noise covariance matrix is ​​equal to the original adaptive process noise covariance matrix multiplied by a coupling gain factor greater than 1; the adjusted final observation noise covariance matrix is ​​equal to the original restricted observation noise covariance matrix multiplied by the same coupling gain factor greater than 1; where the coupling gain factor is equal to 1 plus the sum of the products of the coupling adjustment coefficient and the coupling strength index.

[0053] Furthermore, cross-layer coupling adjustment achieves coordinated optimization between the observation layer and the state layer by calculating the coupling strength index: in, Indicates the first The coupling strength index of an epoch; This represents the function for calculating the correlation coefficient. Indicates the first The observation layer adaptive factor of the epoch; Indicates the first The state layer adaptive factor of the epoch.

[0054] when Exceeding the threshold At the same time, the process noise covariance matrix and the observation noise covariance matrix are coupled and adjusted: in, This represents the coupling strength threshold, used to determine whether cross-layer coupling adjustment is necessary; Indicates the first The final process noise covariance matrix after epoch coupling adjustment; Indicates the first The process noise covariance matrix after adaptive adjustment of the epoch state layer; This represents the coupling adjustment coefficient, which controls the strength of cross-layer coupling; Indicates the first The final observation noise covariance matrix after epoch coupling adjustment; Indicates the first The observation noise covariance matrix after epoch constraint.

[0055] It should be noted that the cross-layer coupling adjustment mechanism analyzes the correlation between the adaptive factors of the observation layer and the state layer, identifies the possible mutual influence between the two layers, and optimizes the overall filtering performance by coordinating and adjusting the covariance matrix, thereby avoiding conflicts between different layers.

[0056] In this embodiment of the invention, step S200 further includes: updating the historical quartile statistics through a dynamic learning rate, wherein the dynamic learning rate is equal to the base learning rate multiplied by 1 minus the negative exponential function of the ratio of observation time to learning time constant; Based on historical statistics, the weight function threshold is optimized. The adaptive first threshold is equal to the sum of the products of the historical median, the historical first adjustment parameter, and the historical interquartile range. The adaptive second threshold is equal to the sum of the products of the historical third quartile, the historical second adjustment parameter, and the historical interquartile range. The first and second historical adjustment parameters are dynamically adjusted based on the environmental stability index.

[0057] Furthermore, a self-learning mechanism based on historical data: through a dynamic learning rate. Update historical quartile statistics; in, Indicates the first The dynamic learning rate of an epoch; It represents the basic learning rate, the fundamental level at which the learning speed is controlled; Indicates the current observation time (unit: seconds); Represents the learning time constant, controlling the convergence characteristics of the learning speed (unit: seconds).

[0058] Optimize the threshold of the weight function based on historical statistics: in, This represents an adaptive first threshold based on historical data; This represents an adaptive second threshold based on historical data; Indicates the historical median; This indicates the historical first adjustment parameter; Indicates the historical interquartile range; Indicates the third quartile in history; This indicates the second historical adjustment parameter. and Adjustments are made dynamically based on the environmental stability index.

[0059] It should be noted that the self-learning mechanism, by accumulating the statistical characteristics of historical observation data, can gradually learn and adapt to the data distribution patterns of a specific environment, thereby achieving continuous parameter optimization and improving the long-term stability and environmental adaptability of the system.

[0060] In this embodiment of the invention, step S300, which calculates the multi-level adaptive factor based on hierarchical robust control, includes: The observation layer adaptive factor is equal to the ratio of the observation layer baseline variance to the observation layer estimated variance; The state layer adaptive factor is equal to the ratio of the state layer baseline variance to the state layer estimated variance; The overall adaptive factor is equal to the product of the observation layer weights and the observation layer adaptive factor, plus the product of the state layer weights and the state layer adaptive factor.

[0061] Specifically, the observation layer adaptive factor: State layer adaptive factor: Comprehensive adaptive factor: ; in, Indicates the baseline variance of the observation layer; Indicates the first Estimated variance of epoch observation layers; Represents the baseline variance of the state layer; Indicates the first epoch state layer estimation variance; Indicates the first Era-based adaptive factor; Indicates the fusion weights of the observation layer; Indicates the state layer fusion weights. and The system is dynamically adjusted based on the reliability of each layer.

[0062] It should be noted that the multi-level adaptive factor design allows for targeted handling of quality issues at different levels. The observation-level adaptive factor mainly reflects the quality changes of the observation data, while the state-level adaptive factor reflects the reliability of the state estimation. Through a reasonable fusion strategy, comprehensive quality control is achieved.

[0063] In this embodiment of the invention, step S300 further includes: Calculate the observation layer quality score, the state layer stability score, and the cross-layer coordination score; Construct a comprehensive filtering quality index, which is equal to the product of the first weighting coefficient and the observation layer quality score, plus the product of the second weighting coefficient and the state layer stability score, plus the product of the third weighting coefficient and the cross-layer coordination score. Based on the comprehensive filtering quality index, at least one of the outlier detection adjustment coefficient, weight function adjustment parameter, and fusion weight is adaptively adjusted.

[0064] Furthermore, multi-index filtering quality assessment: calculating the observation layer quality score, state layer stability score, and cross-layer coordination score; constructing a comprehensive filtering quality index. ; in, This indicates the overall filtering quality index; The weighting coefficients represent the quality score of the observation layer; Indicates the quality score of the observation layer; The weighting coefficients represent the state layer stability scores. This represents the state layer stability score; The weighting coefficients representing the cross-level coordination score; This represents the cross-level coordination score, with parameters adaptively adjusted based on comprehensive quality indicators.

[0065] It should be noted that the multi-index quality evaluation system can comprehensively reflect the operating status of the filter by evaluating the filter performance from different dimensions, providing a scientific basis for parameter adjustment and ensuring that the system always maintains the optimal working state.

[0066] In this embodiment of the invention, step S300, which involves hierarchical adaptive adjustment of the observation noise covariance matrix and the process noise covariance matrix based on the adaptive factor, includes: the adjusted observation noise covariance matrix is ​​the product of the diagonal weight matrix, the basic observation noise covariance matrix, and the constrained observation layer adaptive factor, and the diagonal elements of the diagonal weight matrix are the reciprocals of the final weights. The adjusted process noise covariance matrix is ​​the product of the constrained state layer adaptive factor, the basic process noise covariance matrix, and the stability correction factor; where the stability correction factor is a negative exponential function of the ratio of the maximum value of the difference between the condition number and the condition number threshold to the condition number threshold.

[0067] Specifically, the observation noise covariance matrix is ​​adjusted as follows: in, Indicates the first The observation noise covariance matrix after adaptive adjustment at each epoch observation layer; This represents a diagonal matrix with the reciprocals of the final weights as its diagonal elements; Indicates the first The final weight of each observation; Indicates the first The fundamental observation noise covariance matrix of an epoch; Indicates the first Epoch-constrained observation layer adaptive factor.

[0068] Process noise covariance matrix adjustment: in, Indicates the first The process noise covariance matrix after adaptive adjustment of the epoch state layer; Indicates the first Epoch-constrained state layer adaptive factor; Indicates the first The fundamental process noise covariance matrix of an epoch; Indicates the first The stability correction factor of the epoch, where This represents the function that takes the maximum value.

[0069] It should be noted that the hierarchical adaptive adjustment strategy adjusts the observation noise covariance matrix and the process noise covariance matrix respectively based on the weight information of the observation layer and the stability information of the state layer. This hierarchical processing method can more accurately reflect the changing characteristics of different types of noise and improve the adaptive capability of the filter.

[0070] In this embodiment of the invention, step S400 involves performing Kalman filtering prediction and update recursion based on hierarchical robust processing and adaptively adjusted covariance matrix to obtain the localization result, including: using the optimal state estimate of the previous epoch and the system's state transition matrix to predict the state of the current epoch. Predict the covariance matrix of the current epoch state estimate; calculate the innovation vector and Kalman gain; By using the difference between the actual and predicted observations at the current epoch, and combining it with the Kalman gain, the predicted state is corrected to obtain the optimal state estimate for the current epoch, which is then output as the positioning result.

[0071] Reference Figure 5 In an optional embodiment, the Kalman filter recursion includes a prediction step and an update step: State prediction: in, Indicates based on the first epochal information for the first Prediction and estimation of epoch states; Indicates the first The filtered estimation state of the epoch.

[0072] Covariance prediction: in, Indicates the first The prediction covariance matrix of an epoch; Indicates the first The filtering covariance matrix of an epoch; This represents the transpose of the state transition matrix; Indicates the first The process noise covariance matrix after the epoch has undergone layered protection processing.

[0073] Kalman gain calculation: in, Indicates the first The epochal information matrix (residual covariance matrix); This represents the transpose of the observation matrix; Indicates the first The observation noise covariance matrix after epochal layer protection processing; Indicates the first The Kalman gain matrix of an epoch; Represents the innovation matrix The inverse matrix.

[0074] Status Update: in, Indicates the first State estimation after filtering update at each epoch; Indicates the first The information vector (residual vector) of an epoch.

[0075] Covariance updates are performed using the Joseph stabilization method: in, Indicates the first Temporary covariance matrix of each epoch (Joseph form update result); Indicates updating the matrix; This indicates the transpose of the update matrix; This represents the transpose of the Kalman gain matrix.

[0076] The final covariance matrix is ​​then subjected to hierarchical stability control. in, Indicates the first The final covariance matrix of the epoch (after stability control); This represents the hierarchical stability control function, which performs possible regularization on the covariance matrix based on stability indices.

[0077] It should be noted that the Kalman filter recursion process fully integrates the results of hierarchical robust control, including the adaptively adjusted covariance matrix and stability protection mechanism, to ensure that the filter can operate stably and obtain the optimal positioning results in various complex environments.

[0078] This embodiment employs a hierarchical robust control method. At the observation layer, it implements intelligent outlier detection and progressive weight adjustment based on the quartile method, effectively suppressing the impact of outlier observations on filtering. At the state layer, it establishes a covariance matrix condition number monitoring and numerical stability protection mechanism to ensure the long-term numerical stability of filtering. Through cross-layer coupling adjustment, it achieves coordinated optimization between different layers, avoiding the limitations of single-layer processing. The entire system can adaptively adjust according to real-time changes in the observation environment, significantly improving the accuracy and reliability of static high-precision positioning.

[0079] It should also be noted that this invention establishes a robust adaptive Kalman filter basic model to determine the state equation and observation equation; then, based on quartile statistical theory, it performs intelligent outlier detection, calculating quartiles Q1, Q3, and the interquartile range IQR to determine the outlier detection threshold; next, it employs a hierarchical robust control method, including observation-level robustness processing, state-level stability control, and an adaptive boundary constraint mechanism; furthermore, it calculates multi-level adaptive factors and performs hierarchical covariance matrix adaptive adjustment; finally, it implements a Kalman filter recursive algorithm to establish a multi-index quality assessment system and an intelligent parameter adjustment strategy. Compared with existing technologies, this invention improves positioning accuracy and environmental adaptability.

[0080] Example 2: This example is for vehicle navigation application scenarios. It achieves good dynamic tracking performance while ensuring positioning accuracy through a hierarchical robustness control method.

[0081] Using a complete 8-dimensional state vector: in, Indicates the first Velocity component in the X direction of the epoch (unit: m / s); Indicates the first Velocity component in the Y direction of the epoch (unit: m / s); Indicates the first Velocity component in the Z direction of the epoch (unit: m / s).

[0082] Motion state recognition and hierarchical adjustment: static state ( m / s): Enhance the weights of the observation layer. ; Uniform motion ( m / s): Balance weights, ; Accelerated motion ( m / s): Enhance state layer weights in, The magnitude of the velocity vector (unit: meters per second); The modulus representing the change in velocity (unit: meters per second).

[0083] Stratified environmental monitoring: multipath index in, This represents a multipath index, reflecting the stability of signal quality; Indicates the first Carrier-to-noise ratio of each satellite (unit: dB-Hz). This represents the average carrier-to-noise ratio (CNR) of all visible satellites (unit: dB-Hz). Indicates the number of visible satellites.

[0084] when At this time, activate the enhanced robustness mode: Increased to 0.7, Increased to 2.0, Reduce to 0.5, Increased to 0.25.

[0085] In addition to basic quality indicators, dynamic performance indicators are added: in, This represents the rate of change of position, reflecting the continuity of position estimation (unit: meters per second). Indicates speed consistency, reflecting the consistency between filtering speed and observation speed (dimensionless). Indicates the first The velocity vector estimated by epoch filtering; Indicates the first The observation velocity vector of an epoch.

[0086] Layered quality overall score: in, Indicates the first The dynamic comprehensive quality score of the epoch; Indicates the first Epochal observation quality score; Indicates the first epochal state quality score; This represents the maximum permissible rate of change of position.

[0087] when At that time, the dynamic reinforcement and resistance mode is activated.

[0088] Example 3: This example is for high dynamic platforms such as UAVs, and uses a hierarchical robust control method to handle rapidly changing motion states and complex observation environments.

[0089] The extended state vector contains acceleration information: in, Indicates the first The position vector of an epoch (including) , , Coordinates (unit: meters) Indicates the first The velocity vector of an epoch (including) , , Component (unit: meters per second). Indicates the first Acceleration vector of epoch (including , , Component, unit: meters per second².

[0090] Maneuver detection and hierarchical mode switching: Maneuver indicators in, This indicates the maneuverability index, reflecting the degree of vehicle maneuverability (unit: meters per second²). Indicates the first Acceleration vector from epoch-time GNSS observations; Indicates the first Acceleration vector predicted at each epoch.

[0091] when At m / s², switch to high dynamic hierarchical mode: increase the weight of the state layer. Accelerate the response of the observation layer Enhance cross-layer coupling .

[0092] Multi-sensor hierarchical fusion robustness processing: GNSS / IMU hierarchical fusion residual calculation: in, Represents the GNSS / IMU fusion residual vector; Represents the GNSS observation residual vector; Represents the GNSS observation matrix; This represents the state vector propagated based on the IMU.

[0093] The stratified quartile method was applied to the fusion residuals for statistical analysis.

[0094] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A Beidou positioning adaptive filtering method, characterized in that, The application comprises: Based on the motion state of the carrier and the geometric physical principle between the satellite and the receiver, the dynamic state equation and the observation equation of the Beidou positioning system are established; The observation data of the Beidou positioning system is subjected to outlier detection, and a hierarchical robust control architecture is constructed; Based on the hierarchical robust control, multi-level adaptive factors are calculated, and the observation noise covariance matrix and the process noise covariance matrix are subjected to hierarchical adaptive adjustment according to the adaptive factors; Based on the hierarchical robust processing and the adaptive adjustment of the covariance matrix, the prediction and update recursion of Kalman filtering are performed to obtain the positioning result.

2. The Beidou positioning adaptive filtering method according to claim 1, wherein, The outlier detection of the observation data of the Beidou positioning system comprises: calculating the observation residual vector and performing standardization processing, arranging the absolute value sequence of the standardized residual in ascending order, and then calculating the first quartile, the third quartile, the interquartile range and the median; The outlier detection threshold is determined according to the outlier detection threshold calculation formula, and the outlier detection threshold is equal to the sum of the third quartile and the product of the outlier detection adjustment coefficient and the interquartile range; The outlier detection adjustment coefficient is dynamically adjusted according to the environmental complexity index, specifically: the outlier detection adjustment coefficient is equal to the sum of the base coefficient and the product of the adjustment amplitude and the environmental complexity index function value; The environmental complexity index is calculated based on the weighted combination of the normalized geometric dilution of precision, the normalized multipath index and the carrier-to-noise ratio variation coefficient.

3. The Beidou positioning adaptive filtering method according to claim 2, wherein, The hierarchical robust control architecture comprises: the hierarchical robust control architecture comprises observation layer robust processing, state layer stability control and cross-layer coupling adjustment; The observation layer robust processing is realized by an improved equivalent weight function based on the quartile method statistic, the first threshold of the weight function is equal to the sum of the median and the product of the first adjustment parameter and the interquartile range, the second threshold is equal to the sum of the third quartile and the product of the second adjustment parameter and the interquartile range, and the first adjustment parameter and the second adjustment parameter are dynamically adjusted according to the observation environment; The state layer stability control is realized by monitoring the condition number of the covariance matrix, and the condition number is equal to the ratio of the maximum eigenvalue to the minimum eigenvalue of the covariance matrix. When the condition number exceeds the preset threshold, the stabilization processing is started.

4. The Beidou positioning adaptive filtering method according to claim 3, wherein, The cross-layer coupling adjustment comprises: calculating the coupling strength index, which is equal to the absolute value of the correlation coefficient of the observation layer adaptive factor and the state layer adaptive factor; When the coupling strength index exceeds the threshold, the process noise covariance matrix and the observation noise covariance matrix are subjected to coupling adjustment; The final adjusted process noise covariance matrix is equal to the original adaptive process noise covariance matrix multiplied by a coupling gain factor greater than 1; the final adjusted observation noise covariance matrix is equal to the original limited observation noise covariance matrix multiplied by the same coupling gain factor greater than 1; wherein the coupling gain factor is equal to 1 plus the product of the coupling adjustment coefficient and the coupling strength index.

5. The Beidou positioning adaptive filtering method according to claim 4, wherein, Further comprising: The historical quartile statistics are updated by a dynamic learning rate, which is equal to the base learning rate multiplied by 1 minus the negative exponential function of the ratio of the observation time to the learning time constant; The threshold of the weight function is optimized based on historical statistics, the adaptive first threshold is equal to the sum of the historical median and the product of the historical first adjustment parameter and the historical quartile range, and the adaptive second threshold is equal to the sum of the historical third quartile and the product of the historical second adjustment parameter and the historical quartile range; The historical first adjustment parameter and the historical second adjustment parameter are dynamically adjusted according to the environmental stability index.

6. The Beidou positioning adaptive filtering method according to claim 5, wherein, The multi-level adaptive factors are calculated based on the hierarchical robust control, including: The observation layer adaptive factor is equal to the ratio of the observation layer reference variance to the observation layer estimated variance; The state layer adaptive factor is equal to the ratio of the state layer reference variance to the state layer estimated variance; The comprehensive adaptive factor is equal to the product of the observation layer weight and the observation layer adaptive factor plus the product of the state layer weight and the state layer adaptive factor.

7. The Beidou positioning adaptive filtering method according to claim 6, wherein, Further comprising: The observation layer quality score, the state layer stability score and the cross-layer coordination score are calculated; The comprehensive filtering quality index is constructed, which is equal to the product of the first weight coefficient and the observation layer quality score plus the product of the second weight coefficient and the state layer stability score plus the product of the third weight coefficient and the cross-layer coordination score; At least one of the abnormal value detection adjustment coefficient, the weight function adjustment parameter and the fusion weight is adaptively adjusted according to the comprehensive filtering quality index.

8. The Beidou positioning adaptive filtering method according to claim 7, wherein, The hierarchical adaptive adjustment of the observation noise covariance matrix and the process noise covariance matrix according to the adaptive factor includes: the adjusted observation noise covariance matrix is the product of the diagonal weight matrix and the basic observation noise covariance matrix and the constrained observation layer adaptive factor, the diagonal elements of the diagonal weight matrix are the reciprocals of the maximum weights; The adjusted process noise covariance matrix is the product of the constrained state layer adaptive factor, the basic process noise covariance matrix and the stability correction factor; wherein the stability correction factor is the negative exponential function of the ratio of the maximum value of the difference between the condition number and the condition number threshold to the condition number threshold.

9. The Beidou positioning adaptive filtering method according to claim 8, wherein, Based on the hierarchical robust processing and the adaptively adjusted covariance matrix, the prediction and update recursion of the Kalman filter are performed to obtain the positioning result, including: predicting the state of the current epoch using the optimal state estimation of the last epoch and the state transition matrix of the system; The covariance matrix of the state estimation of the current epoch is predicted; the innovation vector and the Kalman gain are calculated; The actual observation value of the current epoch is used to correct the predicted state, and the optimal state estimation of the current epoch is obtained as the positioning result output.

10. The Beidou positioning adaptive filtering method of claim 9, wherein, Based on the motion state of the carrier and the geometric physical principle between the satellite and the receiver, the dynamic state equation and the observation equation of the Beidou positioning system are established, including: The dynamic state equation is expressed as: wherein, represents the state vector at the epoch, is a state transition matrix, represents the state vector at the epoch. The observation equation is represented as: wherein, represents the epoch, represents the epoch, represents the epoch.

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