Satellite single point positioning method based on partial cycle slip fixing

Abstract

The application provides a satellite single point positioning method based on partial cycle slip fixing, and belongs to the technical field of GNSS precise navigation and positioning, and comprises the following steps: a receiver performs the following steps: judging whether a cycle slip exists in an observed satellite according to received original observation data of the observed satellite; if the cycle slip exists, then: all satellites with the cycle slip are jointly formed into a cycle slip full subset, and the observed satellites in the cycle slip full subset are subjected to cycle slip fixing; the cycle slip full subset after the cycle slip fixing is subjected to inspection, if the cycle slip fixing fails, then the precision factor and the three-dimensional position precision factor PDOP of each subset in the cycle slip full subset are calculated, the subset with the values of the precision factor and the PDOP greater than a threshold value is screened out as a cycle slip subset, and position solving is performed by using the original observation data in the cycle slip subset. The method can screen out a partial cycle slip subset with the optimal precision for precise single point positioning under the condition that the dimension of the partial subset is certain, and further improves the continuity of the high-precision positioning result of the precise single point positioning.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of GNSS precise navigation and positioning, and particularly relates to a satellite single-point positioning method based on partial cycle slip fixing. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) high-precision positioning is largely dependent on high-precision carrier phase observations, and requires high-precision solution of integer ambiguity. When the receiver continuously tracks satellite signals, the integer ambiguity will remain unchanged during continuous signal tracking. However, when the satellite is blocked, the satellite signal quality is poor, or the carrier is highly dynamic, the receiver will lose the lock of the satellite signal, so that the integer ambiguity in the carrier phase observation changes, that is, the cycle slip occurs when the satellite signal is re-locked. Especially in low-cost application scenarios or complex environments, cycle slips occur more frequently. Cycle slip must be effectively handled, otherwise it will have an irreversible impact on high-precision positioning, resulting in the inability to perform high-precision positioning.

[0003] Multiple satellite cycle slips will cause a long re-convergence process for precise point positioning, and the positioning accuracy is low. Cycle slip fixing and repairing can effectively avoid the long re-convergence process, thereby maintaining continuous high-precision positioning.

[0004] From the number of cycle slip fixing, cycle slip fixing can be divided into full subset fixing and partial subset fixing. Compared with partial cycle slip fixing, full subset cycle slip fixing has high dimension, relatively difficult fixing, and low fixing reliability, making it more difficult to effectively fix.

[0005] However, in the prior art, a cycle slip subset screening method using elevation angle subset screening is used. However, this screening method only considers the adverse effect of low elevation angle on cycle slip fixing. The geometric configuration of the partial subset fixed by the screening method may be poor, and the gain of positioning after cycle slip repair may also be small. SUMMARY

[0006] In order to overcome the deficiencies of the prior art, the application provides a satellite single-point positioning method based on partial cycle slip fixing.

[0007] In order to achieve the above purpose, the application provides the following technical scheme:

[0008] A satellite single-point positioning method based on partial cycle slip fixing, characterized in that the receiver performs the following steps:

[0009] According to the received original observation data of the observed satellite, it is judged whether the observed satellite has cycle slip;

[0010] If there is cycle slip, then:

[0011] all satellites with cycle slips are combined to form a cycle slip full subset, and the observation satellites in the cycle slip full subset are fixed for cycle slips;

[0012] The cycle slip full subset after cycle slip fixing is tested, if cycle slip fixing fails, the precision factor and three-dimensional position precision factor PDOP of each subset in the cycle slip full subset are calculated, and the subset with the values of the precision factor and PDOP greater than the threshold value is selected as a cycle slip subset, and the original observation data in the cycle slip subset is used for position solution.

[0013] Further, the expression for judging whether the observation satellites have cycle slips is:

[0014]

[0015] where ΔHMW and ΔGF represent the epoch difference values of the HMW combination and the GF combination respectively, b HMW and b GF respectively represent the threshold values of the HMW combination and the GF combination for detecting cycle slips; and when one of the inequalities is satisfied, it is considered that there is a cycle slip.

[0016] Further, the formula for testing the cycle slip full subset after cycle slip fixing is:

[0017]

[0018] wherein, and respectively represent the optimal solution and the suboptimal solution of cycle slip fixing, μ represents the test threshold value of the fixed solution test; and when the inequality is satisfied, the test is passed, otherwise the test is failed.

[0019] Further, the expression for calculating the precision factor and the three-dimensional position precision factor PDOP of each subset in the cycle slip full subset is:

[0020]

[0021] wherein, p represents the precision factor, Q x,y,z represents the covariance matrix of the three-dimensional position state quantity, which can be obtained according to the state covariance matrix of Kalman filtering, det(·) represents the determinant operation, PDOP represents the three-dimensional position precision factor, h 11 , h 22 and h 33 respectively represent the first three diagonal elements of the observation equation coefficient matrix H k .

[0022] Further, the cycle slip subset is:

[0023]

[0024] In the formula, S represents a set of subsets satisfying the screening condition, s ns (i) represents the i-th subset, p(i) and p th respectively represent the i-th precision factor and the precision factor screening threshold, PDOP(i) and PDOP th respectively represent the i-th DOP value and the DOP value screening threshold, ns represents the current subset dimension, and N represents the full subset dimension, represents the number of combinations, that is, a total of partial subsets.

[0025] Further, the position solution is performed by using the original observation data in the cycle slip subset; the position solution comprises the following steps.

[0026] The cycle slip floating point solution of the cycle slip subset and the covariance matrix thereof are calculated.

[0027] The observation satellites in the cycle slip subset are fixed for cycle slip by using the cycle slip floating point solution and the covariance matrix thereof.

[0028] According to the cycle slip fixing result, the observation satellites are repaired for cycle slip.

[0029] The position solution is performed according to the carrier phase observation of the signal sent by the observation satellites repaired for cycle slip.

[0030] Further, the cycle slip floating point solution of the cycle slip subset and the covariance matrix thereof are calculated; the expression is as follows:

[0031]

[0032]

[0033] In the formula, and respectively represent the cycle slip floating point solution estimate and the covariance matrix thereof, A represents a geometry matrix of cycle slip detection, and y k and R k respectively represent the inter-epoch difference measurement and the covariance matrix thereof.

[0034] Further, the observation satellites in the cycle slip subset are fixed for cycle slip by using the cycle slip floating point solution and the covariance matrix thereof; the fixing for cycle slip comprises the following steps.

[0035] According to the cycle slip floating point solution and the covariance matrix thereof, a fixed solution is obtained by combining the LAMBDA algorithm search:

[0036]

[0037] In the formula, a represents the LAMBDA search, which is based on the cycle slip floating point solution and the covariance matrix thereof Mapping out the cycle slip fixing optimal solution And suboptimal solution

[0038] Further, the cycle slip fixing result is used to repair the cycle slip of the observed satellite, and the expression is as follows:

[0039]

[0040] In the formula, s represents a satellite, i represents a frequency number, And phi i s (k) respectively represent the carrier phase observation after and before repair, and the unit is cycle, Indicates the cycle slip fixing solution.

[0041] Further, the original observation data of the observed satellite is received, and whether the observed satellite has a cycle slip is judged; if the observed satellite does not have a cycle slip, the position is solved according to the original observation data; comprising:

[0042]

[0043] In the formula, k and k-1 represent the epoch number, And P k,k-1 Respectively represent the state one-step prediction value and the covariance matrix thereof, Phi k,k-1 Indicates the one-step transition matrix of the system state from the k-1 epoch to the k epoch, And P k Respectively represent the filtered estimation value of the state and the covariance matrix thereof, Gamma k-1 Indicates the system noise driving matrix, Q k-1 And R k Respectively represent the variance matrix of the system noise and the variance matrix of the measurement noise, K k Is the gain matrix, H k Indicates the coefficient matrix of the observation equation, L k Indicates the observation vector of the k epoch, and I indicates the unit matrix.

[0044] The satellite single point positioning method based on partial cycle slip fixing provided by the application has the following beneficial effects:

[0045] The application evaluates the geometric configuration of different cycle slip subsets by using the PDOP value, screens the cycle slip subsets in combination with the accuracy factor and the DOP value, can effectively select the best cycle slip subset for maintaining the precision of the precise single point positioning, thereby realizes the rapid re-convergence of the precise single point positioning, and provides continuous high-precision positioning results. The problems that the geometric configuration of the screened and fixed partial subset may be poor and the positioning precision after cycle slip repair is insufficient in the prior art are solved. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present application and the design scheme thereof, the drawings required by the present embodiments will be briefly introduced as follows. The drawings in the following description are only partial embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0047] Figure 1 FIG. 1 is a schematic diagram of a satellite single point positioning method based on partial cycle slip fixing according to the present application. DETAILED DESCRIPTION

[0048] In order to make those skilled in the art better understand the technical scheme of the present application and can be implemented, the present application will be described in detail below in combination with the drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical scheme of the present application, and cannot be used to limit the protection scope of the present application.

[0049] Embodiment:

[0050] The present application provides a satellite single point positioning method based on partial cycle slip fixing, specifically as shown in the following steps: Figure 1

[0051] Step 1: Based on k ephemeris measurement information, Kalman filtering is used to estimate the carrier position and other information to obtain the current state and its covariance matrix, and the solving process equation is represented as:

[0052]

[0053] In the above formula, k and k-1 represent ephemeris number, and P k,k-1 respectively represent the state one-step prediction value and its covariance matrix, Φ k,k-1 represents a one-step transition matrix of the system state from k-1 ephemeris to k ephemeris, and P k respectively represent the filtered estimation value of the state and its covariance matrix, Γ k-1 represents the system noise driving matrix, Q k-1 and R k respectively represent the variance matrix of the system noise and the variance matrix of the measurement noise, K k is the gain matrix, H k represents the coefficient matrix of the observation equation, L k represents the observation vector of k ephemeris, and I represents the unit matrix.

[0054] Step 2: Obtain the original observation data of k+1 ephemeris, which is prepared for the subsequent related steps;

[0055] ​Step 3: The cycle slip detection of the observed satellite at the current epoch is performed, and the expression of the detection is as follows:

[0056]

[0057] Where, ΔHMW and ΔGF represent the inter-epoch difference values of the HMW combination and the GF combination respectively, b HMW and b GF represent the threshold values of the HMW combination and the GF combination for detecting the cycle slip, and in the above formula, if one of the inequalities is satisfied, it is considered that there is a cycle slip.

[0058] It is detected whether there is a cycle slip, if there is no cycle slip, the positioning solution of the current epoch is continued, otherwise the steps related to the cycle slip fixing are performed; if it is detected that there is a cycle slip, the steps related to the cycle slip fixing are performed.

[0059] Step 4: If it is detected that there is a cycle slip, the full-subset fixing of the cycle slip is firstly performed to obtain the full-subset cycle slip fixing result.

[0060] Step 5: According to the full-subset fixing result of the cycle slip, the full-subset fixing result is tested, and the specific formula for the testing is as follows:

[0061]

[0062] In the above formula, and represent the optimal solution and the suboptimal solution of the cycle slip fixing respectively, μ represents the testing threshold value of the fixing solution, if the above inequality is satisfied, the testing is passed, otherwise the testing is failed.

[0063] Step 6: If the full-subset fixing of the cycle slip fails, the partial-subset fixing is performed, firstly the dimension of the partial subset is determined, and different partial subsets are selected by combining the observed satellites, then the precision factor and the DOP value of each partial subset combination are calculated according to the state and the covariance matrix, and then all the subsets are sorted according to the precision factor and the DOP value, and the combination with smaller precision factor and DOP value is fixed preferentially.

[0064] The precision factor and the DOP value are calculated as two evaluation indexes for a cycle slip subset, and the calculation expression is as follows:

[0065]

[0066]

[0067] In the above formula, p represents the precision factor, Q x,y,z represents the covariance matrix of the three-dimensional position state quantity, which can be obtained according to the state covariance matrix of the Kalman filter, det(·) represents the determinant operation, and PDOP represents the calculated DOP value, h11 , h 22 , and h 33 represent the first three diagonal elements of the observation equation coefficient matrix H k , respectively.

[0068] According to the precision factors and DOP values calculated by different subsets, a subset set satisfying the requirements can be obtained, and the expression is as follows:

[0069]

[0070] In the above formula, S represents a set of subsets satisfying the screening condition, s ns (i) represents the i-th subset, p(i) and p th represent the i-th precision factor and the precision factor screening threshold, respectively, PDOP(i) and PDOP th represent the i-th DOP value and the DOP value screening threshold, respectively, ns represents the current subset dimension, N represents the full subset dimension, represents the number of combinations, i.e., there are partial subsets in total.

[0071] Step 7: Based on the epoch difference model, the least squares method is used to solve the cycle slip floating point solution of the i-th partial cycle slip subset and its covariance matrix, and the solving formula is as follows:

[0072]

[0073] In the above formula, and represent the cycle slip floating point solution estimate and its covariance matrix, respectively, A represents the geometry matrix of cycle slip detection, y k and R k represent the epoch difference measurement value and its covariance matrix, respectively.

[0074] Step 8: Cycle slip fixing, according to the cycle slip floating point solution and its covariance matrix, combined with the LAMBDA algorithm search to obtain the fixed solution:

[0075]

[0076] In the above formula, a represents the LAMBDA search, which maps the cycle slip fixed optimal solution and the suboptimal solution according to the cycle slip floating point solution and its covariance matrix

[0077] Step 9: Test the partial cycle slip subset fixing result, the specific test method is the same as the cycle slip full subset fixing test method in step 5, only the fixed result is replaced by the partial cycle slip subset fixed result;

[0078] Step 10: judging whether the partial cycle slip subset of the current dimension is solved, and judging whether the current partial subset dimension is the minimum;

[0079] Step 11: according to the cycle slip fixing result passed through the test, repairing the carrier phase observation, and the expression is as follows:

[0080]

[0081] In the above formula, s represents a satellite, i represents a frequency number, And φ i s (k) respectively represent the carrier phase observation after and before repairing, the unit is cycle, ΔN i s (k) represents the cycle slip fixing solution.

[0082] Step 12: completing the current epoch precise point positioning, and estimating the state and covariance matrix based on Kalman filtering, and the specific calculation method and formula are consistent with step 1.

[0083] The application proposes a partial subset selection method based on the positioning accuracy and the geometric distribution of the partial cycle slip subset in the state domain, which can screen the partial cycle slip subset that maintains the optimal positioning accuracy under the condition of a certain subset dimension, so as to effectively realize the rapid re-convergence of precise point positioning.

[0084] The partial subset selection method based on the positioning accuracy and the geometric distribution of the partial cycle slip subset in the state domain can screen the partial cycle slip subset that contributes most to the positioning accuracy under the condition of a certain subset dimension, and then maintain the positioning accuracy reached before the cycle slip occurs to the greatest extent through cycle slip fixing and cycle slip repairing, so as to improve the continuity of high-precision positioning, and has important value and significance for related fields that need high-precision positioning.

[0085] The above-described embodiments are only the preferred specific implementation of the application, the protection scope of the application is not limited thereto, any person skilled in the art can obtain the simple changes or equivalent replacements of the technical solutions within the technical range disclosed by the application, and all of them belong to the protection scope of the application.

Claims

1. A satellite single point positioning method based on partial cycle slip fixing, characterized in that, The receiver performs the following steps: According to the received original observation data of the observation satellite, it is judged whether the observation satellite has cycle slip or not; If there is cycle slip, then: All satellites with cycle slip are collectively formed into a cycle slip full subset, and the observation satellites in the cycle slip full subset are fixed for cycle slip; The cycle slip full subset after cycle slip fixing is tested, if cycle slip fixing fails, the precision factor and three-dimensional position precision factor PDOP of each subset in the cycle slip full subset are calculated, and the subset with the values of the precision factor and PDOP greater than the threshold value is selected as the cycle slip subset, and the original observation data in the cycle slip subset is used for position solution; The expression for judging whether the observation satellite has cycle slip or not is: wherein, and denote the inter-epoch difference values for the HMW combination and the GF combination, respectively, and denote the threshold values for the detection of cycle slips for the HMW combination and the GF combination, respectively; and a cycle slip is considered to exist when one of the inequalities is satisfied.

2. The partial cycle slip fixing based satellite single point positioning method according to claim 1, characterized in that, The formula for testing the cycle slip full subset after cycle slip fixing is: wherein and denote the optimal and suboptimal solution of cycle slip fixing, respectively, denotes the test threshold of the fixing solution test; and the test is passed when the inequality is satisfied, otherwise the test is failed.

3. The partial cycle slip fixing based satellite single point positioning method according to claim 1, characterized in that, The expression for calculating the precision factor and three-dimensional position precision factor PDOP of each subset in the cycle slip full subset is: wherein denotes the precision factor, denotes the covariance matrix of the three-dimensional position state quantity, which can be derived from the state covariance matrix of the Kalman filter, denotes the determinant operation, denotes the three-dimensional position precision factor, , and denote the first three diagonal elements of the coefficient matrix of the observation equation, respectively.

4. The partial cycle slip fixing based satellite single point positioning method according to claim 1, characterized in that, The cycle slip subset is: wherein, represents a set of subsets satisfying a filtering condition, represents the subset, and respectively represent the precision factor and the precision factor filtering threshold, and respectively represent the DOP value and the DOP value filtering threshold, represents the current subset dimension, represents the full subset dimension, represents the combination number, i.e., there are partial subsets in total.

5. The partial cycle slip fixing based single satellite positioning method according to claim 1, wherein, The original observation data in the cycle slip subset is used for position solution, which includes: The cycle slip float solution of the cycle slip subset and its covariance matrix are calculated; The observation satellites in the cycle slip subset are fixed for cycle slip by using the cycle slip float solution and its covariance matrix; According to the cycle slip fixing result, the observation satellites are repaired for cycle slip; The carrier phase observation of the signal sent by the observation satellite after cycle slip repair is used for position solution.

6. The partial cycle slip fixing based satellite single point positioning method according to claim 5, characterized in that, The expression for calculating the cycle slip float solution of the cycle slip subset and its covariance matrix is: wherein and denote the cycle slip float solution estimate and its covariance matrix, respectively, and denote the inter-epoch differential measurements and its covariance matrix, respectively, denotes the geometry matrix of cycle slip detection, which is responsible for converting the geometric position relationship between the satellite and the receiver into the coefficients of the linear equation system.

7. The partial cycle slip fixing based satellite single point positioning method according to claim 6, characterized in that, The observation satellites in the cycle slip subset are fixed for cycle slip by using the cycle slip float solution and its covariance matrix, which includes: According to the cycle slip float solution and its covariance matrix, the fixed solution is searched by combining the LAMBDA algorithm: wherein denotes the LAMBDA search, which is based on the cycle slip float solution and its covariance matrix maps out the cycle slip fixed optimal solution and the suboptimal solution .

8. The partial cycle slip fixing based satellite single point positioning method according to claim 7, characterized in that, The expression for repairing the observation satellites for cycle slip according to the cycle slip fixing result is: In the formula, represents a satellite, represents a frequency number, k represents an observation time sequence number in a satellite positioning process, and is used to distinguish observation data at different time points, and respectively represent carrier phase observations after and before repair, and the unit is cycle, represents a cycle slip fixed solution.

9. The partial cycle slip fixing based satellite single point positioning method according to claim 1, characterized in that, After judging whether the observation satellite has cycle slip or not according to the received original observation data of the observation satellite; If the observation satellite has no cycle slip, then the position solution is performed according to the original observation data; It includes: wherein , denotes the epoch number, and denote the state one-step prediction and its covariance matrix, respectively, denotes the one-step transition matrix of the system state from epoch epoch, and denote the filtered estimate of the state and its covariance matrix, respectively, denotes the system noise driving matrix, and denote the variance matrix of the system noise and the variance matrix of the measurement noise, respectively, is the gain matrix, denotes the coefficient matrix of the observation equation, denotes the observation vector at epoch denotes the identity matrix.

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