A hierarchical evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles

Abstract

A hierarchical evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles. Through PPK positioning solution, the state vector of forward and reverse Kalman filtering of each epoch and its variance-covariance matrix, positioning solution state, and position precision reduction factor PDOP are obtained. Forward and reverse Kalman filtering epochs are co-viewed, and a two-tailed normal test is performed on the mutual difference results of the forward and reverse filtering state vectors after co-viewing. The positioning is graded and evaluated based on the hypothesis test results, the positioning solution state, and the PDOP value, and the result output is optimized. The present invention realizes the effective verification of the reliability of the results of centimeter-level PPK positioning of unmanned aerial vehicles, and the optimization output strategy based on the results of graded evaluation improves the stability of centimeter-level PPK positioning of unmanned aerial vehicles.

Description

Technical Field

[0001] The present invention belongs to the field of centimeter-level PPK (Post-Processing Kinematic) positioning result verification of unmanned aerial vehicles, and in particular relates to a hierarchical evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles. Background Art

[0002] In UAV applications, high-precision positioning capability is one of the key factors to achieve autonomous navigation and precise mission execution. In recent years, GNSS-based real-time kinematic (RTK) positioning technology and post-processing kinematic (PPK) positioning technology have been widely used in UAV navigation due to their high precision and reliability. However, due to the complex movement environment of UAVs, factors such as signal shielding and multipath effects may lead to a decrease in the reliability of the positioning solution. Therefore, how to improve the reliability of PPK positioning results has become one of the important research directions of UAV high-precision positioning technology. Existing research has mostly focused on the improvement of PPK algorithms and the optimization of filtering strategies, but research on the effectiveness of positioning results and optimization of output strategies is still insufficient. Summary of the invention

[0003] In this paper, a hierarchical evaluation method for centimeter-level PPK positioning results of UAVs is proposed. By combining forward and reverse Kalman filtering, two-tailed normal test and comprehensive evaluation of PDOP value, an effective result grading evaluation and optimization output strategy is provided, aiming to further improve the stability and reliability of centimeter-level PPK positioning results of UAVs.

[0004] In order to achieve the above objectives, a hierarchical evaluation method for centimeter-level PPK positioning results of UAVs is invented. The method includes the following steps:

[0005] Step S1: Obtain the state vector of the forward and reverse Kalman filter of each epoch and its variance-covariance matrix, the positioning solution state, and the position precision reduction factor PDOP through PPK positioning solution;

[0006] Step S2: Perform forward and reverse Kalman filtering epoch common view, and perform a two-tailed normality test on the mutual difference results of the forward and reverse filtering state vectors after common view;

[0007] Step S3: Combine the hypothesis test results, the positioning solution status and the PDOP value to perform positioning graded evaluation and optimize the result output.

[0008] The present invention provides a hierarchical evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles, and establishes a reliability hierarchical evaluation mechanism by comprehensively analyzing and testing various key parameters in the PPK positioning solution process (such as forward and reverse Kalman filter state vectors and their variance covariance matrices, positioning solution states, position precision reduction factor PDOP, etc.). Through this mechanism, the present invention aims to effectively check and improve the reliability of centimeter-level PPK positioning results of unmanned aerial vehicles, and optimize the output strategy based on the hierarchical evaluation results to improve the stability of centimeter-level positioning of unmanned aerial vehicles, and ensure its accurate navigation and mission execution capabilities in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 It is an implementation flow chart of the hierarchical evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles according to the present invention;

[0010] Figure 2 is a schematic diagram of the PPK positioning trajectory of drone data according to an embodiment of the present invention;

[0011] Figure 3 It is a schematic diagram of the fixed solution deviation of the forward and reverse filtering of the UAV data PPK positioning according to an embodiment of the present invention;

[0012] Figure 4 1 is a schematic diagram of PPK positioning and grading results of drone data according to an embodiment of the present invention. DETAILED DESCRIPTION

[0013] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0014] like Figure 1 As shown, this embodiment discloses a hierarchical evaluation method for centimeter-level PPK positioning results of drones, and the specific steps are as follows:

[0015] Step S1, through PPK positioning solution, obtain the state vector and its variance-covariance matrix, positioning solution state, and position precision reduction factor PDOP of the forward and reverse Kalman filters of each epoch.

[0016] Step S2, perform forward and reverse Kalman filtering epoch co-viewing, and perform a two-tailed normal test on the mutual difference results of the forward and reverse filtering state vectors after the common view. Specifically, in the PPK positioning solution, for the same epoch, the position at that moment is objectively unique. From the perspective of the positioning solution results of each epoch, it is mainly obtained by solving the observation values ​​of each epoch (the same observation values ​​are used in the forward and reverse directions). When the carrier ambiguity solution used is correct and the state prediction models of filtering adjacent epochs are correct, the forward and reverse positioning results should be the same. When the actual processes such as quality control and ambiguity resolution change due to different state predictions, the forward and reverse results will produce a certain mutual difference. At this time, the correctness of the mutual difference should be tested. A set of actual measured UAV PPK positioning results were used for experimental verification. Figure 2 The flight trajectory of the drone.

[0017] The positioning result of the forward filter And the positioning results of reverse filtering Subtract, where the superscript f and b Respectively represent the forward and backward signs, subscript k express k moment; considering the uncertainty of the forward and reverse state predictions, the difference is considered Theoretically, it satisfies the normal distribution with a mean of 0, that is, it is considered that the mathematical expectations of the positioning results of the two assumptions are the same. At this time, only the random noise that satisfies the normal distribution remains, so it can be As a hypothesis test quantity, the reliability of the forward and reverse positioning results is tested. Taking the test of plane positioning results as an example, After standardization, the positioning results are tested for hypothesis. From the perspective of application needs, the positioning in the N direction and the E direction should meet the error requirements at the same time, and the positioning results have only two hypotheses: reliable and unreliable. Therefore, the forward and reverse positioning results are reliable (the N and E directions meet the requirements at the same time) as the original hypothesis. , it can be considered that Established:

[0018] (1)

[0019] The alternative hypothesis is that the forward and reverse positioning results are unreliable , it can be considered that Established:

[0020] (2)

[0021] In formula (1) and (2): and They are The components in the E and N directions, and They are The variance in the E and N directions, is the confidence level, is the normal distribution quantile. Principle, standardized hypothesis test quantity distribution The probability within the interval is 0.9973. If the standardized hypothesis test quantity distribution Outside the interval, the null hypothesis Not true, alternative hypothesis The forward and reverse positioning results are unreliable, so .in, and Can be The variance-covariance matrix of According to the state update formula of Kalman filtering: (3)

[0022] In the formula, express Parameter estimation at time Indicates from Time prediction to Parameter estimation at time express The gain matrix at time; and Respectively The observation value matrix and observation design matrix at the moment. According to the error propagation law, we can get The calculation formula is:

[0023] (4)

[0024] Where: and The forward and reverse filtering prediction state vectors are The variance-covariance matrix of and are the gain matrices for forward and reverse filtering, respectively, and are the observation design matrices for forward and backward filtering, respectively.

[0025] By using the hypothesis test judgment based on the above formula (1) and formula (2), it can be adaptively determined whether the mutual difference between the forward and reverse positioning results is abnormal (out of limit). The forward and reverse positioning results of the drone data in the embodiment are checked according to the above method, such as Figure 3 shown.

[0026] Step S3, combining the hypothesis test results, the positioning solution status and the PDOP value to perform positioning graded evaluation and optimize the result output. Specifically including:

[0027] When the states of both the forward and reverse filtering positioning solutions are floating-point solutions, the positioning is unreliable and the positioning result is output according to the PODP test result; when one of the forward and reverse filtering is a fixed solution but the ratio is less than the evaluation threshold, the positioning is suspicious and the positioning output is an ambiguity fixed solution; when both the forward and reverse filtering are fixed but the state vector mutual difference exceeds the limit, the positioning is suspicious and the positioning result is output according to the PODP test result; when one of the forward and reverse filtering is a fixed solution and the ratio is greater than the evaluation threshold, the positioning is reliable and the positioning output is an ambiguity fixed solution; when both the forward and reverse filtering are fixed and the state vector mutual difference does not exceed the limit, the positioning is reliable and the positioning result is obtained by weighting the forward and reverse filtering states.

[0028] In the positioning result output stage, after obtaining the forward and reverse positioning results and passing the two-tailed normal test, establishing a suitable positioning grading evaluation system to optimize the output results is the key to the final presentation of PPK positioning. At this time, facing the centimeter-level positioning needs of drones, positioning grading is performed from the ambiguity fixed state, and on this basis, the results are optimized and output in combination with the distribution state of satellites (PDOP).

[0029] The positioning classification method is shown in the following table:

[0030] Table 1: PPK positioning classification method and optimization output strategy

[0031]

[0032] When the PDOP result is (0,0), it means that the PDOP corresponding to the satellites used in the forward and reverse directions meet the PDOP threshold requirements; the result is (1,0) which means that the forward direction does not meet the requirements but the reverse direction does; the result is (0,1) which means that the forward direction meets the requirements but the reverse direction does not; the result is (1,1) which means that neither of them meets the requirements. Considering that the unit weighted mean error of the carrier phase is generally 2mm, the error can be considered to be magnified after the inter-station difference. At this time, the positioning accuracy can be determined based on the PDOP value and the weighted mean error of the observation value. Since carrier positioning plays a major role in PPK positioning, the PDOP threshold is mainly determined based on the following formula:

[0033] (5)

[0034] In the formula, is the positioning threshold, is the double difference carrier phase measurement accuracy. When the positioning threshold condition is given, the corresponding PDOP threshold can be determined.

[0035] The final result is output according to the PDOP conditions in the table. If the weighted average method is used for output, the weight is determined according to the inverse of the variance of the forward and reverse positioning results.

[0036] The present invention provides a grading evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles. Through PPK positioning solution, the state vector of forward and reverse Kalman filtering of each epoch and its variance-covariance matrix, the positioning solution state (including: ultra-wide lane fixed solution, wide lane fixed solution, narrow lane fixed solution, floating point solution), and the position precision reduction factor PDOP are obtained; forward and reverse Kalman filtering epochs are viewed together, and a two-tailed normal test is performed on the mutual difference results of the forward and reverse filtering state vectors after the common view; and the positioning grading evaluation is performed in combination with the hypothesis test results, the positioning solution state and the PDOP value, and the result output is optimized, such as Figure 4 The present invention realizes the effective verification of the reliability of the centimeter-level PPK positioning result of the UAV, and the optimization output strategy based on the result of the graded evaluation improves the stability of the centimeter-level PPK positioning of the UAV.

Claims

1. A hierarchical evaluation method for centimeter-level PPK positioning results of unmanned aerial vehicles, characterized in that: The steps include: Step S1: Through PPK positioning solution, obtain the state vector of the forward and reverse Kalman filter of each epoch of the UAV and its variance-covariance matrix, positioning solution state, and position precision reduction factor PDOP; Step S2: Perform forward and reverse Kalman filtering epoch common view, and perform a two-tailed normality test on the mutual difference results of the forward and reverse filtering state vectors after common view; Specifically include: The positioning result of the forward filter And the positioning results of reverse filtering The difference is calculated, where the superscript f and b represent the forward and backward signs respectively, and the subscript k represents the k moment. Considering the uncertainty of the forward and reverse state prediction, the difference is considered to be Theoretically, it satisfies the normal distribution with a mean of 0, that is, it is assumed that the mathematical expectations of the positioning results of the two assumptions are the same. At this time, only the random noise that satisfies the normal distribution remains. k As a hypothesis test quantity to test the reliability of the forward and reverse positioning results; ΔX k After standardization, the positioning results are tested for hypothesis. From the perspective of application needs, the positioning in the N direction and the E direction should meet the error requirements at the same time, and the positioning results have only two hypotheses: reliable and unreliable. Therefore, the forward and reverse positioning results are reliable as the null hypothesis H0. When the N and E directions meet the following equation (1), the null hypothesis H0 is considered to be established: The forward and reverse positioning results are unreliable as an alternative hypothesis H a , the alternative hypothesis H is considered to be a Established: In formulas (1) and (2): ΔX E and ΔX N are ΔX k The components in the E and N directions, and are ΔX k The variance in the E and N directions, α is the confidence level, is the normal distribution quantile; according to the 3σ principle, the probability that the standardized hypothesis test quantity is distributed in the interval (-3σ, 3σ) is 0.9973; if the standardized hypothesis test quantity is distributed outside the interval (-3σ, 3σ), the original hypothesis H0 is considered to be invalid, and the alternative hypothesis H a The forward and reverse positioning results are unreliable, and α=0.9973 is taken; among them, and By ΔX k The variance-covariance matrix of Get; According to the state update formula of Kalman filtering: X k =X k,k-1 +K k (L k -A k X k,k-1 ) (3) Where, X k represents the parameter estimation at time k; X k,k-1 K represents the parameter estimation from time k-1 to time k; k represents the gain matrix at time k; L k and A k They represent the observation value matrix and observation design matrix at time k respectively; according to the error propagation law, The calculation formula is: Where: and The forward and reverse filtering prediction state vectors ΔX are k,k-1 The variance-covariance matrix, K f and K b are the gain matrices for forward and reverse filtering, respectively, A f and A b are the observation design matrices for forward and reverse filtering, respectively; By using the hypothesis test judgment according to the above formula (1) and formula (2), it is adaptively determined whether the mutual difference between the forward and reverse positioning results of the UAV is abnormal or exceeds the limit; Step S3: Combine the hypothesis test results, the positioning solution status and the PDOP value to perform positioning classification evaluation and optimize the result output; Specifically include: When the states of the forward and reverse filtering positioning solutions are both floating point solutions, the positioning is unreliable, and the positioning result is output according to the PDOP test result; when one of the forward and reverse filtering is a fixed solution but the ratio is less than the evaluation threshold, the positioning is suspicious, and the positioning output is an ambiguity fixed solution; when both the forward and reverse filtering are fixed, but the state vector mutual difference exceeds the limit, the positioning is suspicious, and the positioning result is output according to the PDOP test result; when one of the forward and reverse filtering is a fixed solution and the ratio is greater than the evaluation threshold, the positioning is reliable, and the positioning output is an ambiguity fixed solution; when both the forward and reverse filtering are fixed and the state vector mutual difference does not exceed the limit, the positioning is reliable, and the positioning result is obtained by weighting the forward and reverse filtering states; When the PDOP test result is (0,0), it means that the PDOPs corresponding to the satellites used in the forward and reverse directions meet the PDOP threshold requirements; when the result is (1,0), it means that the forward direction does not meet the requirements but the reverse direction does; when the result is (0,1), it means that the forward direction meets the requirements but the reverse direction does not; when the result is (1,1), it means that neither of them meets the requirements. The PDOP threshold is determined according to formula (5): s p =s φ ·PDOP (5) In the formula, σ p is the positioning threshold, σ φ is the double-difference carrier phase measurement accuracy; when the positioning threshold condition is given, the corresponding PDOP threshold can be determined; the output of the final result is output according to the preset PDOP condition.

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