Positioning method for GNSS quality control based on M estimation of w-test

Abstract

The embodiment of the present invention discloses a positioning method for M-estimation GNSS quality control based on w-test, including: step 1: judging whether the requirements for w-test are met, if so, entering step 2, otherwise entering step 4; step 2: performing w-test, if the w-test passes, entering step 4, if the w-test fails, entering step 3; step 3: judging whether the satellite numbers corresponding to the maximum test amount in the w-test and the maximum test amount in the M-estimation are the same, and finally considering the satellite corresponding to the optimal solution position as a new full set to calculate the positioning solution based on the same and different satellite numbers; step 4: performing M-estimation and outputting the corresponding positioning solution. The present invention eliminates gross errors through w-test and reduces the weight of gross errors through M-estimation to jointly achieve the acquisition of the user's optimal solution position, thereby achieving quality control of satellite pseudo-range observations in an urban environment, thereby ensuring that users obtain reliable positioning quality.

Description

Technical Field

[0001] The present invention relates to the field of Beidou navigation, and in particular to a positioning method for M estimation GNSS quality control based on w-test. Background Art

[0002] With the official completion of my country's BeiDou Navigation System, the precise positioning services provided by the BeiDou Navigation System and other global satellite navigation systems (GNSS) are improving transportation efficiency, strengthening agricultural precision management, ensuring public safety, optimizing urban management, monitoring electric power and geological disasters, enriching personal location services, and promoting the development of Internet of Vehicles and mobile communications. However, due to the fragility of the global satellite navigation system itself and the complexity of the environment, the positioning service performance obtained by users under the condition of poor satellite observations is poor, that is, due to the multipath interference of satellite signals from surrounding buildings, some error terms in satellite observations cannot be modeled in the filtering algorithm, such as non-line-of-sight signals and multipath interference signals. However, when these error terms accumulate to a certain extent, the filter will not converge, and the user's positioning accuracy will be seriously reduced. Therefore, it is necessary to control the quality of satellite observations.

[0003] Quality control refers to eliminating the fault or suppressing the impact of the fault on the system when there is a fault in the system, so that the system can obtain stable and reliable results. Among them, the traditional fault elimination method is to eliminate the largest fault first when there is an abnormality in the system data, and then repeatedly calculate the remaining data in the system until no fault is detected. However, the traditional fault elimination method is difficult to meet the situation where the satellite observation data contains multiple gross errors in a complex environment, that is, it is impossible to accurately eliminate the corresponding gross errors, and the situation of false elimination may occur. Another idea of ​​the quality control algorithm is to use robust estimation to assign appropriate weights to the observations to suppress the impact of erroneous data on the system. The commonly used method is to perform weighted solution based on the quality of satellite signals, that is, to use one or more characteristic information related to the GNSS signal (satellite elevation angle, carrier-to-noise ratio or a combination of the two, etc.) to assign corresponding weights to the pseudo-range observations to suppress the harm caused to the system by poor quality GNSS signals. However, in the actual environment, the weighted quality control algorithm is difficult to accurately weight the observation data, which is mainly caused by the complexity of the scene.

[0004] Therefore, there is an urgent need for a technical solution for quality control of satellite pseudorange observations received by satellite receivers in urban environments to ensure that users obtain reliable positioning quality. Summary of the invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a positioning method for M-estimation GNSS quality control based on w-test to ensure positioning quality.

[0006] In order to solve the above technical problems, an embodiment of the present invention proposes a positioning method for M estimation GNSS quality control based on w-test, including:

[0007] Step 1: Collect GNSS observation data and determine whether the current number of observations meets the requirements for w-test. If yes, proceed to step 2, otherwise proceed to step 4;

[0008] Step 2: Perform gross error detection on GNSS observation data based on the w test. If the w test passes, proceed to step 4; if the w test fails, proceed to step 3.

[0009] Step 3: Determine whether the satellite numbers corresponding to the maximum test quantity in the w test and the maximum test quantity in the M estimate are the same. If they are the same, remove the satellite observations from the full set of observations, regard the remaining satellites as a new full set, and return the new full set of satellite observations to step 2 for re-w test;

[0010] If they are different, calculate the user position after deleting the satellite corresponding to the maximum test amount from the M estimate and the w test respectively, and then select the optimal solution position from the w test and the M estimate according to the error between the position and the previous moment. Finally, the satellite corresponding to the optimal solution position is regarded as the new full set calculation positioning solution, and the new full set satellite observation quantity is returned to step 2 to re-perform the w test;

[0011] Step 4: Perform M estimation on the GNSS observation data and output the corresponding positioning solution.

[0012] The beneficial effects of the present invention are as follows: the present invention achieves the optimal solution position of the user by eliminating gross errors through w-test and reducing the weight of gross errors through M-estimation, thereby achieving quality control of satellite pseudo-range observations received by satellite receivers in an urban environment, thereby ensuring that users obtain reliable positioning quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flowchart of a positioning method for M estimation GNSS quality control based on w-test according to an embodiment of the present invention. DETAILED DESCRIPTION

[0014] It should be noted that, in the absence of conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The present invention is further described in detail below in conjunction with the drawings and specific embodiments.

[0015] In the embodiments of the present invention, if there are directional indications (such as up, down, left, right, front, back, etc.), they are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0016] In addition, in the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features.

[0017] Please refer to Figure 1 The positioning method of M estimation GNSS quality control based on w-test in the embodiment of the present invention comprises steps 1 to 4.

[0018] Step 1: Collect GNSS observation data and determine whether the current number of observations meets the requirements for the w test. If yes, proceed to step 2, otherwise proceed to step 4. When the redundancy of the current observation is greater than 1, the w test is satisfied.

[0019] Step 2: Perform gross error detection on the GNSS observation data based on the w test. If the w test passes, proceed to step 4; if the w test fails, proceed to step 3.

[0020] The w test method is as follows: linearize the GNSS measurement model. That is, the expression is

[0021] (1)

[0022] in, is the difference between the observed pseudorange and the predicted pseudorange, is the observation matrix, It is the correction number of the user position (positioning solution) and receiver clock error, is the error vector. Thus The weighted least squares solution of is:

[0023] (2)

[0024] in, is the weighting matrix in the w test, that is , for The weighted least squares solution of represents the transpose of the observation matrix H; get After that, the final residual vector can be obtained :

[0025] (3)

[0026] in, is the unit matrix of the corresponding dimension, S is ;

[0027] Get the residual vector After that, the sum of squares of the residual vector SSE is used as the detection statistic for GNSS fault detection, which is defined as:

[0028] (4)

[0029] When detecting GNSS faults, a global test is first performed. That is, when it is assumed that none of the observed satellites have faults and the observation error follows a Gaussian distribution, the test statistic should follow a degree of freedom of The chi-square distribution of is the total number of observed satellites, is the dimension of the desired state quantity. At this time, the detection statistic is compared with the global threshold. If it exceeds the threshold, it means that there is a faulty satellite among the observed satellites. The global threshold The expression is:

[0030] (5)

[0031] in, is the false alarm rate, which is determined according to the specific application scenario. When the global detection fails, local detection is performed, that is, the traditional w test method, and the residual corresponding to each satellite is normalized as a new detection statistic. The w test value of each satellite The specific expression is:

[0032] (6)

[0033] in is a unit vector whose ith element is 1. Assuming that the ith satellite is fault-free, the corresponding satellite observation noise is The variance of hour, Should follow a normal distribution . At this time, With local threshold Comparison is performed, and the corresponding satellite that exceeds the threshold is judged as a faulty satellite. The expression of the local threshold is:

[0034] (7)

[0035] Among them, N is a normal distribution, and the subscript ;

[0036] The w test only identifies one faulty star at a time. At the same time, in order to confirm whether there are any faulty satellites among the remaining satellites, all the remaining satellites after elimination are re-considered as a new set, and weighted least squares estimation is continued until all tests pass or the degree of freedom condition is no longer satisfied.

[0037] Step 3: Determine the maximum test quantity in the corresponding w test The maximum test quantity in M ​​estimation Are the satellite numbers corresponding to the two the same? If they are the same, remove the satellite observations from the full set of observations, regard the remaining satellites as a new full set, and return the new full set of satellite observations to step 2 for re-w test; until the w test passes or the observations are not enough for the w test, the positioning solution is output through M estimation.

[0038] If they are different, calculate the user position after deleting the satellite corresponding to the maximum test amount from the M estimate and the w test respectively (the w test and the M estimate are two different ways of calculating the test amount, so the maximum test amounts of the two may be different. When they are different, calculate the position after removing the maximum test amount in the w test and the position after removing the maximum test amount in the M estimate. For example, there are 10 stars now, the largest w test amount corresponds to the ninth star, and the largest M estimate test amount corresponds to the tenth star, then calculate the w test positioning solution of the first to eighth plus the tenth star and the M estimate positioning solution of the first to ninth stars), and then select the optimal solution position from the w test and the M estimate based on the error between the positions at the previous moment, and finally, based on the same or different satellite numbers, the satellite corresponding to the optimal solution position is regarded as the new full set calculation positioning solution, and the new full set satellite observation amount is returned to step 2 for re-w test. Until the w test passes or the observation amount is not enough for w test, the positioning solution is output through M estimation.

[0039] Step 4: Perform M estimation on the GNSS observation data and output the solution position after robust estimation, which is the corresponding positioning solution.

[0040] The M estimation method is as follows: M estimation suppresses the influence of gross errors on the positioning solution results by reducing the weight of GNSS pseudo-range observations containing gross errors in the solution process, thereby achieving positioning quality control. M estimation based on maximum likelihood estimation theory is a commonly used robust estimator. It is essentially a weighted least squares estimation. Different weights are assigned to each observation information according to the standardized residual. Its objective function It can be expressed as

[0041] (8)

[0042] In the formula, For the The pseudorange residuals corresponding to the satellites, is the median absolute deviation of all satellite pseudorange residuals, which is expressed as:

[0043] (9)

[0044] represents the median; the M estimated test quantity of each satellite is recorded Then the corresponding weighted matrix is ​​obtained by the corresponding weighted method , that is, by designing a suitable weight function To suppress the influence of abnormal observations, the present invention adopts the Cauchy weight function:

[0045] (10)

[0046] is the weight matrix P used in the M estimation. The value of corresponds to the value calculated by the weight function.

[0047] Finally, according to the weighted matrix , calculate the weighted least squares estimation result in the M estimation iteration:

[0048] (11)

[0049] Among them, k represents the kth time, T represents the matrix transpose, This is the solution corresponding to the M estimate;

[0050] if If it is greater than the threshold value, After correcting the corresponding state quantities, recalculate the corresponding , , , until it is less than the threshold value, the iteration stops and the corresponding robust estimation result is output.

[0051] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A positioning method for GNSS quality control based on M estimation of w-test, characterized in that: include: Step 1: Collect GNSS observation data and determine whether the current number of observations meets the requirements for w-test. If yes, proceed to step 2, otherwise proceed to step 4; Step 2: Perform gross error detection on GNSS observation data based on the w test. If the w test passes, proceed to step 4; if the w test fails, proceed to step 3. Step 3: Determine whether the satellite numbers corresponding to the maximum test quantity in the w test and the maximum test quantity in the M estimate are the same. If they are the same, remove the satellite observations from the full set of observations, regard the remaining satellites as a new full set, and return the new full set of satellite observations to step 2 for re-w test; If they are different, calculate the user position after deleting the satellite corresponding to the maximum test amount from the M estimate and the w test respectively, and then select the optimal solution position from the w test and the M estimate according to the error between the position and the previous moment. Finally, the satellite corresponding to the optimal solution position is regarded as the new full set calculation positioning solution, and the new full set satellite observation quantity is returned to step 2 to re-perform the w test; Step 4: Perform M estimation on the GNSS observation data and output the corresponding positioning solution; In step 2, the w test is performed according to the following method: Linearize the GNSS measurement model, and the expression is: ； in, is the difference between the observed pseudorange and the predicted pseudorange, is the observation matrix, is the correction number of the user position and the receiver clock error state, is the error vector; The weighted least squares solution of is: ； in, is the weighting matrix, that is , for The weighted least squares solution of represents the transpose of the observation matrix H; get After that, we get the final residual vector : ； in, ; Get the residual vector After that, the sum of squares of the residual vector is used as the detection statistic for GNSS fault detection, which is defined as: ； Among them, SSE is the sum of squares of residual vectors. When detecting GNSS faults, global detection is performed first. That is, when it is assumed that none of the observed satellites have faults and the observation error obeys Gaussian distribution, the detection statistic should obey the degree of freedom of The chi-square distribution of is the total number of observed satellites, is the dimension of the desired state quantity; at this time, the detection statistic is compared with the global threshold. If it exceeds the threshold, it means that there is a faulty satellite among the observed satellites, where the global threshold expression is: ； in, is the global threshold, is the false alarm rate, which is determined according to the specific application scenario. When the global detection fails, local detection is performed, and the residual corresponding to each satellite is normalized as a new detection statistic. The specific expression is: ； in, is the w test quantity, is a unit vector with the ith element being 1. Assuming that the ith satellite is fault-free, the corresponding satellite observation noise is The variance of hour, Should follow a normal distribution , at this time will With local threshold For comparison, the corresponding satellite exceeding the threshold is judged as a faulty satellite, where the expression of the local threshold is: ； Where N is a normal distribution, the subscript ; The w test only identifies one faulty star at a time. The corresponding satellite is removed; at the same time, in order to confirm whether there are any faulty satellites among the remaining satellites, all the remaining satellites after the removal are re-considered as a new full set, and the weighted least squares estimation is continued until all tests pass or the degree of freedom condition is no longer met; In step 4, M is estimated according to the following method: Different weights are assigned to each observation information according to the standardized residual, and its objective function It can be expressed as: ； In the formula, For the The pseudorange residuals corresponding to the satellites, is the median absolute deviation of all satellite pseudorange residuals, which is expressed as: ； Denote M as the estimated test quantity Then the corresponding weighted matrix P is obtained by different weighting methods, that is, by the preset weight function To suppress the influence of abnormal observations; Finally, according to the weighted matrix , calculate the weighted least squares estimation result in the M estimation iteration: ； if If it is greater than the threshold value, After correcting the corresponding state quantities, recalculate the corresponding , , , until it is less than the threshold value, the iteration stops and the corresponding robust estimation result is output.

2. The positioning method for GNSS quality control based on w-test M estimation as claimed in claim 1, characterized in that: Preset weight function is the Cauchy weight function: ； in, is the (i,i)th value in the weighting matrix P used in the M estimate.

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