A method to improve the accuracy of GNSS carrier positioning fixed solution

Abstract

The present invention discloses a method for improving the accuracy of GNSS carrier positioning fixed solutions, comprising: obtaining an ambiguity real number solution #imgabs0# and a corresponding variance matrix #imgabs1#, a coordinate real number solution #imgabs2# and a corresponding variance matrix #imgabs3#, #imgabs4# and #imgabs5#, a covariance matrix #imgabs6#, and a mapping matrix K from observation values ​​to ambiguity and positioning solution parameters. a and K b ; Based on the real ambiguity solution #imgabs7# and its variance matrix #imgabs8#, the LAMBDA algorithm is used to obtain the optimal candidate solution and the suboptimal candidate solution; a ratio test is performed on whether the optimal candidate solution is the true ambiguity value; an ambiguity residual constraint is established, and the systematic deviation of the real ambiguity solution is estimated #imgabs9# and the systematic deviation in the coordinate real solution is calculated #imgabs10# The original fixed solution #imgabs13# is corrected by #imgabs11# and #imgabs12# to obtain the corrected fixed solution #imgabs14# and its variance is calculated #imgabs15# This method can improve the positioning accuracy of the coordinate fixed solution and further expand the application of GNSS high-precision positioning technology.

Description

Technical Field

[0001] The present invention relates to the field of satellite positioning technology, and in particular to a method for improving the accuracy of a GNSS carrier positioning fixed solution. Background Art

[0002] The carrier wave is an essential measurement for achieving precise GNSS positioning. However, receivers can only measure fractions of a full revolution. To equal the distance between the satellite and the ground, the carrier wave must be added to an unknown integer multiple of the carrier wavelength. This unknown integer is called the ambiguity. Therefore, correctly resolving this ambiguity is a prerequisite for achieving precise GNSS carrier wave positioning.

[0003] Currently, the steps for resolving integer ambiguities can be divided into three main steps: (1) Ignoring the integer nature of the ambiguity, the least squares estimation is used in the real domain to obtain the real solution of the ambiguity and other unknowns, also known as the floating-point solution; (2) Based on the real solution of the ambiguity and the variance matrix, an integer vector is found as a candidate integer solution for the ambiguity; (3) The candidate integer solution is verified. If it passes the verification, the ambiguity is fixed and the integer solution of the ambiguity is used to obtain the fixed solution of other parameters; otherwise, the real solution is maintained.

[0004] If ambiguities can be fixed, it is generally believed that the accuracy of the fixed solution for positioning parameters is significantly improved compared to the real solution. However, even if ambiguities can be fixed, the fixed solution still contains the influence of unmodeled errors, that is, systematic bias. To date, few studies have addressed the systematic bias in the fixed solution to further improve its accuracy.

[0005] With the popularization of satellite positioning technology, a method to improve the accuracy of GNSS carrier positioning fixed solution is needed to achieve high-precision and high-reliability satellite positioning. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for improving the accuracy of GNSS carrier positioning fixed solutions, which can achieve high-precision and high-reliability positioning using satellite positioning technology.

[0007] To achieve the above functions, the present invention designs a method for improving the accuracy of a GNSS carrier positioning fixed solution. The following steps S1 to S6 are performed to correct the systematic deviation in the fixed solution and improve the positioning accuracy of the fixed solution:

[0008] Step S1: Based on the data from the GNSS observation station, collect the GNSS carrier positioning equation and obtain the ambiguity real number solution from the GNSS carrier positioning equation and its variance matrix Coordinate real number solution and its variance matrix Real number solution to ambiguity and coordinate real number solutions The covariance matrix of And the mapping matrix K from observations to ambiguity and positioning solutions a and K b ;

[0009] Step S2: Real number solution based on ambiguity and its variance matrix Use the LAMBDA algorithm to obtain the optimal candidate solution and the suboptimal candidate solution;

[0010] Step S3: Use the Ratio test to test whether the optimal candidate solution is the ambiguity true value. If it passes the test, the optimal candidate solution is considered to be the ambiguity true value. And solve it according to the coordinate real number Calculate the fixed solution and its variance matrix

[0011] Step S4: Establish the observation equation of the ambiguity residual constraint, establish the state equation of the ambiguity real number solution system deviation, and form the Kalman filter equation. Based on the Kalman filter equation, estimate the ambiguity real number solution system deviation estimate

[0012] Step S5: Solve the system bias estimate based on the ambiguity real number Compute systematic deviations in real solutions of coordinates

[0013] Using ambiguity real number to solve system deviation estimation And the mapping matrix K obtained in step S1 a , estimate the unmodeled error: use the unmodeled error estimate And the mapping matrix K obtained in step S1 b , calculate the coordinate real number solution system deviation:

[0014] Step S6: Solve the system bias estimate based on the ambiguity real number Systematic deviations in the real solutions of the sum coordinates The original fixed solution Make corrections and get the corrected fixed solution And calculate its variance matrix

[0015] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0016] The present invention designs a method for improving the accuracy of GNSS carrier positioning fixed solutions. Focusing on the coordinate fixed solution, the present invention aims to improve the positioning accuracy of the fixed solution by establishing corresponding solution steps through the use of ambiguity real number solution residual constraints and targeting the systematic deviation therein.

[0017] The beneficial effect of this method is that it can further improve the positioning accuracy of the fixed solution and further expand the application scenarios of GNSS carrier precise positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The present invention provides a flowchart of a method for improving the accuracy of a GNSS carrier positioning fixed solution. DETAILED DESCRIPTION

[0019] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0020] The embodiment of the present invention provides a method for improving the accuracy of GNSS carrier positioning fixed solution, referring to Figure 1 , perform the following steps S1-S6 to correct the systematic deviation in the fixed solution and improve the positioning accuracy of the fixed solution:

[0021] Step S1: Based on the data from the GNSS observation station, collect the GNSS carrier positioning equation and obtain the ambiguity real number solution from the GNSS carrier positioning equation and its variance matrix Coordinate real number solution and its variance matrix Real number solution to ambiguity and coordinate real number solutions The covariance matrix of And the mapping matrix K from observations to ambiguity and positioning solutions a and K b ;

[0022] Step S2: Real number solution based on ambiguity and its variance matrix Use the LAMBDA algorithm to obtain the optimal candidate solution and the suboptimal candidate solution;

[0023] Step S3: Use the Ratio test to test whether the optimal candidate solution is the ambiguity true value. If it passes the test, the optimal candidate solution is considered to be the ambiguity true value. And solve it according to the coordinate real number Calculate the fixed solution and its variance matrix

[0024] The specific steps of step S3 are as follows:

[0025] Step S3.1: Set the Ratio test threshold Ratio * ;

[0026] Step S3.2: Calculate the Ratio test value according to the following formula:

[0027]

[0028] Where Ratio represents the Ratio test value, N is the optimal candidate solution, and N1 is the suboptimal candidate solution; if Ratio>Ratio * , then the optimal candidate solution N is considered to be the true value of the ambiguity

[0029] Step S3.3: According to the fuzzy truth value and coordinate real number solutions Calculate fixed solution and its variance matrix As follows:

[0030]

[0031] Where, is the real number solution of the ambiguity The variance matrix of is the coordinate real number solution The variance matrix of is the real number solution of the ambiguity and coordinate real number solutions The covariance matrix of .

[0032] Step S4: Establish the observation equation of the ambiguity residual constraint, establish the state equation of the ambiguity real number solution system deviation, and form the Kalman filter equation. Based on the Kalman filter equation, estimate the ambiguity real number solution system deviation estimate

[0033] The specific steps of step S4 are as follows:

[0034] Step S4.1: Real number solution based on ambiguity and its variance matrix The true value of the fuzzy degree passed the Ratio test As well as the dimension n of the ambiguity vector, the observation equation of the ambiguity residual constraint is established:

[0035]

[0036] In the above formula (4), δa represents the system deviation of the real-number solution of the ambiguity to be estimated;

[0037] Step S4.2: Establish the state equation of the fuzzy real number solution system deviation:

[0038] δa k =δa k-1 +η k , ηk ~N(0,Q k ) (5)

[0039] In the above formula (5), k and k-1 represent the current epoch and the previous epoch respectively, δa k represents the real number solution deviation of the ambiguity at the kth epoch, η k represents process noise, Q k represents the process noise η k The variance matrix, Q k As follows:

[0040]

[0041] Where cycle represents the unit of ambiguity (week);

[0042] Step S4.3: Based on equations (5) and (6), the Kalman filter equation is as follows:

[0043]

[0044] Where, represents the observation vector, whose variance matrix is ​​set to D L =2n; represents the coefficient matrix; ε k and η k represent observation noise and process noise respectively;

[0045] Step S4.4: Solve the Kalman filter equation shown in equation (6) as follows to obtain an estimate of the system deviation of the ambiguity real solution:

[0046]

[0047] Where, and They represent the predicted value of the system deviation of the real-number solution of the ambiguity at the current epoch and its variance matrix, I represents the identity matrix, and Represent the ambiguity real number solution system deviation estimate and its variance matrix corresponding to the previous epoch; if it is the initial epoch, the value is K k is the gain matrix in the calculation process; is the estimate of the systematic bias of the real-number solution to the ambiguity at the current epoch; for The variance matrix of .

[0048] Step S5: Solve the system bias estimate based on the ambiguity real number Compute systematic deviations in real solutions of coordinates

[0049] The specific steps of step S5 are as follows:

[0050] Step S5.1: Use the ambiguity real number to solve the system bias estimate And the mapping matrix K obtained in step S1 a , estimate the unmodeled error:

[0051]

[0052] In formula (9), is the unmodeled error estimate, is the system deviation estimate of the ambiguity real number solution obtained by equation (8) is its variance matrix;

[0053] Step S5.2: Using the unmodeled error estimate And the mapping matrix K obtained in step S1 b , calculate the coordinate real number solution system deviation:

[0054]

[0055] Where, is the coordinate real number solution system deviation.

[0056] Step S6: Solve the system bias estimate based on the ambiguity real number Systematic deviations in the real solutions of the sum coordinates The original fixed solution Make corrections and get the corrected fixed solution And calculate its variance matrix

[0057] The specific steps of step S6 are as follows:

[0058] Step S6.1: According to the original fixed solution Ambiguity real number solution system deviation estimation and the systematic deviation of the coordinate real number solution Calculate the corrected fixed solution for:

[0059]

[0060] In formula (11), is the real number solution of the ambiguity The variance matrix of is the coordinate real number solution and the real number solution of ambiguity The covariance matrix of

[0061] Step S6.2: Calculate the corrected fixed solution according to the following formula The variance matrix of :

[0062]

[0063] Where, The fixed solution after correction The variance matrix of .

[0064] The following is an application embodiment of the present invention:

[0065] The data for this example comes from two consecutive observation stations approximately 103 kilometers apart. The observation instruments used at both stations are Trimble R9 receivers equipped with choke antennas. The observation epoch interval is set to 1 second, with a cutoff elevation angle of 10 degrees. The specific implementation process of the present invention is further illustrated using data from the 3500th epoch:

[0066] Step S1: Obtain the real number solution of the ambiguity from the carrier positioning equation and its variance matrix Coordinate real number solution and its variance matrix and The covariance matrix of And the mapping matrix K a and K b :

[0067]

[0068]

[0069] Step S2: Based on the ambiguity real number solution and its variance matrix, the LAMBDA algorithm is used to obtain the optimal candidate solution and the suboptimal candidate solution:

[0070] Optimal candidate solution: N = (-42 -5 -89 145 -58 -68 -64 -82 177 -7) T

[0071] Second-best candidate solution: N1 = (-40 -5 -91 143 -59 -66 -64 -84 175 -8) T

[0072] Step S3: Use the Ratio test to confirm whether the optimal candidate solution is the ambiguity true value; if it passes the test, the optimal candidate solution is considered to be the ambiguity true value, and the real number solution is Correction to obtain a fixed solution and its variance matrix

[0073] According to the failure rate of 0.005 and the fuzziness dimension of 10, the Ratio test threshold is 1 / 0.68;

[0074]

[0075] Therefore, the optimal candidate solution is considered to be the true value of the ambiguity, that is,

[0076] Depend on and coordinate real number solutions Calculate fixed solution And its variance matrix is:

[0077]

[0078] Step S4: Establish the residual constraint of the ambiguity real number solution and estimate the ambiguity real number solution system deviation:

[0079] The Kalman filter equation for estimating the ambiguity real solution deviation is shown in equation (7), where:

[0080] L k =-158.851

[0081]

[0082] According to formula (8), the ambiguity real number solution system deviation estimation is obtained and its variance matrix

[0083] Step S5: Solve the system bias estimate based on the ambiguity real number Compute systematic deviations in real solutions of coordinates

[0084] First, the system deviation estimation is solved based on the ambiguity real number solution. and the mapping matrix K a The estimated unmodeled error is:

[0085]

[0086] Second, the unmodeled error estimate and the mapping matrix K b Compute systematic deviations in real solutions of coordinates

[0087] Step S6: and The original fixed solution Make corrections and get the corrected fixed solution And calculate its variance

[0088] First, according to the original fixed solution Ambiguity real number solution system deviation estimation and the systematic deviation of the coordinate real number solution Calculate the corrected fixed solution for:

[0089]

[0090] Secondly, the corrected fixed solution is calculated by formula (12): The variance matrix of :

[0091]

[0092] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A method for improving the accuracy of GNSS carrier positioning fixed solution, characterized in that: Perform the following steps S1 to S6 to correct the systematic deviation in the fixed solution and improve the positioning accuracy of the fixed solution: Step S1: Based on the data from the GNSS observation station, collect the GNSS carrier positioning equation and obtain the ambiguity real number solution from the GNSS carrier positioning equation and its variance matrix Coordinate real number solution and its variance matrix Real number solution to ambiguity and coordinate real number solutions The covariance matrix of And the mapping matrix K from observations to ambiguity and positioning solutions a and K b ; Step S2: Real number solution based on ambiguity and its variance matrix Use the LAMBDA algorithm to obtain the optimal candidate solution and the suboptimal candidate solution; Step S3: Use the Ratio test to test whether the optimal candidate solution is the ambiguity true value. If it passes the test, the optimal candidate solution is considered to be the ambiguity true value. And solve it according to the coordinate real number Calculate the fixed solution and its variance matrix Step S4: Establish the observation equation of the ambiguity residual constraint, establish the state equation of the ambiguity real number solution system deviation, and form the Kalman filter equation. Based on the Kalman filter equation, estimate the ambiguity real number solution system deviation estimate Step S5: Solve the system bias estimate based on the ambiguity real number Compute systematic deviations in real solutions of coordinates Using ambiguity real number to solve system deviation estimation And the mapping matrix K obtained in step S1 a , estimate the unmodeled error; use the unmodeled error to estimate And the mapping matrix K obtained in step S1 b , calculate the systematic deviation of the coordinate real number solution; Step S6: Solve the system bias estimate based on the ambiguity real number Systematic deviations in the real solutions of the sum coordinates The original fixed solution Make corrections and get the corrected fixed solution And calculate its variance matrix 2. A method for improving the accuracy of GNSS carrier positioning fixed solution according to claim 1, characterized in that: The specific steps of step S3 are as follows: Step S3.1: Set the Ratio test threshold Ratio * ; Step S3.2: Calculate the Ratio test value according to the following formula: Where Ratio represents the Ratio test value, N is the optimal candidate solution, and N1 is the suboptimal candidate solution; if Ratio>Ratio * , then the optimal candidate solution N is considered to be the true value of the ambiguity Step S3.3: According to the fuzzy truth value and coordinate real number solutions Calculate fixed solution and its variance matrix As follows: Where, is the real number solution of the ambiguity The variance matrix of is the coordinate real number solution The variance matrix of is the real number solution of the ambiguity and coordinate real number solutions The covariance matrix of .

3. The method for improving the accuracy of GNSS carrier positioning fixed solution according to claim 1, characterized in that: The specific steps of step S4 are as follows: Step S4.1: Real number solution based on ambiguity and its variance matrix The true value of the fuzzy degree passed the Ratio test As well as the dimension n of the ambiguity vector, the observation equation of the ambiguity residual constraint is established: In the above formula (4), δa represents the system deviation of the real-number solution of the ambiguity to be estimated; Step S4.2: Establish the state equation of the fuzzy real number solution system deviation: da k =da k-1 +n k , the k ~N(0,Q k ) (5) In the above formula (5), k and k-1 represent the current epoch and the previous epoch respectively, δa k represents the real number solution deviation of the ambiguity at the kth epoch, η k represents process noise, Q k represents the process noise η k The variance matrix, Q k As follows: Where cycle represents the unit of ambiguity; Step S4.3: Based on equations (5) and (6), the Kalman filter equation is as follows: Where, represents the observation vector, whose variance matrix is ​​set to D L =2n; represents the coefficient matrix; ε k and η k represent observation noise and process noise respectively; Step S4.4: Solve the Kalman filter equation shown in equation (6) as follows to obtain an estimate of the system deviation of the ambiguity real solution: Where, and They represent the predicted value of the system deviation of the real-number solution of the ambiguity at the current epoch and its variance matrix, I represents the identity matrix, and Represent the ambiguity real number solution system deviation estimate and its variance matrix corresponding to the previous epoch; if it is the initial epoch, the value is K k is the gain matrix in the calculation process; is the estimate of the systematic bias of the real-number solution to the ambiguity at the current epoch; for The variance matrix of .

4. The method for improving the accuracy of GNSS carrier positioning fixed solution according to claim 3, characterized in that: The specific steps of step S5 are as follows: Step S5.1: Use the ambiguity real number to solve the system bias estimate And the mapping matrix K obtained in step S1 a , estimate the unmodeled error: In formula (9), is the unmodeled error estimate, is the system deviation estimate of the ambiguity real number solution obtained by equation (8) is its variance matrix; Step S5.2: Using the unmodeled error estimate And the mapping matrix K obtained in step S1 b , calculate the coordinate real number solution system deviation: Where, is the coordinate real number solution system deviation.

5. The method for improving the accuracy of GNSS carrier positioning fixed solution according to claim 3, characterized in that: The specific steps of step S6 are as follows: Step S6.1: According to the original fixed solution Ambiguity real number solution system deviation estimation and the systematic deviation of the coordinate real number solution Calculate the corrected fixed solution for: In formula (11), is the real number solution of the ambiguity The variance matrix of is the coordinate real number solution and the real number solution of ambiguity The covariance matrix of Step S6.2: Calculate the corrected fixed solution according to the following formula The variance matrix of : Where, is the corrected fixed solution The variance matrix of .

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