Beidou single-frequency dual ionospheric model weighted least squares SPP positioning method

Abstract

The present application relates to a Beidou single-frequency dual-ionosphere model weighted least squares SPP positioning method. The method comprises: capturing visible stars, calculating the ionosphere puncture point of the captured satellite, if the grid point information around the puncture point meets the use requirements of the ionosphere delay solution, that is, the grid ionosphere model is used to calculate the ionosphere delay, otherwise the broadcast ionosphere model is used for calculation, and then the weight model corresponding to the two ionosphere models is used to calculate the weight of each satellite, and a combined weight matrix is ​​constructed and substituted into the pseudorange observation equation for weighted least squares solution. The weight ratio coefficient of the dual ionosphere model is updated using the positioning solution result, and the weight ratio coefficients before and after two adjacent updates are compared to see whether they meet the stop condition. When the stop condition is met, the final positioning result is output. The use of this method can improve positioning accuracy.

Description

Technical Field

[0001] The present application relates to the field of satellite navigation technology, and in particular to a Beidou single-frequency dual-ionospheric model weighted least squares SPP positioning method. Background Art

[0002] At present, due to the low cost of single-frequency GNSS receivers, small calculation amount and low power consumption of single-frequency signal reception and data processing, most scenarios use single-frequency receivers or adopt single-frequency working mode, which makes it of great significance to improve the positioning performance of satellite navigation single-frequency standard point positioning (SPP). The main error sources of satellite navigation positioning include satellite-related errors, signal propagation-related errors and receiver-related errors. When satellite signals propagate through the ionosphere, a large number of charged particles in the ionosphere cause the path of satellite signals to bend and the propagation speed to change, thereby generating ionospheric errors. Among the various error influences of Beidou single-frequency positioning, ionospheric errors are closely related to factors such as observation time and location, satellite signal frequency, etc., and are the most influential type of errors. The navigation positioning error caused by ionospheric errors can reach several meters or even hundreds of meters. Therefore, it is crucial to achieve effective ionospheric error correction to reduce its impact on satellite navigation positioning.

[0003] Beidou single-frequency SPP positioning can use the broadcast ionosphere model broadcast in the navigation message and the grid ionosphere model in the augmentation system to correct the ionospheric error. The broadcast ionosphere model is given by an empirical formula. Due to the complex ionospheric error mechanism and multiple sources of influencing factors, the ionospheric error correction capability of the broadcast ionosphere model is relatively weak. The ionospheric delay varies with the user's time and space dimensions on a global scale. Therefore, the grid ionosphere model divides the ionosphere into multiple grids, providing a real-time grid ionosphere model to correct the ionospheric delay error for each grid area. Usually, the grid point ionosphere information is included in the satellite-based augmentation information, which is broadcast by the GEO satellite, and the coverage area is generally part or all of the area covered by the GEO satellite. When the parameters of the four grid points near the grid where the satellite signal puncture point is located are valid, the single-frequency SPP positioning can obtain higher ionospheric error correction accuracy by performing ionospheric error correction through rectangular weighted interpolation; when the four grid parameters around the puncture point are not completely valid, the parameters of the three surrounding grid points can be selected according to a certain selection strategy and the grid data can be continued to be used through triangular weighted interpolation; but when the valid grid point parameter data is insufficient for interpolation calculation or the puncture point is not within the coverage of the grid point, the grid ionosphere model cannot be used to obtain the satellite ionospheric delay correction number. Therefore, if only the broadcast ionosphere model is used, the ionospheric error accuracy is relatively low; if only the grid ionosphere model is used, some or even all of the satellite signals received may not be able to obtain the ionospheric delay correction number, so that the number of available satellites participating in the positioning solution is too small, resulting in reduced accuracy or positioning failure. The combined use of these two ionosphere models will help improve the single-frequency SPP positioning performance.

[0004] Some researchers combined the broadcast ionospheric information and grid point ionospheric information in the calculation of Beidou B3I single-frequency positioning ionospheric error, and proposed to first use the broadcast ionospheric information to simulate and generate a set of complete grid point ionospheric errors within the grid coverage range, and then use the actually received valid grid point ionospheric information to update the corresponding grid point ionospheric errors, forming the grid point ionospheric information superimposed by the two. For puncture points within the grid coverage range, the zenith ionospheric error is calculated according to the grid ionospheric model method; for puncture points outside the grid coverage range, the zenith ionospheric error is calculated according to the broadcast ionospheric model method. The advantage of this method of superimposing two models is that satellite signals and grid information can be fully utilized, but the ionospheric delay of a single satellite signal may be obtained entirely from the actual valid grid point information, or entirely from the grid point information generated by the broadcast ionospheric model simulation, which will make the ionospheric error accuracy unknown, and the resulting heteroscedasticity will reduce the effectiveness of subsequent positioning solutions. Summary of the invention

[0005] Based on this, it is necessary to provide a Beidou single-frequency dual-ionospheric model weighted least squares SPP positioning method that can improve positioning accuracy in response to the above technical problems.

[0006] A Beidou single-frequency dual-ionospheric model weighted least squares SPP positioning method, the method comprising:

[0007] Search and capture all visible satellites and calculate the position information of the ionospheric puncture point for the captured visible satellites;

[0008] According to the position information of the ionospheric puncture point of each visible satellite, it is judged whether the grid ionospheric information of the current visible satellite meets the requirements for ionospheric delay solution;

[0009] If yes, the first ionospheric delay correction number and the first weighted least squares weight matrix are obtained by solving the grid ionospheric model based on BDSBAS;

[0010] If not, the second ionospheric delay correction number and the second weighted least squares weight matrix are obtained based on the BDGIM model solution; the weighted least squares weight in the second weighted least squares weight matrix is ​​constructed according to the weight ratio coefficient of the dual ionospheric model and the user ionospheric distance error variance of the second ionospheric delay correction number; the dual ionospheric model weight ratio coefficient is defined as the ratio of the residual posterior variance of the two ionospheric models of the grid ionosphere and the BDGIM;

[0011] constructing a combined weight matrix according to the first weighted least squares weight matrix and the second weighted least squares weight matrix;

[0012] Substitute the combined weight matrix into the least squares solution formula to perform positioning solution and obtain the positioning solution result;

[0013] The positioning solution result is used to update the weight coefficient of the dual ionosphere model, and the weight coefficients before and after two consecutive updates are compared to see whether they meet the stop condition. When the stop condition is met, the final positioning result is output.

[0014] The above-mentioned Beidou single-frequency dual-ionosphere model weighted least squares SPP positioning method first captures the visible stars, calculates the ionosphere puncture point of the captured satellite, and if the grid point information around the puncture point meets the requirements for the use of ionosphere delay solution, the grid ionosphere model is used to calculate the ionosphere delay, otherwise the broadcast ionosphere model is used for calculation, and then the weight model corresponding to the two ionosphere models is used to calculate the weight of each satellite, and the combined weight matrix is ​​constructed and substituted into the pseudorange observation equation for weighted least squares solution. This application is based on the weighted least squares method. For each satellite Taking into account the heteroskedasticity between satellites and the two models, a combined weight matrix framework of the joint dual ionosphere model is constructed. First, when calculating the grid ionosphere delay correction number for satellites using the grid ionosphere model, the standard deviation of the user ionosphere distance error is synchronously estimated, and it is used as the basis for setting the weights of satellites using the grid ionosphere model. Second, in view of the uncertainty in the use of empirical values ​​of elevation angles when setting weights for satellites using the broadcast ionosphere model, the residual posterior variance relationship of the positioning solution of the two ionosphere models is combined to constrain it, thereby improving its reliability and greatly improving positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flowchart of a Beidou single-frequency dual ionospheric model weighted least squares SPP positioning method in an embodiment;

[0016] Figure 2 The present invention is a flowchart of a Beidou single-frequency dual ionospheric model weighted least squares SPP positioning method in an embodiment. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0018] In one embodiment, Figure 1 and Figure 2 As shown, a Beidou single-frequency dual ionospheric model weighted least squares SPP positioning method is provided, comprising the following steps:

[0019] Step 102, searching and capturing all visible satellites and calculating the position information of the ionospheric puncture points for the captured visible satellites.

[0020] Specifically, the receiver calculates the latitude and longitude of the ionospheric piercing point for all visible satellites captured during the search.

[0021] by It represents the geocentric angle between the user and the ionospheric piercing point, in radians, and its calculation formula is:

[0022]

[0023] In the above formula, Indicates the satellite altitude angle in radians; Indicates the height of the ionosphere thin layer, and different ionosphere models have different values; Represents the approximate Earth radius.

[0024] The geographical latitude of the ionospheric piercing point projected on the Earth's surface , the calculation formula is:

[0025]

[0026] In the above formula, Indicates the user's geographical latitude, Indicates the satellite azimuth, in radians.

[0027] For the BDGIM model, the geographic longitude of the ionospheric puncture point projected on the Earth's surface The calculation formula is:

[0028]

[0029] In the above formula, Indicates the user's geographic longitude in radians.

[0030] For the grid ionosphere model in the BDSBAS-B1C signal, the geographic longitude of the ionosphere puncture point projected on the earth's surface The calculation formula is:

[0031] (1) When and or and

[0032] hour, The calculation formula is:

[0033]

[0034] (2) In other cases, The calculation formula is:

[0035] .

[0036] In addition, it should be noted that the BDGIM model is the Beidou Global Broadcast Ionospheric Delay Correction Model, and the BDSBAS in the BDSBAS grid ionospheric model represents the Beidou Satellite-Based Augmentation System.

[0037] Step 104, judging whether the grid ionosphere information of the currently visible satellites meets the use requirements of ionosphere delay solution according to the position information of the ionosphere puncture point of each visible satellite; if so, obtaining the first ionosphere delay correction number and the first weighted least squares weight matrix based on the grid ionosphere model solution of BDSBAS; if not, obtaining the second ionosphere delay correction number and the second weighted least squares weight matrix based on the BDGIM model solution; the weighted least squares weights in the second weighted least squares weight matrix are constructed according to the weight ratio coefficient of the dual ionosphere model and the user ionosphere distance error variance of the second ionosphere delay correction number; the weight ratio coefficient of the dual ionosphere model is defined as the ratio of the residual posterior variance of the two ionosphere models, the grid ionosphere model and the BDGIM model.

[0038] Specifically, for satellites that preferentially use the grid ionosphere model to calculate ionospheric delay corrections, the matrix also calculates the standard deviation of the user ionospheric distance error at the puncture point through the grid ionosphere model, and uses the standard deviation as the basis for constructing satellite weights; for satellites that use the BDGIM model to calculate ionospheric delay corrections, an empirical model based on satellite elevation angles is used to estimate the standard deviation of the user ionospheric distance error, and the standard deviation is used as the basis for constructing satellite weights, and is constrained by combining the residual posterior variance relationship of the positioning solutions of the two models to reduce the problem that the standard deviation of the ionospheric delay correction is estimated based on empirical values, and its accuracy has a certain uncertainty.

[0039] Step 106: construct a combined weight matrix according to the first weighted least squares weight matrix and the second weighted least squares weight matrix.

[0040] Steps 104 to 106 construct a combined weight matrix of a joint dual ionosphere model. By combining two ionosphere models, the matrix ensures that all received satellite signals participate in the subsequent positioning solution, avoiding the problem that some satellite signals are discarded due to the lack of grid ionosphere delay correction numbers, resulting in too few available satellites participating in the positioning solution, thereby reducing the accuracy or failing to position; it also avoids the heteroscedasticity problem caused by simply superimposing the two models. The matrix constructed in this way uses weights to reflect the real-time accuracy difference of the ionosphere delay correction numbers calculated by the two models, which can effectively improve the positioning performance.

[0041] Step 108, substitute the combined weight matrix into the least square solution formula to perform positioning solution and obtain the positioning solution result; use the positioning solution result to update the weight ratio coefficient of the dual ionosphere model, compare the weight ratio coefficients before and after two adjacent updates to see whether they meet the stop condition, and output the final positioning result when the stop condition is met.

[0042] Compared with the prior art, the Beidou single-frequency dual-ionosphere model weighted least squares SPP positioning method provided in the present application first captures the visible stars, calculates the ionosphere piercing points of the captured satellites, and if the grid point information around the piercing points meets the requirements for ionospheric delay solution, the grid ionosphere model is used to calculate the ionospheric delay, otherwise the broadcast ionosphere model is used for calculation, and then the weight models corresponding to the two ionosphere models are proposed to calculate the weight of each satellite, construct a combined weight matrix and substitute it into the pseudorange observation equation for weighted least squares solution. Based on the weighted least squares method, the present application constructs a combined weight matrix framework of a joint dual ionosphere model for the heteroscedasticity between each satellite and the two models. First, when calculating the grid ionosphere delay correction number, the standard deviation of the user ionosphere distance error is synchronously estimated, and it is used as the basis for setting the weight of the satellite using the grid ionosphere model; second, for the uncertainty of using the empirical value of the elevation angle when setting the weight of the satellite using the broadcast ionosphere model, the residual posterior variance relationship of the positioning solution of the two ionosphere models is combined to constrain it, thereby improving its reliability and greatly improving the positioning accuracy.

[0043] In one embodiment, a first ionospheric delay correction number and a first weighted least squares weight matrix are obtained by solving a grid ionospheric model based on BDSBAS, including:

[0044] Calculate the ionospheric vertical delay at the puncture point according to the position information of the ionospheric puncture point of each visible satellite and simultaneously calculate the error variance of the ionospheric vertical delay at the puncture point;

[0045] The first ionospheric delay correction is calculated by multiplying the ionospheric vertical delay at the puncture point by the tilt factor, and the user ionospheric distance error standard deviation at the puncture point is calculated by multiplying the tilt factor by the error variance of the ionospheric vertical delay at the puncture point;

[0046] The weighted least squares weights of the grid ionosphere model of the currently visible satellites are set using the standard deviation of the user ionosphere distance error at the puncture point, and the first weighted least squares weight matrix is ​​constructed according to all the weighted least squares weights calculated based on the grid ionosphere model.

[0047] In one embodiment, the weighted least squares weight of the grid ionosphere model of the currently visible satellite is set using the standard deviation of the user ionosphere distance error at the puncture point, and a first weighted least squares weight matrix is ​​constructed according to all weighted least squares weights calculated based on the grid ionosphere model, including:

[0048] The weighted least squares weight of the currently visible satellite is set using the standard deviation of the user ionospheric distance error at the puncture point:

[0049] .

[0050] in, Represents the grid ionospheric model. The weighted least squares weights of the visible satellites, is the standard deviation of the user ionospheric distance error at the visible satellite penetration point, , represents the tilt factor, represents the standard deviation of the error of the ionospheric vertical delay at the puncture point;

[0051] The first weighted least squares weight matrix is ​​constructed based on all weighted least squares weights calculated based on the grid ionosphere model:

[0052] .

[0053] Among them, the first weighted least squares weight matrix is a diagonal weight matrix, Represents the number of weighted least squares weights calculated based on the grid ionosphere model, that is, the number of satellites for which the first ionospheric delay correction is calculated using the grid ionosphere model.

[0054] In a specific embodiment, the ionospheric vertical delay at the puncture point is calculated using a rectangular interpolation method or a triangular interpolation method according to the number of ionospheric grid points selected around the puncture point.

[0055] (1) Calculation of vertical delay of ionosphere at the puncture point

[0056] The ionospheric vertical delay at the puncture point is calculated using rectangular interpolation or triangular interpolation according to the number of ionospheric grid points selected around the puncture point.

[0057] Assume that the latitude and longitude of a satellite’s puncture point are and longitude , then the ionospheric vertical delay at the puncture point is for:

[0058]

[0059] in, m The number of grid points selected around the puncture point, its value is 3 or 4; For the surrounding p The ionospheric vertical delay at each grid point; According to the location of the puncture point and the p The geometric distribution relationship of the grid point positions is calculated The weight of .

[0060] At the same time, the error variance of the ionospheric vertical delay at the puncture point is calculated:

[0061] ;

[0062] In the above formula, the grid ionospheric degradation parameter is Calculated as follows:

[0063] ;

[0064] ;

[0065] in, t For the current moment, , , , , All were sent by telegram. In order to use the grid point GIVEI broadcast by the message, the error standard deviation of the ionospheric vertical delay is obtained by looking up the table. Indicates rounding down.

[0066] (2) Calculation of ionospheric delay correction at the puncture point

[0067] Ionospheric delay correction Calculate as follows:

[0068] ;

[0069] In the formula, is the ionospheric tilt delay at the puncture point, i Indicates that the current calculation is i satellites, is the tilt factor, as follows:

[0070] ;

[0071] in, is the approximate radius of the Earth; E is the satellite altitude angle; is the height of the ionosphere thin layer, and is taken as 350km in the calculation.

[0072] Standard deviation of user ionospheric distance error at the puncture point for:

[0073] .

[0074] (3) Calculate the weights of the weighted least squares method

[0075] The present invention calculates the user ionospheric distance error standard deviation at the puncture point The estimated value of is used as the basis for setting the satellite weights used in the weighted least squares method using the grid ionosphere model. i For a satellite, its ionospheric delay correction is calculated using the grid ionosphere model. The weight set by the weighted least squares method for this satellite is:

[0076] ;

[0077] In the above formula, represents the first i The standard deviation of the user ionospheric range error at the satellite penetration point.

[0078] (4) Construct the first weighted least squares weight matrix

[0079] The first weighted least squares weight matrix is ​​constructed based on all weighted least squares weights calculated based on the grid ionosphere model:

[0080] ;

[0081] In the above formula, represents the first weighted least squares weight matrix, which is a diagonal weight matrix; Represents the number of weighted least squares weights calculated based on the grid ionosphere model, that is, the number of satellites for which the first ionospheric delay correction is calculated using the grid ionosphere model.

[0082] In one embodiment, the second ionospheric delay correction number and the second weighted least squares weight matrix are obtained based on the BDGIM model solution, including:

[0083] Calculate the second ionospheric delay correction of the currently visible satellite according to the BDGIM model;

[0084] The user ionospheric range error variance of the second ionospheric delay correction is evaluated using a weighted model based on the satellite elevation angle, and the weighted least squares weights based on the BDGIM model are constructed according to the weight ratio coefficients of the dual ionosphere model. The second weighted least squares weight matrix is ​​constructed according to all the weighted least squares weights calculated based on the BDGIM model.

[0085] In one embodiment, the second ionospheric delay correction number of the currently visible satellite is calculated according to the BDGIM model, specifically:

[0086] ;

[0087] in, Indicates the first i The second ionospheric delay correction for the visible satellites, To convert the ionospheric delay from the vertical direction to the slant direction, is the ionospheric delay prediction value, Ionospheric delay model parameters broadcast in navigation messages, is the function value calculated according to the puncture point position and observation time, f It is the carrier frequency corresponding to the current signal, in Hertz.

[0088] In one embodiment, the user ionospheric distance error variance of the second ionospheric delay correction number is evaluated using a weighted model based on the satellite elevation angle, and a weighted least squares weight based on the BDGIM model is constructed according to the weight ratio coefficient of the dual ionospheric model, and a second weighted least squares weight matrix is ​​constructed according to all weighted least squares weights calculated based on the BDGIM model, including:

[0089] The user ionospheric range error variance of the second ionospheric delay correction is evaluated using a weighted model based on the satellite elevation angle:

[0090] .

[0091] in, is the user ionospheric range error variance of the second ionospheric delay correction number, is the satellite elevation angle, a , b is the set experience value;

[0092] The weight of the weighted least square method based on the BDGIM model is constructed according to the weight ratio coefficient of the dual ionosphere model:

[0093] ;

[0094] in, Represents the first i The weighted least squares weights of the visible satellites, is the standard deviation of the user ionospheric range error of the second ionospheric delay correction number of the visible satellite, is the weight coefficient of the defined dual ionosphere model;

[0095] The second weighted least squares weight matrix is ​​constructed based on all weighted least squares weights calculated based on the BDGIM model:

[0096] ;

[0097] Among them, the second weighted least squares weight matrix is a diagonal weight matrix, Indicates the number of weighted least squares weights calculated based on the BDGIM model, that is, the number of satellites for which the second ionospheric delay correction is calculated using the BDGIM model.

[0098] In a specific embodiment, the first i Satellite ionospheric delay correction number The formula is as follows:

[0099] ;

[0100] in, is the projection function that converts the ionospheric delay from the vertical direction to the inclined direction, which is related to the grid ionospheric tilt factor has exactly the same form, but the ionospheric thin layer height The recommended value is 400 km; f is the carrier frequency corresponding to the current signal, in Hertz; is the ionospheric delay prediction value; Ionospheric delay model parameters broadcast for navigation messages; is the function value calculated according to the puncture point position and observation time:

[0101] ;

[0102] in, is the regularization function; is the standard Legendre function; and are the latitude and longitude of the ionospheric piercing point, respectively; , It is a function-related parameter, and the corresponding value is obtained by looking up the table.

[0103] The present invention selects the elevation angle empirical sine function model to estimate the variance of the ionospheric delay correction number of the BDGIM model, and its calculation formula is:

[0104] ;

[0105] in, is the satellite elevation angle, a , b is the experience value set, for example .

[0106] The variance of the ionospheric delay correction is estimated based on empirical values, and its accuracy has a certain degree of uncertainty. The present invention constrains the residual posterior variance relationship of the positioning solution of the two ionospheric models to improve its reliability. The weight calculation formula for the weighted least squares method of visible satellites is as follows:

[0107] ;

[0108] In the above formula is the weight coefficient of the dual ionosphere model defined, which is the ratio of the residual posterior variances of the two ionosphere models, as shown in the following formula:

[0109] ;

[0110] in, is the residual a posteriori variance of the satellite-based positioning solution using the grid ionosphere model; It is the residual posterior variance of the satellite positioning solution using the BDGIM model. The initial value of is set to 1.

[0111] The second weighted least squares weight matrix is ​​constructed based on all weighted least squares weights calculated based on the BDGIM model:

[0112] ;

[0113] in, represents the second weighted least squares weight matrix, which is a diagonal weight matrix; Indicates the number of weighted least squares weights calculated based on the BDGIM model, that is, the number of satellites for which the second ionospheric delay correction is calculated using the BDGIM model.

[0114] In one embodiment, the combined weight matrix is ​​substituted into the least squares solution formula to perform positioning solution, and a positioning solution result is obtained, including:

[0115] Substitute the combined weight matrix into the least squares solution formula for positioning solution, and the positioning solution result is:

[0116] ;

[0117] in, represents the combination weight matrix, represents the first weighted least squares weight matrix calculated based on the grid ionosphere model, is the second weighted least squares weight matrix calculated based on the BDGIM model, , , , Indicates the user's location coordinates. represents the initial position coordinates of the receiver when performing the least squares solution, represents the receiver clock error, It represents the initial value of the clock error when the receiver performs the least squares solution. , represents the coefficient matrix calculated based on the grid ionosphere model, represents the coefficient matrix calculated based on the BDGIM model, represents the constant term vector calculated based on the grid ionosphere model, Represents the constant term vector calculated based on the BDGIM model.

[0118] In a specific embodiment, since the errors of each satellite are independent, the weighted least squares method assigns a greater weight to a satellite with a smaller error, so that it plays a greater role in positioning solution.

[0119] The actual distance from the satellite to the user's location r It can be expressed as:

[0120] ;

[0121] in, It is i The actual distance from the satellite to the user, It is i The position coordinates of the satellites, are the user's location coordinates.

[0122] The pseudorange observation equation can be simplified as:

[0123] ;

[0124] in, It is i The pseudorange after the pseudorange measurement error is corrected by the satellites, is the receiver clock error.

[0125] For the coordinates in the pseudorange observation equation and clock difference Find the partial derivative as follows:

[0126] .

[0127] Assume that the initial position of the receiver when performing the least squares solution is ,and The initial value of ,make , , , the nonlinear positioning equation is linearized as:

[0128] .

[0129] Simplify the above formula to:

[0130] ;

[0131] Then the least squares solution of the above matrix equation can be expressed as the following formula:

[0132] ;

[0133] The combination weight matrix is W , which is composed as follows:

[0134] ;

[0135] In the above formula, the weights of each satellite are divided into two groups: is the first weighted least squares weight matrix calculated based on the grid ionosphere model, It is the second weighted least squares weight matrix calculated based on the BDGIM model.

[0136] The combined weight matrix W Substituting into the least squares solution formula, we can get the weighted least squares solution expression:

[0137] .

[0138] In one embodiment, the dual ionosphere model weight coefficients are updated using the positioning solution results, including:

[0139] After calculating the residual vector using the positioning solution result, the weight coefficient of the dual ionosphere model is updated according to the Hermelt variance estimation method and the residual posterior variance of the two models estimated by the residual vector;

[0140] The residual vector is calculated using the positioning solution result:

[0141] ;

[0142] Among them, the residual vector is expressed as , represents the residual vector calculated based on the grid ionosphere model, Represents the residual vector calculated based on the BDGIM model. , , , Indicates the user's location coordinates. represents the initial position of the receiver when performing the least squares solution, represents the receiver clock error, It represents the initial value of the clock error when the receiver performs the least squares solution. , represents the coefficient matrix calculated based on the grid ionosphere model, represents the coefficient matrix calculated based on the BDGIM model, represents the constant term vector calculated based on the grid ionosphere model, Represents the constant term vector calculated based on the BDGIM model.

[0143] In one embodiment, the weight coefficients of the dual ionosphere model are updated according to the Hermelt variance estimation method and the residual posterior variance of the residual vector estimation grid ionosphere and BDGIM models, including:

[0144] According to the Hermelt variance estimation method and the residual vector estimation, the residual posterior variances of the grid ionosphere and BDGIM models are and , which is expressed as follows:

[0145] ;

[0146] in, represents the first weighted least squares weight matrix calculated based on the grid ionosphere model, Represents the second weighted least squares weight matrix calculated based on the BDGIM model. The matrix S The expression is as follows:

[0147] , and are the number of satellites for calculating ionospheric delay corrections using the grid ionosphere model and the BDGIM model, respectively. , and The expression is as follows:

[0148] ;

[0149] Then the updated weight coefficient is:

[0150] .

[0151] In one embodiment, comparing the weight coefficients before and after two adjacent updates to see whether they meet a stop condition, and outputting a final positioning result when the stop condition is met, includes:

[0152] The weight coefficients before and after two consecutive updates are and , compare the absolute value of the difference between the two with the set threshold T Relationship:

[0153] if , then the stop condition is met and the positioning result is output;

[0154] if , then the stopping condition is not met, and a new weight coefficient is used Update the second weighted least squares weight matrix and recalculate the positioning result until the stop condition is met.

[0155] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0156] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0157] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0158] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A Beidou single-frequency dual ionospheric model weighted least squares SPP positioning method, characterized in that: The method comprises: Search and capture all visible satellites and calculate the position information of the ionospheric puncture point for the captured visible satellites; According to the position information of the ionospheric puncture point of each visible satellite, it is judged whether the grid ionospheric information of the current visible satellite meets the use requirements of ionospheric delay solution; If yes, the first ionospheric delay correction number and the first weighted least squares weight matrix are obtained by solving the grid ionospheric model based on BDSBAS; If not, the second ionospheric delay correction number and the second weighted least squares weight matrix are obtained based on the BDGIM model solution; the weighted least squares weight in the second weighted least squares weight matrix is ​​constructed according to the dual ionospheric model weight ratio coefficient and the user ionospheric distance error variance of the second ionospheric delay correction number; the dual ionospheric model weight ratio coefficient is defined as the ratio of the residual posterior variance of the two ionospheric models of the grid ionosphere and the BDGIM; constructing a combined weight matrix according to the first weighted least squares weight matrix and the second weighted least squares weight matrix; Substituting the combined weight matrix into the least squares solution formula to perform positioning solution and obtain a positioning solution result; The positioning solution result is used to update the weight coefficient of the dual ionosphere model, and the weight coefficients before and after two consecutive updates are compared to see whether they meet the stop condition. When the stop condition is met, the final positioning result is output.

2. The method according to claim 1, characterized in that The first ionospheric delay correction number and the first weighted least squares weight matrix are obtained by solving the grid ionospheric model based on BDSBAS, including: Calculating the ionospheric vertical delay at the puncture point based on the position information of the ionospheric puncture point of the currently visible satellite and simultaneously calculating the error variance of the ionospheric vertical delay at the puncture point; The first ionospheric delay correction number is calculated by multiplying the ionospheric vertical delay at the puncture point by the tilt factor, and the user ionospheric distance error standard deviation at the puncture point is calculated by multiplying the tilt factor by the error variance of the ionospheric vertical delay at the puncture point; The weighted least squares weights of the grid ionosphere model of the currently visible satellite are set using the standard deviation of the user ionosphere distance error at the puncture point, and a first weighted least squares weight matrix is ​​constructed according to all weighted least squares weights calculated based on the grid ionosphere model.

3. The method according to claim 2, characterized in that The weighted least squares weights of the currently visible satellites are set using the standard deviation of the user ionospheric distance error at the puncture point, and a first weighted least squares weight matrix is ​​constructed according to all weighted least squares weights calculated based on the grid ionospheric model, including: The weighted least squares weight of the currently visible satellite is set using the standard deviation of the user ionospheric distance error at the puncture point: in, Represents the grid ionospheric model based on The weighted least squares weights of the visible satellites, is the standard deviation of the user ionospheric distance error at the visible satellite penetration point, , represents the tilt factor, represents the standard deviation of the error of the ionospheric vertical delay at the puncture point; The first weighted least squares weight matrix is ​​constructed based on all weighted least squares weights calculated based on the grid ionosphere model: Among them, the first weighted least squares weight matrix is a diagonal weight matrix, Represents the number of weighted least squares weights calculated based on the grid ionosphere model, that is, the number of satellites for which the first ionospheric delay correction is calculated using the grid ionosphere model.

4. The method according to claim 1, characterized in that: The second ionospheric delay correction number and the second weighted least squares weight matrix are obtained based on the BDGIM model, including: Calculate the second ionospheric delay correction of the currently visible satellite according to the BDGIM model; The user ionospheric range error variance of the second ionospheric delay correction is evaluated using a weighted model based on the satellite elevation angle, and the weighted least squares weights based on the BDGIM model are constructed according to the weight ratio coefficients of the dual ionosphere model. The second weighted least squares weight matrix is ​​constructed according to all the weighted least squares weights calculated based on the BDGIM model.

5. The method according to claim 4, characterized in that The second ionospheric delay correction number of the currently visible satellite is calculated according to the BDGIM model, specifically: in, Indicates the first The second ionospheric delay correction for the visible satellites, To convert the ionospheric delay from the vertical direction to the slant direction, is the ionospheric delay prediction value, Ionospheric delay model parameters broadcast in navigation messages, is the function value calculated according to the puncture point position and observation time, f It is the carrier frequency corresponding to the current signal, in Hertz.

6. The method according to claim 4, characterized in that The user ionospheric distance error variance of the second ionospheric delay correction is evaluated using a weighted model based on satellite elevation angle, and the weighted least squares weights based on the BDGIM model are constructed according to the weight ratio coefficients of the dual ionospheric model. The second weighted least squares weight matrix is ​​constructed according to all the weighted least squares weights calculated based on the BDGIM model, including: The user ionospheric range error variance of the second ionospheric delay correction is evaluated using a weighted model based on the satellite elevation angle: in, is the user ionospheric range error variance of the second ionospheric delay correction number, is the satellite elevation angle, a , b is the set experience value; The weight of the weighted least square method based on the BDGIM model is constructed according to the weight ratio coefficient of the dual ionosphere model: in, Represents the first The weighted least squares weights of the visible satellites, is the standard deviation of the user ionospheric range error of the second ionospheric delay correction number of the visible satellite, is the weight coefficient of the defined dual ionosphere model; The second weighted least squares weight matrix is ​​constructed based on all weighted least squares weights calculated based on the BDGIM model: Among them, the second weighted least squares weight matrix is a diagonal weight matrix, Indicates the number of weighted least squares weights calculated based on the BDGIM model, that is, the number of satellites for which the second ionospheric delay correction is calculated using the BDGIM model.

7. The method according to claim 1, characterized in that Substitute the combined weight matrix into the least squares solution formula to perform positioning solution, and obtain the positioning solution result, including: Substitute the combined weight matrix into the least squares solution formula for positioning solution, and the positioning solution result is obtained as follows: in, represents the combination weight matrix, represents the first weighted least squares weight matrix calculated based on the grid ionosphere model, is the second weighted least squares weight matrix calculated based on the BDGIM model, , , , , Indicates the user's location coordinates. represents the initial position coordinates of the receiver when performing the least squares solution, represents the receiver clock error, It represents the initial value of the clock error when the receiver performs the least squares solution. , represents the coefficient matrix calculated based on the grid ionosphere model, represents the coefficient matrix calculated based on the BDGIM model, represents the constant term vector calculated based on the grid ionosphere model, Represents the constant term vector calculated based on the BDGIM model.

8. The method according to claim 1, characterized in that The positioning solution results are used to update the weight coefficients of the dual ionosphere model, including: After calculating the residual vector using the positioning solution result, the weight coefficient of the dual ionosphere model is updated according to the Hermelt variance estimation method and the residual posterior variance of the grid ionosphere and BDGIM models estimated by the residual vector; The residual vector calculated by using the positioning solution result is: Among them, the residual vector is expressed as , represents the residual vector calculated based on the grid ionosphere model, represents the residual vector calculated based on the BDGIM model, , , , , Indicates the user's location coordinates. represents the initial position of the receiver when performing the least squares solution, represents the receiver clock error, It represents the initial value of the clock error when the receiver performs the least squares solution. , represents the coefficient matrix calculated based on the grid ionosphere model, represents the coefficient matrix calculated based on the BDGIM model, represents the constant term vector calculated based on the grid ionosphere model, Represents the constant term vector calculated based on the BDGIM model.

9. The method according to claim 8, characterized in that The weight coefficients of the dual ionosphere model are updated by estimating the residual posterior variance of the grid ionosphere and BDGIM models according to the Hermelt variance estimation method and the residual vector, including: According to the Hermelt variance estimation method and the residual vector, the residual posterior variances of the grid ionosphere and BDGIM models are estimated as follows: and , which is expressed as follows: in, represents the first weighted least squares weight matrix calculated based on the grid ionosphere model, Represents the second weighted least squares weight matrix calculated based on the BDGIM model. The matrix S The expression is as follows: in, and are the number of satellites for calculating ionospheric delay corrections using the grid ionosphere model and the BDGIM model, respectively. , and The expression is as follows: ； The updated weight coefficient is 。 10. The method according to claim 1, characterized in that Compare the weight coefficients before and after two consecutive updates to see if they meet the stop condition. When the stop condition is met, output the final positioning result, including: The weight coefficients before and after two consecutive updates are and , compare the absolute value of the difference between the two with the set threshold T Relationship: if , then the stop condition is met and the positioning result is output; if , then the stopping condition is not met, and a new weight coefficient is used The second weighted least squares weight matrix calculated based on the BDGIM model is updated, and the positioning result is recalculated until the stop condition is met.

Images