An adaptive Kalman filter algorithm for dynamic precise point positioning

Abstract

The present invention discloses an adaptive Kalman filter algorithm for dynamic precise single-point positioning. Belonging to the field of satellite navigation positioning, the Kalman filter algorithm can adaptively estimate and adjust the measurement noise covariance matrix, the steps are: initialize the noise variance of each pseudorange and carrier phase observation based on the empirical random model; perform Kalman filtering to calculate the measurement residual of each pseudorange and carrier phase observation; if the observation is not the first time, perform outlier detection and processing on the measurement residual based on the normal distribution hypothesis test; estimate the measurement noise variance of each observation based on the covariance matching principle; update the observation noise covariance matrix, perform Kalman filtering again, and output the positioning result. The present invention takes into account the influence of the surrounding environment on the observation noise and multipath error, and the estimation of the observation noise standard deviation can better approximate its actual level, obtain a better filtering result, and thus improve the accuracy and reliability of the positioning result.

Description

Technical Field

[0001] The invention belongs to the field of satellite navigation and positioning, and relates to an adaptive Kalman filtering algorithm for precise single-point positioning. Background Art

[0002] The Kalman filter, one of the most popular data fusion algorithms, is widely used in satellite navigation and positioning. Because the filter's performance depends on the accuracy of the function model and prior knowledge of process and measurement noise, optimal estimates of the state parameters can only be obtained when both are accurate. For precise point positioning, the function model has been extensively studied, but obtaining accurate prior statistical information about process and observation noise remains a challenging problem. Typically, prior statistical information about process and measurement noise is obtained by analyzing sample data and assumed to be constant. However, in most practical applications, process noise and measurements often vary over time. Using inaccurate or erroneous prior statistical information about process and measurement noise can degrade filter performance and, in severe cases, cause filter divergence, severely impacting positioning accuracy and reliability. In satellite navigation and positioning, measurement noise is more susceptible to environmental uncertainty than process noise, making accurate prior statistical information more difficult to obtain. Therefore, adaptive estimation of the measurement noise variance is particularly important. Summary of the Invention

[0003] Purpose of the invention: The purpose of the present invention is to provide an adaptive Kalman filter algorithm for precise point positioning to cope with state estimation when the measurement noise covariance matrix is ​​unknown or inaccurate.

[0004] Technical solution: The present invention provides an adaptive Kalman filter algorithm for dynamic precise point positioning; the specific steps are as follows:

[0005] Step (1), initializing the noise standard deviation of each pseudorange and carrier phase observation according to the empirical random model;

[0006] Step (2), executing the standard Kalman filter algorithm to calculate the measurement residuals of each pseudorange and carrier phase observation;

[0007] Step (3) determines whether the observed data appears for the first time. If not, perform outlier detection and processing on the measurement residuals based on the normal distribution hypothesis test; if yes, skip this step;

[0008] Among them, the following hypothesis test is constructed

[0009] H0:r≤T,H1:r>T (1)

[0010] In the formula, H0 is the hypothesis of no abnormal observation; H1 is the hypothesis of abnormal observation; r is the test statistic, and its calculation formula is

[0011]

[0012] Where, v i,k is the measurement residual of the i-th observation at the k-th epoch, is the estimate of the standard deviation of the measurement noise of the i-th observation at the previous epoch; a is the significance level of the normal distribution hypothesis test; outliers in the measurement residuals are detected by comparing the test statistic r with the test threshold T; if r>T, it indicates that there is a large disturbance in the measurement residuals at that epoch, and to avoid affecting the reliability of the measurement noise variance estimate, the corresponding observation is eliminated;

[0013] Step (4), calculating the measurement noise variance of each observation according to the noise variance estimation model;

[0014] Based on the covariance matching principle, the noise variance of each observation is calculated according to the following formula, and the estimation formula of the measurement residual variance is:

[0015]

[0016] Where, is the estimated variance of the measurement residual of the i-th observation at the k-th epoch;

[0017]

[0018] Where, is the sample variance estimate of the i-th observation, is the predicted state covariance matrix.

[0019] Furthermore, to improve the sample variance To improve the accuracy of the estimation, the sample variance is expanded. This is because the estimation of the measurement noise variance obtained by formula (4) is a theoretical estimation under the assumption that the observations from different satellites are independent of each other and the measurement noise obeys the Gaussian normal distribution. However, in practical applications, due to the influence of various error sources such as multipath error, the measurement error usually does not strictly obey the Gaussian normal distribution. The sample variance estimation calculated by formula (4) is very conservative. The sample variance expansion processing model is:

[0020]

[0021] Where s is the expansion coefficient, el is the satellite elevation angle, Estimation of the sample variance after expansion;

[0022] Step (5), update the measurement noise covariance matrix,

[0023] The updated measurement noise covariance matrix is

[0024]

[0025] Where diag{·} represents the diagonalization operation; Kalman filtering is performed again to output the positioning result.

[0026] This method is based on the covariance matching principle and integrates the empirical random model to construct an adaptive estimation model of measurement noise variance. It avoids the limitation of the covariance matching method that the measurement residual vectors must be of the same type and dimension at each utilization moment, and overcomes the disadvantage that the empirical random model cannot adapt to dynamic changes in the user environment.

[0027] Beneficial effects: Compared with the prior art, the adaptive Kalman filtering algorithm proposed in the present invention can adaptively estimate the observation noise variance of pseudorange and carrier phase; since the online estimation method proposed in the present invention takes into account the impact of the surrounding environment on observation noise and multipath error, the estimation of the observation noise standard deviation can better approximate its actual level, so that a better filtering result can be obtained, thereby further improving the accuracy and reliability of the positioning result. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flowchart of the process of the present invention;

[0029] Figure 2 A schematic diagram of a GPS satellite sky map showing dynamic shipborne test data according to an embodiment of the present invention;

[0030] Figure 3 Schematic diagram of the estimation result of the measurement noise variance of the PRN27 satellite in an embodiment of the present invention;

[0031] Figure 4 Schematic diagram of positioning results in three directions of northeast sky in a shipborne dynamic experiment in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] The embodiment of the present invention provides a specific process of an adaptive Kalman filter algorithm for dynamic precise point positioning; the specific steps are as follows:

[0034] Step (1), initializing the noise standard deviation of each pseudorange and carrier phase observation according to the empirical random model;

[0035] Specifically, an empirical random model based on altitude angle can be used, namely:

[0036]

[0037] Where σ0 is the nominal variance factor, el is the satellite elevation angle;

[0038] Step (2), executing the standard Kalman filter algorithm to calculate the measurement residuals of each pseudorange and carrier phase observation;

[0039] Specifically, the calculation formula for the measurement residual is

[0040]

[0041] Where V k is the measurement residual vector, Z k is the original pseudorange and carrier phase observation vector, H k is the observation matrix, Estimate the state parameters;

[0042] Step (3) determines whether the observed data appears for the first time. If not, perform outlier detection and processing on the measurement residuals based on the normal distribution hypothesis test; if yes, skip this step;

[0043] Among them, the method for processing the outlier detection test is:

[0044] Construct the following hypothesis test

[0045] H0:r≤T,H1:r>T (3)

[0046] In the formula, H0 is the hypothesis of no abnormal observation; H1 is the hypothesis of abnormal observation; r is the test statistic, and its calculation formula is

[0047]

[0048] Where, v i,k is the measurement residual of the i-th observation at the k-th epoch, is the estimate of the standard deviation of the measurement noise of the i-th observation at the previous epoch; a is the significance level of the normal distribution hypothesis test; outliers in the measurement residuals are detected by comparing the test statistic r with the test threshold T; if r>T, it indicates that there is a large disturbance in the measurement residuals at that epoch, and to avoid affecting the reliability of the measurement noise variance estimate, the corresponding observation is eliminated;

[0049] Step (4), calculating the measurement noise variance of each observation according to the noise variance estimation model;

[0050] Based on the covariance matching principle, the noise variance of each observation is calculated according to the following formula:

[0051] Specifically, the estimation formula for the residual variance of each observation is:

[0052]

[0053] Where, is the estimated variance of the measurement residual of the i-th observation at the k-th epoch;

[0054]

[0055] Where, is the sample variance estimate of the i-th observation, is the predicted state covariance matrix.

[0056] Furthermore, to improve the sample variance To improve the accuracy of the estimation, the sample variance is expanded. This is because the estimation of the measurement noise variance obtained by formula (6) is a theoretical estimation under the assumption that the observations from different satellites are independent of each other and the measurement noise obeys the Gaussian normal distribution. However, in practical applications, due to the influence of various error sources such as multipath error, the measurement error usually does not strictly obey the Gaussian normal distribution. The sample variance estimation calculated by formula (6) is very conservative. The sample variance expansion processing model is:

[0057]

[0058] Where s is the expansion coefficient, el is the satellite elevation angle, Estimation of the sample variance after expansion;

[0059] Step (5), update the measurement noise covariance matrix,

[0060] Specifically, the updated measurement noise covariance matrix is:

[0061]

[0062] Where diag{·} represents the diagonalization operation; Kalman filtering is performed again to output the positioning result.

[0063] The present invention provides a set of test results based on dynamic shipborne data. The following three filtering schemes are used to perform dynamic precise point positioning:

[0064] Scheme 1 (KF_nominal): Using the empirical estimation model, the model parameter σ0 is set to the nominal value σ IF_P0 ≈0.9m, the carrier phase is set to σ IF_L0 ≈0.009m;

[0065] Scheme 2 (KF_optimal): Using the empirical estimation model, the model parameter σ0 is set to the optimal value, and the standard deviation of the pseudorange observation is set to σ IF_P0≈7.0m, the carrier phase is set to σ IF_L0 ≈0.03m;

[0066] Figure 2 The star map of the GPS satellite for the shipborne experiment is shown in the following figure. The estimation of the measurement noise variance of GPS PRN27 satellite obtained by the above three schemes is as follows: Figure 3 As shown; Figure 4 The positioning results in three directions of the northeast sky in the shipborne dynamic experiment are shown in Table 1. The statistical results of positioning error and convergence time are shown in Table 1.

[0067] Table 1

[0068]

[0069] from Figure 3 It can be seen that the PPP positioning error of the KF_nominal filtering scheme fluctuates significantly, and the time required for the positioning error to converge to 0.5m in the three directions of northeast and sky is the longest; among the three filtering schemes of KF_nominal, KF_optimal and KF_adaptive, the positioning effect of the KF_nominal filtering scheme is the worst; compared with KF_nominal, the positioning results of KF_optimal and KF_adaptive are significantly improved; from the statistical results in the table, it can be seen that compared with the KF_nominal filtering scheme, the PPP positioning accuracy of the KF_optimal filtering scheme in the three directions of ENU is improved by 0.24m, 0.65m and 1.55m respectively, and the convergence time is shortened by 11217 s; the PPP positioning accuracy of the KF_adaptive filtering scheme is improved by 0.28m, 0.78m and 1.61m in the three ENU directions, and the convergence time is reduced by 11300s; further comparison of the positioning results of the KF_optimal and KF_adaptive filtering schemes shows that the PPP positioning performance using the KF_adaptive filtering scheme is slightly better than that of the KF_optimal filtering scheme; the PPP positioning accuracy of the KF_adaptive filtering scheme is improved by 0.04m, 0.13m and 0.06m in the three directions of northeast and sky, respectively, compared with the KF_optimal filtering scheme; in summary, the Kalman filter based on adaptive estimation of measurement noise variance based on measurement residual proposed in the present invention can effectively improve the positioning performance.

[0070] The advantages of the present invention are that: the method is based on the covariance matching principle and simultaneously integrates the empirical random model to construct an adaptive estimation model for the measurement noise variance, avoiding the limitation of the covariance matching method that the measurement residual vectors are of the same type and dimension at each utilization moment, and overcoming the disadvantage that the empirical random model cannot adapt to dynamic changes in the user environment.

[0071] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. An adaptive Kalman filter algorithm for dynamic precise point positioning; characterized in that: The specific steps are as follows: Step (1), initializing the noise standard deviation of each pseudorange and carrier phase observation according to the empirical random model; Step (2), executing the standard Kalman filter algorithm to calculate the measurement residuals of each pseudorange and carrier phase observation; Step (3) determines whether the observed data appears for the first time. If not, outlier detection and processing are performed on the measurement residuals based on the normal distribution hypothesis test; If yes, skip this step; Step (4), constructing an adaptive estimation model of measurement noise variance based on the covariance matching principle and integrating the empirical random model, and calculating the measurement noise variance of each observation according to the adaptive estimation model; Step (5): Update the measurement noise covariance matrix, perform Kalman filtering again, and output the positioning result.

2. The adaptive Kalman filter algorithm for dynamic precise point positioning according to claim 1, characterized in that: In step (3), the outlier detection and processing of the measurement residuals are specifically as follows: Construct the following hypothesis test: H0:r≤T,H1:r>T Where H0 is the hypothesis of no abnormal observation; H1 is the hypothesis of abnormal observation; r is the test statistic, and its calculation formula is Where, v i,k is the measurement residual of the i-th observation at the k-th epoch, is the estimate of the standard deviation of the measurement noise of the i-th observation at the previous epoch; a is the significance level of the normal distribution hypothesis test; outliers of the measurement residuals are detected by comparing the size of the test statistic r with the test threshold T; if r>T, it indicates that there is a large disturbance in the measurement residuals at this epoch. In order to avoid affecting the reliability of the estimation of the measurement noise variance, the corresponding observations are eliminated.

3. The adaptive Kalman filter algorithm for dynamic precise point positioning according to claim 1, characterized in that: In step (4), the estimation formula of the measurement noise variance is: Where, is the estimated variance of the measurement residual of the i-th observation at the k-th epoch; is the sample variance estimate of the i-th observation, is the predicted state covariance matrix.

4. The adaptive Kalman filter algorithm for dynamic precise point positioning according to claim 3, characterized in that: The expansion process is performed according to the obtained measurement residual sample variance, and the sample variance expansion process model is: Where s is the expansion coefficient, el is the satellite elevation angle, Estimated variance of the sample after expansion.

5. The adaptive Kalman filter algorithm for dynamic precise point positioning according to claim 1, characterized in that: In step (5), the updated measurement noise covariance matrix is: Where diag{·} represents the diagonalization operation.

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