Robust filtering method based on satellite mass evaluation

Abstract

The present application relates to the field of satellite positioning technology, and particularly relates to a robust filtering method based on satellite quality evaluation, comprising the following steps: step 1: a receiver collects navigation messages in real time; step 2: single point positioning is used to obtain the receiver position and signal quality evaluation parameters; step 3: satellite signal quality evaluation is performed to determine whether the observation matrix is full rank; step 4: a robustness factor is calculated, and a Kalman gain is calculated; step 5: multi-epoch joint observation is performed to establish full-rank complete geometric constraints to solve new predicted values; and step 6: the current epoch parameters are retained, and the next epoch is solved. The scheme of the present application has the advantages that it can be used to reduce the influence of weak satellite signal strength, multipath effect and the like on positioning accuracy, and improve the continuous positioning calculation capability.

Description

Technical Field

[0001] This invention relates to the field of satellite positioning technology, specifically to a relative positioning method based on robust filtering and multi-epoch joint observation interpolation using satellite quality assessment. Background Technology

[0002] Thanks to the global networking of the BeiDou Navigation Satellite System, satellite positioning schemes have been widely applied. From pseudorange point positioning to carrier phase differential positioning (RTK), and then to network RTK, positioning accuracy can reach the millimeter level. However, due to the specific requirements of satellite signals, the carrier frequency is ultimately chosen in the ultra-high frequency (UHF) range. In complex environments such as the wilderness or urban canyons, satellite signals face problems such as obstruction by tree canopies or tall buildings, reduced signal strength, uneven satellite geometric distribution, and multipath effects. These issues drastically degrade the accuracy of satellite positioning, and may even render positioning impossible.

[0003] In the satellite positioning process, the Kalman filter is an indispensable component. Considering the characteristics of satellite positioning, Kalman filters are typically improved. To address the challenges of nonlinear systems, the Extended Kalman Filter (EKF) was developed. To overcome the accuracy degradation problem in high-dimensional state spaces, Haykin proposed the Capable Kalman Filter (CKF) method. To address the outlier problem caused by observation errors and multipath propagation, the concept of robust Kalman filtering was proposed. Yang Yuanxi proposed that the IGGIII model can construct an equivalent weight matrix of observation variance using a weighting factor for different residual values. Most research on robust filtering focuses on different calculation schemes for the weighting factor. However, in practical applications, due to the correlation of signals between epochs, when the number of visible satellites is insufficient for relative positioning calculation, some gross errors can affect other observations, causing abnormal weighting phenomena. Summary of the Invention

[0004] The purpose of this invention is to provide a robust filtering method based on satellite quality assessment, which aims to enhance the robustness of Kalman filtering, reduce the probability of outliers, and provide a solution for continuous output of calculation results when there are insufficient visible satellites for calculation.

[0005] To achieve the above objectives, this invention provides a robust filtering method based on satellite quality assessment, comprising the following steps:

[0006] Step 1: The receiver collects navigation messages in real time;

[0007] Step 2: Single-point positioning to obtain receiver location and signal quality assessment parameters;

[0008] Step 3: Perform satellite signal quality assessment to determine if the observation matrix is ​​full rank;

[0009] Step 4: Calculate the robustness factor and the Kalman gain;

[0010] Step 5: Multi-epoch joint observations to establish full-rank complete geometric constraints for solving new predicted values;

[0011] Step 6: Retain the parameters of the current epoch and proceed to the next epoch solution.

[0012] During the real-time acquisition of navigation messages by the receiver, a multi-mode single-frequency receiver is used to receive single-frequency signals from BeiDou and GPS satellites, and the observation data and navigation messages are decoded and converted into RTCM3 format.

[0013] In the process of obtaining receiver position and signal quality assessment parameters through single-point positioning, pseudorange and carrier phase observation values ​​are extracted from the observation data. The receiver position is obtained using pseudorange single-point positioning, and the satellite-to-ground vector of each satellite is obtained. From this, the accuracy factor and satellite elevation angle are calculated to provide iterative initial values ​​for Kalman filtering.

[0014] In the process of satellite signal quality assessment and determining whether the observation matrix is ​​full rank, a coarse assessment of the satellite signal is performed based on PDOP and elevation angle. The PDOP threshold is set to 4 and the satellite elevation angle is set to 20°. For the filtered satellites, it is determined whether the observation matrix is ​​full rank. If the signal quality assessment is passed, the process proceeds to step 4 of claim 1. If the assessment is not passed, it is considered that the current epoch observation value itself cannot complete the solution process, and step 4 is skipped.

[0015] The process of calculating the robustness factor and Kalman gain includes the following steps:

[0016] 1) Obtain pseudorange residuals and carrier phase residuals from observations and one-step predictions, calculate the Mahalanobis distance of the residual vectors that follow a Gaussian distribution, and perform a chi-square test on the residual vectors;

[0017] 2) Set the chi-square test threshold as a hyperparameter of the Huber loss function, normalize the Mahalanobis distance of the residual vector, and calculate the Huber loss function after comparing it with the hyperparameter to obtain a more robust measurement error covariance matrix.

[0018] 3) Calculate the Kalman filter gain using the new error covariance matrix, and update the state estimate and the state mean square error matrix, skipping step 5.

[0019] The process of establishing full-rank complete geometric constraints to solve for new predictions for multi-epoch joint observations includes the following steps:

[0020] 1) Exit the calculation of the filter gain, and stack the predicted values ​​and residual values ​​of the first N epochs of observation data to obtain a new measurement matrix to obtain a set of satellite observation equations with complete geometric constraints;

[0021] 2) Use Lagrange interpolation to interpolate the predicted values ​​and residuals to obtain new fitted values. Assuming there are n satellite observations in the first N epochs, construct an n-1 degree basic polynomial;

[0022] 3) Obtain the fitting polynomial curve p(x) of the residuals and predicted values, and then obtain the predicted values ​​X of each satellite at the current epoch. k Update the state estimate and the state mean square error matrix.

[0023] In the process of retaining the parameters of the current epoch and entering the solution of the next epoch, the predicted values ​​and residual vectors are retained to provide measurement data for joint observation in subsequent epochs. The calculation of the filtering gain part of the Kalman filter measurement update is completed, and the subsequent solution continues.

[0024] The beneficial effects of this invention are:

[0025] This invention aims to reduce the impact of weak satellite signal strength and multipath effects on positioning accuracy and improve continuous positioning capabilities. An improved filtering scheme for complex environments is proposed. Before calculating the Kalman gain, satellite quality is assessed, and observations with poor signal quality are analyzed using multi-epoch joint observations to avoid contaminating subsequent epoch calculations. In the weighting part of the measurement covariance matrix, the Mahalanobis distance of the residual vector is calculated first, and the hyperparameters of the Huber loss function are tuned accordingly, resulting in faster loss rate in areas with large residuals. This invention enhances the robustness of the Kalman filter and reduces the probability of outliers. In cases where there are insufficient visible satellites, multi-epoch joint observations are used to ensure continuous output of results and reduce the impact on the filtering gain. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below.

[0027] Figure 1 This is a flowchart illustrating a robust filtering method based on satellite quality assessment.

[0028] Figure 2 This is a block diagram of a specific robust filtering algorithm. Detailed Implementation

[0029] This invention provides a robust filtering method based on satellite quality assessment, which enhances the robustness of Kalman filtering, prevents filter divergence, and reduces the probability of outliers. It can continuously output positioning results and reduce the impact on the Kalman filtering system when the number of visible satellites is insufficient.

[0030] The embodiments of this application are described below with reference to the accompanying drawings. It should be understood that the embodiments described below with reference to the accompanying drawings are exemplary descriptions for explaining the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions of the embodiments of this application.

[0031] The purpose of this application is to solve the Kalman filter divergence problem in the positioning process caused by insufficient visible satellites, concentrated satellite distribution, and excessive residuals in complex environments such as urban canyons and under trees. Due to poor satellite quality, the complete solution process cannot be completed. The multi-epoch joint observation interpolation proposed in this invention avoids contaminating the observation covariance matrix and affecting subsequent epoch solutions.

[0032] Please see Figure 1 This application provides a robust filtering method based on satellite quality assessment, the steps of which include the following:

[0033] Step 1: The receiver collects navigation messages in real time. Specifically, it uses a multi-mode single-frequency receiver to receive single-frequency signals from Beidou and GPS satellites, and decodes them to obtain observation data and navigation messages. The data format is converted to RTCM3 format.

[0034] Step 2: Single-point positioning is used to obtain receiver position and signal quality assessment parameters. Pseudorange and carrier phase observations are extracted from the observation data. The receiver position is obtained using pseudorange single-point positioning. The satellite-to-ground vectors of each satellite are obtained. The accuracy factor and satellite elevation angle are calculated to provide initial values ​​for Kalman filtering iteration.

[0035] Step 3: Perform satellite signal quality assessment to determine if the observation matrix is ​​full rank. Specifically, perform a coarse assessment of the satellite signal based on PDOP and elevation angle, where the PDOP threshold is set to 4 and the satellite elevation angle is set to 20°. For the filtered satellites, determine if the observation matrix is ​​full rank. If the signal quality assessment is passed, proceed to Step 4. If the assessment is not passed, it is considered that the current epoch observation value itself cannot complete the solution process, and Step 4 is skipped.

[0036] Step 4: Calculate the robustness factor and the Kalman gain, including the following steps:

[0037] The pseudorange residual and carrier phase residual are obtained by observing the values ​​and predicting the values ​​in one step. The Mahalanobis distance of the residual vector that follows a Gaussian distribution is calculated, and the chi-square test is performed on the residual vector.

[0038] The chi-square test threshold is set as a hyperparameter of the Huber loss function. The Mahalanobis distance of the residual vector is normalized and compared with the hyperparameter. The Huber loss function is then calculated to obtain a more robust measurement error covariance matrix.

[0039] Calculate the Kalman filter gain using the new error covariance matrix, and update the state estimate and the state mean square error matrix, skipping step 5;

[0040] Step 5: Multi-epoch joint observations to establish full-rank complete geometric constraints to solve for new predicted values, including the following steps:

[0041] The calculation of the filter gain is terminated, and the predicted values ​​and residual values ​​of the first N epochs of observation data are stacked to obtain a new measurement matrix to obtain a set of satellite observation equations with complete geometric constraints.

[0042] Lagrange interpolation is used to interpolate the predicted values ​​and residuals to obtain new fitted values. Assuming there are n satellite observations in the first N epochs, an n-1 degree fundamental polynomial is constructed.

[0043] The fitted polynomial curve p(x) of the residuals and predicted values ​​is obtained, and then the predicted values ​​X of each satellite at the current epoch are obtained. k Update the state estimate and the state mean square error matrix;

[0044] Step 6: Retain the parameters of the current epoch and proceed to the next epoch solution. Specifically, retain the predicted values ​​and residual vectors to provide measurement data for joint observations in subsequent epochs, complete the calculation of the filter gain part of the Kalman filter measurement update, and continue the subsequent solution.

[0045] In this embodiment, before calculating the filtering gain using Kalman filtering, a coarse screening based on satellite signal quality assessment is performed to exclude observations with poor signal quality. An augmented matrix of observations is constructed using joint observations from multiple epochs. This matrix, combined with the residuals of each satellite and the one-step prediction, generates a new prediction value for the current epoch using Lagrange interpolation, thus avoiding contamination of other observations and the Kalman filtering system. Furthermore, a Huber loss function is proposed to reduce the weight of the covariance matrix, and Mahalanobis distance based on the residuals is used as a comparison of hyperparameters. This correlates the tuning function with the residuals, achieving faster loss speed even when the residuals are much larger than the hyperparameters. Please refer to [link to relevant documentation]. Figure 2 The following will explain the specific steps:

[0046] Step 1: Receive GNSS satellite signals in real time using a receiver. To make the solution more universal, this invention uses a multi-mode single-frequency receiver to receive BeiDou and GPS single-frequency signals and decode them to obtain observation data and navigation messages. First, single-point positioning is performed to obtain the receiver's position. Taking the nth satellite as an example, the pseudorange observation equation for receiver R is expressed as:

[0047]

[0048] The carrier phase observation equation is:

[0049]

[0050] Where ρ (n)For pseudorange observations, φ (n) For carrier phase observations, r (n) =||x (n) -x|| represents the geometric distance between receiver R and satellite n, δt R With δt (n) Let I and T be the receiver clock error and satellite clock error, respectively; I and T be the atmospheric delay; N be the integer ambiguity; and ξ be the random noise. When determining the receiver position, equation (1) can be rewritten as:

[0051]

[0052] in, Given the pseudorange observations after error correction, if there are N satellites forming a nonlinear system of equations, linearizing it yields the following matrix equations:

[0053]

[0054] in

[0055] Represents r (n) The partial derivative with respect to x in x k-1 The value at that location, i.e.:

[0056]

[0057] Then H = (G T G) -1 The trace of the weight matrix H is represented as the geometric precision factor (PDOP). PDOP reflects the geometric distribution of the satellite relative to the receiver. The more dispersed the geometric distribution, the stronger the correlation between PDOP and positioning error; a smaller PDOP value results in a smaller positioning error. For satellites with excessively low elevation angles, errors caused by atmospheric delay and multipath effects are difficult to eliminate. The elevation angle parameter is obtained from the satellite-to-ground vector when calculating the receiver position. This provides initial values ​​for time updates in the Kalman filter.

[0058] Step 3: Conduct satellite quality assessment. First, exclude satellites with an elevation angle less than 20°. For the remaining satellites, check if the observation matrix is ​​full rank and determine if the PDOP is less than 4. If successful, proceed to the next step; otherwise, proceed to Step 4.

[0059] Step 3.1: Calculate the pseudorange residual and carrier phase residual, and assign a robust factor to the current epoch observation based on the chi-square test results of the residuals.

[0060]

[0061] Wherein, residual v kThis represents the difference between the observed value and the one-step predicted value. Since the square of the Mahalanobis distance of the residual vector, which follows a Gaussian distribution, follows a chi-square distribution, a chi-square test is performed on the residual vector. The formula for calculating the Mahalanobis distance is:

[0062]

[0063] Where μ is the mean residual of the first N epochs, ∑ -1 Let D be the covariance matrix. mk The square of the number follows a chi-square distribution:

[0064]

[0065] Based on the branch office's hypothesis testing method, it is assumed that the residual vector has completely eliminated the influence of observation errors and system noise, meaning the probability that the residual vector follows a normal distribution is α.

[0066]

[0067] In the formula, Let T be a chi-square distribution with a significance level of α, and T be the detection threshold. The choice of threshold determines the robustness of the filter.

[0068] Step 3.2: Set the detection threshold from Step 3 as a hyperparameter of the Huber loss function. This allows the normalized residuals to directly participate in the tuning of the robustness factor. The Huber function expression is:

[0069]

[0070] The Huber function is a tuned function combining MAE (linear error) and MSE (squared error). MSE loss is faster, while MAE is more robust and provides a smoother gradient descent. The tuning of the hyperparameter δ determines the function's emphasis on MAE and MSE. In generating the robustness factor, it ensures smooth filtering iterations while reducing sensitivity to outliers. For excessively large residual variance matrices, appropriate inflation is applied to reduce their weight in calculating the filter gain.

[0071] Step 3.3: Calculate the filter gain Gain and update the state estimate and state mean square error matrix for subsequent calculations.

[0072]

[0073] in, Let R be the mean square error matrix of the estimated values, and let R be the observation covariance matrix.

[0074] Step 4: For the observations that failed the initial screening of satellite data in Step 3, if the number of satellites is too small, the observation equations will be rank deficient and unable to solve the system of equations. If the satellite geometric precision factor is too large, it is generally believed that even after establishing the double-difference equations, the residual value will be too large, making it difficult to fix the integer ambiguity. Here, we choose to fit the observations of the first 5 epochs to obtain new predicted values, skip the Kalman filter gain, and continue with the subsequent calculations.

[0075] Step 4.1: Use multi-epoch joint observation interpolation to obtain the predicted values ​​from the observation data of the first 5 epochs. and residual value v k The augmented matrices are stacked separately to obtain satellite observations with full geometric constraints.

[0076] Step 4.2: Use Lagrange interpolation to interpolate the predicted values ​​and residuals to obtain new fitted values. Assuming there are N satellite observations in the first 5 epochs, construct N (n-1)th degree basic polynomials that satisfy the following condition: L i (x) in x i The function value at x is equal to 1. j The function value at that point is equal to 0, that is...

[0077]

[0078] Where x j To divide x i The residual values ​​of other satellites, L i (x) represents the current satellite prediction value. The (n-1)th degree polynomial is constructed as follows:

[0079]

[0080] Step 4.3: Obtain the fitting polynomial curve p(x) of the residuals and predicted values, and then obtain the predicted values ​​X of each satellite at the current epoch. k Skip the calculation of the filter gain and continue with the subsequent solution steps.

[0081] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A robust filtering method based on satellite quality assessment, characterized in that, Includes the following steps: Step 1: The receiver collects navigation messages in real time; Step 2: Single-point positioning to obtain receiver location and signal quality assessment parameters; Step 3: Perform satellite signal quality assessment to determine if the observation matrix is ​​full rank; Step 4: Calculate the robustness factor and the Kalman gain; The process of calculating the robustness factor and the Kalman gain includes the following steps: 1) Obtain pseudorange residuals and carrier phase residuals from observations and one-step predictions, calculate the Mahalanobis distance of the residual vectors that follow a Gaussian distribution, and perform a chi-square test on the residual vectors; 2) Set the chi-square test threshold as a hyperparameter of the Huber loss function, normalize the Mahalanobis distance of the residual vector, and calculate the Huber loss function after comparing it with the hyperparameter to obtain a more robust measurement error covariance matrix. 3) Calculate the Kalman filter gain using the new error covariance matrix, and update the state estimate and the state mean square error matrix, skipping step 5; Step 5: Multi-epoch joint observations to establish full-rank complete geometric constraints for solving new predicted values; The process of establishing full-rank complete geometric constraints through multi-epoch joint observations to solve for new predicted values ​​includes the following steps: 1) Exit the calculation of the filter gain, and stack the predicted values ​​and residual values ​​of the first N epochs of observation data to obtain a new measurement matrix to obtain a set of satellite observation equations with complete geometric constraints; 2) Use the Lagrange interpolation method to interpolate the predicted value and the residual to obtain a new fitted value. Assuming that there are n satellite observations in the first N epochs, construct an n-1 degree basic polynomial. 3) Obtain the fitting polynomial curves of the residuals and predicted values. This allows us to obtain the predicted values ​​of each satellite at the current epoch. Update the state estimate and the state mean square error matrix; Step 6: Retain the parameters of the current epoch and proceed to the next epoch solution.

2. The robust filtering method based on satellite quality assessment as described in claim 1, characterized in that, In step 1, during the real-time acquisition of navigation messages by the receiver, a multi-mode single-frequency receiver is used to receive single-frequency signals from BeiDou and GPS satellites, and the observation data and navigation messages are decoded and converted into RTCM3 format.

3. The robust filtering method based on satellite quality assessment as described in claim 1, characterized in that, In step 2, during the process of obtaining receiver position and signal quality assessment parameters through single-point positioning, pseudorange and carrier phase observation values ​​are extracted from the observation data. The receiver position is obtained using pseudorange single-point positioning, and the satellite-to-ground vector of each satellite is obtained. The accuracy factor and satellite elevation angle are then calculated to provide initial values ​​for Kalman filtering iteration.

4. The robust filtering method based on satellite quality assessment as described in claim 1, characterized in that, In step 3, during the process of satellite signal quality assessment and determining whether the observation matrix is ​​full rank, a coarse assessment of the satellite signal is performed based on PDOP and elevation angle. The PDOP threshold is set to 4, and the satellite elevation angle is set to 20°. For the filtered satellites, it is determined whether the observation matrix is ​​full rank. If the signal quality assessment is passed, proceed to step 4. If the assessment is not passed, it is considered that the current epoch observation value itself cannot complete the solution process, and step 4 is skipped.

5. The robust filtering method based on satellite quality assessment as described in claim 1, characterized in that, In step 6, during the process of retaining the current epoch parameters and proceeding to the next epoch solution, the predicted values ​​and residual vectors are retained to provide measurement data for joint observations in subsequent epochs. The calculation of the filtering gain part of the Kalman filter measurement update is completed, and subsequent solutions are continued.

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