GNSS single-epoch positioning method based on phase error MCMC fast estimation

Abstract

The application discloses a GNSS single epoch positioning method based on phase error MCMC fast estimation, and particularly relates to the following steps: 1, collecting observation data, forming an observation equation and solving the equation to obtain a float ambiguity solution and a corresponding variance matrix; 2, using the variance matrix to calculate an integer transformation matrix and performing integer transformation on the variance matrix; 3, calculating a sample value of the bias according to a previous sample and a conditional probability density function; 4, correcting the float solution according to the sample value, solving the ambiguity, and determining whether the sample is dominant according to the effect of the previous sample value to select the sample value; 5, repeating steps 3-4 to obtain a sample set of a certain number of error parameters, estimating the bias value and realizing single epoch positioning. The application can realize single epoch positioning in the case that there is bias related to ambiguity, and is suitable for the field of GLONASS and multi-system GNSS combined data processing.

Description

Technical Field

[0001] This invention belongs to the field of Global Navigation Satellite System (GNSS) location services, specifically relating to a GNSS single-epoch positioning method based on rapid estimation of phase error MCMC. Background Technology

[0002] GNSS observations typically include ranging code pseudorange and carrier phase observations. While phase observations offer high accuracy, they contain unknown integer ambiguities. Fixing these integer ambiguities is fundamental for rapid and high-precision GNSS positioning. In GNSS multi-constellation integrated navigation and positioning, some phase errors are related to GNSS ambiguities and require model estimation or correction using known values ​​to quickly fix these ambiguities. Examples include GLONASS inter-frequency offsets and non-zero inter-system offsets in baselines composed of different receiver types. Traditional least-squares estimation of these errors requires assistance from other systems or known coordinate information, making it difficult to obtain accurate estimates quickly. Particle filter estimation methods, using preset values, can successfully estimate these errors and converge relatively quickly; however, this method is computationally intensive and has a certain convergence time, making it difficult to achieve single-epoch error estimation. Summary of the Invention

[0003] To overcome the above problems, this invention provides a GNSS single-epoch positioning method based on rapid estimation of phase error MCMC (Markov Chain Monte Carlo method).

[0004] The present invention provides a GNSS single-epoch positioning method based on fast estimation of phase error MCMC, comprising the following steps:

[0005] Step 1: Collect observation data, assemble observation equations and solve the equations to obtain the ambiguity floating-point solution and the corresponding variance-covariance matrix (hereinafter referred to as the variance matrix).

[0006] Step 2: Calculate the integer transformation matrix Z using the variance-covariance matrix, and perform an integer transformation on the variance-covariance matrix.

[0007] Step 3: Based on the initial sample value, sample the phase error according to the known probability density distribution function to generate a sample value x0 of the error parameter, and determine the conditional probability on which the next sample value is generated.

[0008] Step 4: Correct the floating-point solution of ambiguity using the sample value of the error, find the optimal integer solution, determine the weight of the sample based on the ambiguity fixing effect of the search algorithm, and judge whether the sample is dominant in order to discard the sample.

[0009] Step 5: Repeat steps 3-4 to obtain a sample set of error parameters, estimate the value of phase error based on the sample set, correct the error using the estimated value, and solve for parameters such as coordinate components.

[0010] Furthermore, step 1 specifically involves:

[0011] S11. Establish the observation equation, and set the sum of the error parameter and the ambiguity as parameter z.

[0012] S12. Solve the observed equations to obtain the floating-point solution for the combined parameter z. Sum of variances

[0013] Furthermore, step 2 is implemented using the integer transformation algorithm of the LAMBDA (Least Squares Estimate Adjustment Search Algorithm) method, as follows:

[0014] S21. Solve the variance matrix for floating-point operations. Perform L T DL decomposition, has Where L is a unit lower triangular matrix and D is a diagonal matrix.

[0015] S22, according to L T The DL decomposition results in an integer transformation matrix Z, and |Z| = 1.

[0016] S23. Perform integer transformations on the variance-covariance matrix, and we have: right.

[0017] Furthermore, step 3 specifically involves generating an initial sample value x0 within the possible range of parameter values; and selecting the conditional probability density Q(x′). i |x i-1 For i>0, the next sample value is obtained from the previous sample value based on the conditional density.

[0018] Furthermore, step 4 specifically involves:

[0019] S41. Use the sample value x′ generated in step 3. i Correct the corresponding integer ambiguity floating-point solution have in This is the estimated ambiguity value after error correction.

[0020] S42. Transform the corrected floating-point unambiguity using the integer transformation matrix from step 2, i.e.

[0021] S43. Using the ambiguity search steps in the LAMBDA method, the ambiguity is fixed to obtain the optimal and suboptimal integer ambiguity vectors.

[0022] S44. Based on the ambiguity fixation effect, such as RAITO value and success rate, update the sampled value x′. i The right w i .

[0023] S45, Calculation Simultaneously, uniformly distributed random numbers μ ~ [0, 1] are generated. The value of the i-th particle is determined according to the following formula.

[0024]

[0025] Furthermore, step 5 specifically involves:

[0026] S51. Repeat steps 3-4 to obtain a sample set containing sample values ​​and weights for the error parameters. Where N is the number of samples required.

[0027] S52. To calculate the magnitude of the error value based on the sample values, the following methods can be used: Alternatively, the sample value with the largest weight can be used as the estimate.

[0028] S53. Correct the phase error using the error value by subtracting the error from the observation equation or from the normal equation.

[0029] S54. Solve the equation to obtain the floating-point solution of the ambiguity and its variance matrix, fix the integer ambiguity to obtain the integer solution, and take the integer solution as the truth value.

[0030] S55. Obtain the true value of the ambiguity to get the value of the unknown coordinates and achieve positioning.

[0031] Furthermore, replace steps S53-S55 in step 5 with:

[0032] (1) Correct the floating-point solution generated in step 1 directly using the estimated error value. have

[0033] (2) Using the ambiguity fixing method, based on the corrected floating-point solution Obtaining integer solutions from the variance matrix

[0034] (3) Adding the estimated error value to the fixed integer solution, we get the true value of the sum of ambiguity and error value. Use this parameter as the true value of z in step 1, and calculate the fixed solution of the coordinates according to the following formula.

[0035]

[0036]

[0037] This is the fixed coordinate solution for single-epoch positioning. For the corresponding variance matrix, For single-epoch positioning, the coordinate floating-point solution is... for and The covariance matrix.

[0038] The beneficial technical effects of this invention are as follows:

[0039] (1) The present invention adopts the MCMC method, which takes into account the effect of the previous sample when generating the next sample, which significantly improves the sampling efficiency. It can use fewer samples to obtain a more accurate bias estimate, and reduce the amount of calculation of error estimation under the same accuracy.

[0040] (2) This invention adjusts the sampling position, estimating DCPB in the model instead of directly estimating DIFB. After obtaining the floating-point solution of the sum of bias and ambiguity and obtaining the integer transformation matrix, sampling is performed, which significantly reduces the computational load of a single sample, improves the efficiency of bias estimation, and greatly reduces the computation time of single-epoch positioning. Ultimately, it is possible to obtain an accurate single-epoch fixed solution without significantly increasing the computational load. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the positioning method of the present invention.

[0042] Figure 2 The DCPB value is calculated for the baseline full-day single epoch of the example.

[0043] Figure 3 The baseline full-day single-epoch positioning results are shown in the example.

[0044] Figure 4 This is a statistical summary of the time spent solving the baseline at each epoch of the example implementation. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0046] The flowchart of a GNSS single-epoch positioning method based on fast estimation of phase error MCMC according to the present invention is as follows: Figure 1 As shown, the specific steps include:

[0047] Step 1: Collect observation data, assemble observation equations and solve the equations to obtain the ambiguity floating-point solution and the corresponding variance-covariance matrix (hereinafter referred to as the variance matrix).

[0048] S11. Collect observations such as code pseudorange and carrier phase, and perform preprocessing such as gross error removal and cycle slip detection.

[0049] S12. Establish the observation equation, and combine the error parameter and ambiguity into a single parameter z.

[0050] S13. Solve the observed equations to obtain the floating-point solution for the combined parameter z. Sum of variances

[0051] Step 2: Calculate the integer transformation matrix Z using the variance-covariance matrix, and perform an integer transformation on the variance-covariance matrix.

[0052] S21. Solve the variance matrix for floating-point operations. Perform L T DL decomposition, has

[0053] S22, according to L T The DL decomposition results in an integer transformation matrix Z, and |Z| = 1.

[0054] S23. Perform integer transformations on the variance-covariance matrix, and we have:

[0055] Step 3: Generate an initial sample value x0 within the possible range of parameter values, and select the conditional probability density Q(x′). i |x i-1 For i = 1, 2, ..., N, the next sample value is obtained from the previous sample value based on the conditional density, and the sample value generated in this step is denoted as x′. i .

[0056] Step 4: Correct the floating-point solution of ambiguity using the sample value of the error, find the optimal integer solution, determine the weight of the sample based on the ambiguity fixing effect of the search algorithm, and judge whether the sample is dominant in order to discard the sample.

[0057] S41. Use the sample value x′ generated in step 3. i Correct the corresponding integer ambiguity floating-point solution have in This is the estimated ambiguity value after error correction.

[0058] S42. Transform the corrected floating-point unambiguity using the integer transformation matrix from step 2, i.e.

[0059] S43. Using the ambiguity search steps in the LAMBDA method, the ambiguity is fixed to obtain the optimal and suboptimal integer ambiguity vectors.

[0060] S44. Based on the ambiguity fixation effect, such as RAITO value and success rate, update the sampled value x′. i The right w i .

[0061] S45, Calculation Simultaneously, uniformly distributed random numbers μ ~ [0, 1] are generated. The value of the i-th particle is determined according to the following formula.

[0062]

[0063] Step 5: Repeat steps 3-4 to obtain a sample set of error parameters, estimate the value of phase error based on the sample set, correct the error using the estimated value, and solve for parameters such as coordinate components.

[0064] S51. Repeat steps 3-4 to obtain a sample set containing sample values ​​and weights for the error parameters. Where N is the number of samples required.

[0065] S52. To calculate the magnitude of the error value based on the sample values, the following methods can be used: Alternatively, the sample value with the largest weight can be used as the estimate.

[0066] S53. Directly correct the floating-point solution generated in step 1 using the estimated error value. have

[0067] S54. Using the ambiguity fixing method, based on the corrected floating-point solution... Obtaining integer solutions from the variance matrix

[0068] S55. Adding the estimated error value to the fixed integer solution, we get the true value of the sum of the ambiguity and the error value. Use this parameter as the true value of z in step 1, and calculate the fixed solution of the coordinates according to the following formula.

[0069]

[0070]

[0071] This is a fixed solution for single-epoch positioning. Let be the corresponding variance matrix.

[0072] This embodiment employs the method of the present invention to achieve GLONASS single-epoch positioning when the inter-frequency deviation is not zero. Single-epoch processing is performed on data from a GLONASS short baseline on the 137th day of 2020. The inter-frequency deviation rates of GLONASS's L1 and L2 frequencies are considered to be the same. A parameter is set, and the estimated DCPB value for the entire day's single-epoch calculation is as follows: Figure 2As shown, the positioning results are as follows: Figure 3 As shown, gray dots represent localization results without DCPB correction, black dots represent fixed solutions obtained using this method, and black asterisks represent floating-point solutions. It is evident that this method can achieve good single-epoch localization results. The time taken is compared with the traditional particle filter method (Conventional PF) and the method without phase bias estimation, as shown in the figure. Figure 4 As shown, the computation time did not increase significantly.

[0073] This invention employs the MCMC method, considering the effect of the previous sample when generating the next sample. This allows for obtaining a more accurate bias estimate using fewer samples. Simultaneously, it adjusts the sampling position, estimating DCPB in the model instead of directly estimating DIFB. Sampling is performed after obtaining the floating-point solution of the sum of bias and ambiguity, and then calculating the integer transformation matrix. This significantly reduces the computational load per sample, improving the efficiency of bias estimation. This invention is suitable for parameter estimation of biases related to ambiguity and can be applied in data processing for GNSS systems such as BeiDou, GPS, GLONASS, Galileo, as well as Japan's pseudozenith satellite system and India's NAVIC system.

Claims

1. A GNSS single-epoch positioning method based on rapid estimation of phase error MCMC, characterized in that, Includes the following steps: Step 1: Collect observation data, assemble observation equations and solve the equations to obtain the ambiguity floating-point solution and the corresponding variance-covariance matrix; S11. Establish the observation equation, and set the sum of the error parameter and the ambiguity as parameter z; S12. Solve the observed equations to obtain the floating-point solution for the combined parameter z. Sum of variances ; Step 2: Calculate the integer transformation matrix Z using the variance-covariance matrix, and perform an integer transformation on the variance-covariance matrix; S21. Solve the variance matrix for floating-point operations. Performing upper triangular Cholesky decomposition, we have ; S22. Obtain the integer transformation matrix based on the Cholesky decomposition results. And there are ; S23. Perform integer transformations on the variance-covariance matrix, and we have: ; Step 3: Based on the initial sample value, sample the phase error according to the known probability density distribution function to generate a sample value of the error parameter. To determine the conditional probability upon which the next sample value is generated; Step 4: Correct the floating-point solution of ambiguity using the sample value of the error, find the optimal integer solution, determine the weight of the sample based on the ambiguity fixing effect of the search algorithm, and judge whether the sample is dominant in order to discard the sample. S41. Use the sample values ​​generated in step 3 to correct the merging parameters. ; S42. Transform the corrected floating-point deambiguity using the integer transformation matrix from step 2; S43. Using the ambiguity search steps in the LAMBDA method, the ambiguity is fixed to obtain the optimal and suboptimal integer ambiguity vectors. S44. Update the weights of the sampled values ​​based on the ambiguity fixation effect; S45. Based on the current sample weights and the previous sample weights, determine whether to use the newly generated sample values; Step 5: Repeat steps 3-4 to obtain a sample set of error parameters, estimate the value of phase error based on the sample set, correct the error using the estimated value, and solve for the coordinate component parameters.

2. The GNSS single-epoch positioning method based on rapid estimation of phase error MCMC according to claim 1, characterized in that, Step 5 specifically involves: S51. Repeat steps 3-4 to obtain a sample set containing sample values ​​and weights for the error parameters. ,in The required number of samples; S52. Calculate the magnitude of the error value based on the sample values; S53. Correct the phase error using the error value by subtracting the error from the observation equation or from the normal equation; S54. Solve the equation to obtain the floating-point solution of the ambiguity and its variance matrix, fix the integer ambiguity to obtain the integer solution, and take the integer solution as the truth value; S55. Obtain the true value of the ambiguity to get the value of the unknown coordinates and achieve positioning.

3. The GNSS single-epoch positioning method based on rapid estimation of phase error MCMC according to claim 2, characterized in that, Steps S53-S55 can be replaced with: (1) Correct the floating-point solution generated in step 1 directly using the estimated error value; (2) Using the ambiguity fixing method, the integer solution is obtained based on the corrected floating-point solution and the VC matrix; (3) Add the estimated error value to the fixed integer solution and use it as the true value of the sum of ambiguity and error value to solve the coordinate parameters.

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