Tropospheric modeling accuracy calibration method and positioning method based on posterior residual error

Abstract

This invention discloses a method and apparatus for calibrating tropospheric modeling accuracy based on posterior residuals, relating to the field of GNSS high-precision positioning technology. The method includes: constructing an ionospherically independent combined observation equation based on GNSS observation data uploaded by a sample terminal; substituting the fixed carrier phase ambiguity of the sample terminal into the ionospherically independent combined observation equation to determine the posterior residual of the sample terminal; determining the zenith tropospheric modeling variance at the location of the sample terminal based on the posterior residual; constructing an accuracy function based on the coordinates of the sample terminal's location and the zenith tropospheric modeling variance; determining the zenith tropospheric modeling variance at the location of the terminal to be positioned based on the accuracy function and the coordinates of the terminal to be positioned; and distributing the zenith tropospheric modeling variance to the terminal to be positioned. The solution of this application can improve the positioning accuracy of GNSS.

Description

Technical Field

[0001] This application relates to the field of high-precision positioning and atmospheric error modeling technology for global navigation satellite systems, and in particular to a tropospheric modeling accuracy calibration method and positioning method based on a posteriori residuals. Background Technology

[0002] Global Navigation Satellite System (GNSS) high-precision positioning technology is widely used in intelligent transportation, unmanned platform navigation, precision surveying, water conservancy monitoring, and geological disaster monitoring. Its positioning modes include, but are not limited to, Real-time Dynamic Differential Positioning (RTK) and Regional Augmentation Positioning. Regional Augmentation Positioning further includes Precise Point Real-time Dynamic Positioning (PPP-RTK). Among these positioning modes, tropospheric delay is one of the important sources of error affecting positioning accuracy. Tropospheric delay is closely related to water vapor distribution, air pressure, temperature, topographic elevation changes, and local meteorological conditions, and its spatial variation usually exhibits significant regional differences. Summary of the Invention

[0003] This application discloses a method and apparatus for calibrating the accuracy of tropospheric modeling based on posterior residuals, which can improve the positioning accuracy of global navigation satellite systems; the method for calibrating the accuracy of tropospheric modeling based on posterior residuals includes: The server performs a tropospheric modeling accuracy calibration step, which includes: The observation data uploaded by the sample terminal is obtained, and an ionospherically independent combined observation equation is constructed based on the observation data. The fixed carrier phase ambiguity is then substituted into the ionospherically independent combined observation equation to determine the posterior residual. Based on the posterior residuals, statistical processing is performed, and combined with the tropospheric projection function and satellite elevation angle, the zenith tropospheric modeling variance at the location of the sample terminal is determined; Based on the variance and location information of zenith tropospheric modeling from multiple sample terminals, a three-dimensional thin-plate spline radial basis function interpolation method with elevation difference weighting coefficients is used to construct a tropospheric modeling accuracy function. Based on the location coordinates of the terminal to be located, the zenith tropospheric modeling variance of the location of the terminal to be located is predicted using the tropospheric modeling accuracy function, and the predicted zenith tropospheric modeling variance and the tropospheric delay parameter are sent to the terminal to be located. The terminal performs an adaptive positioning step, which includes: Receive the tropospheric delay parameters and zenith tropospheric modeling variance sent by the server; Based on the tropospheric delay parameters, GNSS observation equations and tropospheric pseudo-observation constraint equations are constructed. Based on the received zenith tropospheric modeling variance, the tropospheric pseudo-observation weights are determined, and an extended weight matrix containing the tropospheric pseudo-observation weights is constructed. The extended weight matrix is ​​used to solve the GNSS observation equation and the tropospheric pseudo-observation constraint equation using weighted least squares to obtain the positioning result of the terminal to be positioned.

[0004] Preferably, the specific process of determining the posterior residual in the tropospheric modeling accuracy calibration step performed by the server includes: Based on the carrier phase observations and pseudorange observations uploaded by the sample terminal, an ionospherically independent combined observation equation that eliminates the influence of first-order ionospheric delay is constructed. The integer ambiguity obtained by the fixed solution of the sample terminal is substituted into the ionosphere-independent combined observation equation as a known quantity to eliminate the influence of ambiguity floating-point deviation on the residual. Based on the ionospherically independent combined observation equation after substituting integer ambiguity, the difference between the observed value and the model prediction value is calculated to obtain the posterior residual.

[0005] Preferably, the specific process of determining the zenith tropospheric modeling variance in the server-side tropospheric modeling accuracy calibration step includes: Statistical analysis is performed on multiple posterior residuals of the same sample terminal within a preset time window, and the variance of the unit-weighted posterior residual is calculated. Obtain the tropospheric projection function values ​​and satellite elevation angles when the sample terminal observes each satellite; Based on the unit-weighted posterior residual variance, the tropospheric projection function value, and the satellite elevation angle, the effects of observation noise and multipath error are separated, and the zenith tropospheric modeling variance at the location of the sample terminal is obtained by inversion.

[0006] Preferably, the method of constructing the tropospheric modeling accuracy function using a three-dimensional thin-plate spline radial basis function interpolation method that incorporates elevation difference weighting coefficients specifically includes: Using the three-dimensional position coordinates of multiple sample terminals as nodes and the corresponding zenith troposphere modeling variance as node values, a three-dimensional thin-plate spline radial basis function model is constructed. When calculating the spatial distance between any two sample terminal nodes, the horizontal Euclidean distance and the elevation difference are multiplied by preset weighting coefficients and then combined to obtain the weighted spatial distance. Based on the weighted spatial distance, the coefficients of the radial basis function model of the three-dimensional thin plate spline are solved to obtain the tropospheric modeling accuracy function, which can characterize the spatial distribution characteristics of tropospheric modeling accuracy in terrain undulation areas.

[0007] Preferably, in the adaptive positioning step performed on the terminal side, determining the tropospheric pseudo-observation weights based on the received zenith tropospheric modeling variance specifically includes: The reciprocal of the received zenith tropospheric modeling variance is used as the initial weight of the tropospheric pseudo-observations; When the variance of the zenith tropospheric modeling is greater than a preset variance threshold, the initial weights are reduced according to a preset attenuation factor to obtain the final tropospheric pseudo-observation weights. When the variance of the zenith tropospheric modeling is less than or equal to a preset variance threshold, the initial weights are directly used as the final tropospheric pseudo-observation weights.

[0008] Preferably, in the adaptive positioning step performed on the terminal side, the GNSS observation equation and the tropospheric pseudo-observation constraint equation are jointly solved using weighted least squares with the extended weight matrix, specifically including: Based on the extended weight matrix, the GNSS observation equations and the tropospheric pseudo-observation constraint equations are combined into a joint observation equation set; The normal equations of the joint observation equation set are constructed to obtain a normal equation matrix that includes the weights of tropospheric pseudo-observations; The normal equation matrix is ​​solved to simultaneously estimate the position parameters and tropospheric wet delay residual parameters of the terminal to be located, which are used as the positioning result.

[0009] Preferably, the sample terminal is a crowdsourced terminal that has completed carrier phase ambiguity fixing and whose positioning results meet a preset accuracy threshold; the method further includes: The server continuously receives new observation data and location information uploaded by sample terminals according to a preset update cycle; The nodes and coefficients of the tropospheric modeling accuracy function are dynamically updated based on the newly received data to reflect the spatiotemporal variation characteristics of the tropospheric modeling accuracy in real time.

[0010] The tropospheric modeling accuracy calibration system based on posterior residuals is applicable to the aforementioned tropospheric modeling accuracy calibration method based on posterior residuals, including the server side and the terminal side. The server includes: The posterior residual calculation module is used to acquire the observation data uploaded by the sample terminal, construct the ionosphere-independent combined observation equation based on the observation data, and substitute the fixed carrier phase ambiguity into the ionosphere-independent combined observation equation to determine the posterior residual. The modeling variance inversion module is used to perform statistical processing based on the posterior residuals and, in conjunction with the tropospheric projection function and the satellite elevation angle, determine the zenith tropospheric modeling variance at the location of the sample terminal. The accuracy function construction module is used to model the variance and location information of the zenith troposphere based on multiple sample terminals. It uses a three-dimensional thin-plate spline radial basis function interpolation method with elevation difference weighting coefficients to construct the troposphere modeling accuracy function. The accuracy prediction and distribution module is used to predict the zenith tropospheric modeling variance of the location of the terminal to be located based on the location coordinates of the terminal to be located using the tropospheric modeling accuracy function, and then distribute the predicted zenith tropospheric modeling variance and the tropospheric delay parameter to the terminal to be located. The terminal side includes: The data receiving module is used to receive the tropospheric delay parameters and zenith tropospheric modeling variance sent by the server. The equation construction module is used to construct GNSS observation equations and tropospheric pseudo-observation constraint equations based on the tropospheric delay parameters. The weight adaptive module is used to determine the tropospheric pseudo-observation weights based on the received zenith tropospheric modeling variance, and to construct an extended weight matrix containing the tropospheric pseudo-observation weights. The joint solution module is used to perform weighted least squares joint solution of the GNSS observation equation and the tropospheric pseudo-observation constraint equation using the extended weight matrix to obtain the positioning result of the terminal to be positioned.

[0011] A computer device includes: a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the computer instructions to perform any of the tropospheric modeling accuracy calibration methods based on posterior residuals.

[0012] A computer-readable storage medium storing computer instructions for causing a computer to execute any of the tropospheric modeling accuracy calibration methods based on posterior residuals.

[0013] Compared with the prior art, the technical solution of this application has the following technical effects: This invention obtains the zenith tropospheric modeling variance at a given location by solving the posterior residual based on sample terminal observation data. It can intuitively reflect the true error level of the tropospheric model at the corresponding location based on the actual observation information of the terminal. The calculation is carried out based on the observation combination that eliminates ionospheric delay, reducing the impact of ionospheric interference factors on the modeling variance solution process, and ensuring that the obtained zenith tropospheric modeling variance fits the true modeling error state of the local atmospheric delay.

[0014] This invention combines terminal three-dimensional coordinates with elevation weights to construct a thin-plate spline accuracy function, which can simultaneously take into account the differences in tropospheric accuracy caused by changes in planar distance and terrain elevation, and completely restore the spatial distribution variation law of tropospheric modeling accuracy in the region. It can adapt to various complex regions with large terrain undulations and uneven water vapor distribution, and accurately predict the zenith tropospheric modeling variance corresponding to any point in the region.

[0015] This invention synchronously sends the predicted zenith tropospheric modeling variance to the terminal to be located. The terminal can calculate the weight value corresponding to the pseudo-observation of the troposphere based on this index, thereby autonomously adjusting the constraint strength of the tropospheric constraint equation in the overall solution process. This allows the tropospheric constraint strength to change flexibly with the local model accuracy status, adapting to the reliability of the tropospheric model at different locations.

[0016] This invention integrates navigation observation equations with adaptively adjusted tropospheric constraint equations for joint solution. It relies on the adapted extended weight matrix to complete coordinate solution, which can weaken the systematic positioning error caused by deviations in the tropospheric model, improve the stability of the overall positioning solution process, and continuously optimize the accuracy of navigation and positioning results in complex atmospheric environments.

[0017] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings.

[0018] The above and other objects, advantages and features of this application will become more apparent to those skilled in the art from the following detailed description of specific embodiments in conjunction with the accompanying drawings. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 A flowchart illustrating the accuracy calibration method for tropospheric modeling based on posterior residuals provided for some embodiments of this application; Figure 2 A flowchart illustrating the process of a terminal to be located, provided for some embodiments of this application; Figure 3 A schematic diagram of a tropospheric modeling accuracy calibration device provided for some embodiments of this application; Figure 4 Schematic diagram of a positioning device provided for some embodiments of this application; Figure 5 This is a schematic diagram of the structure of a computer device provided for some embodiments of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.

[0022] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0023] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.

[0024] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.

[0025] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.

[0026] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion.

[0027] Example 1: This application provides a tropospheric modeling accuracy calibration method based on posterior residuals, which can improve terminal positioning accuracy and the reliability of carrier phase ambiguity fixation. The tropospheric modeling accuracy calibration method can be applied to the server side, such as... Figure 1 As shown, the method for calibrating the accuracy of tropospheric modeling includes the following steps: S101. Based on the observation data of the Global Navigation Satellite System uploaded by the sample terminal, an ionospherically independent combined observation equation is constructed, and the fixed carrier phase ambiguity of the sample terminal is substituted into the ionospherically independent combined observation equation to determine the posterior residual of the sample terminal.

[0028] In this embodiment, the sample terminal is a crowdsourced positioning terminal that has completed the positioning calculation, including but not limited to vehicles, drones, mobile phones and other devices equipped with the Global Navigation Satellite System.

[0029] Global Navigation Satellite System (GNSS) observation data (hereinafter referred to as observation data) refers to the data observed during communication between the sample terminal and the satellite, including but not limited to carrier phase observations and pseudorange observations. Carrier phase observations refer to the fractional phase of the carrier wave that the sample terminal can directly observe by tracking the satellite carrier signal. Corresponding to carrier phase observations is carrier phase ambiguity, which the sample terminal cannot directly observe. Pseudorange observations refer to the distance between the satellite and the sample terminal directly measured by demodulating the ranging code sent by the satellite. Because satellite signals experience path delays when passing through the ionosphere and troposphere, and factors such as satellite orbit, receiver and satellite clock errors, and hardware deviations also introduce errors, pseudorange observations do not equal the true geometric distance between the satellite and the terminal.

[0030] Each sample terminal has observation links with multiple satellites. For example, sample terminal C1 has observation links with satellites S1, S2, and S3, and sample terminal C2 has observation links with satellites S1, S3, and S4. For any sample terminal C, if there is an observation link between sample terminal C and satellite S, sample terminal C can use multi-frequency mode to observe satellite S and obtain multiple sets of observation data corresponding to satellite S. Multi-frequency mode means that sample terminal C observes satellite S based on multiple carrier frequency bands. Each carrier frequency band corresponds to a set of observation data. For example, after sample terminals C1 and C2 observe satellites S1 and S2 based on carrier frequency bands f1 and f2 respectively, they can obtain the observation data shown in Table 1.

[0031] Table 1 Observational Data

[0032] Each sample terminal can construct the global navigation satellite system observation equation as shown in expression (1) based on the observation data of each carrier frequency band.

[0033]

[0034] Where L represents the carrier phase observation value, This represents the true geometric distance calculated based on satellite coordinates and sample terminal coordinates, where f represents the carrier frequency band and I represents the ionospheric electron content. λ represents ionospheric delay, T represents tropospheric delay, λ represents carrier wavelength, N represents carrier phase ambiguity, and ε represents noise.

[0035] For example, based on the two sets of observation data of satellite S1 from sample terminal C1 in Table 1, two global navigation satellite system observation equations as shown in expressions (2) and (3) can be obtained.

[0036]

[0037]

[0038] in, The observation equation constructed by sample terminal C1 based on observation data D11. The observation equation is constructed for sample terminal C1 based on observation data D12. , The set of observation equations for satellite S1 is formed by the sample terminal C1.

[0039] Each sample terminal can construct a set of observation equations for each satellite it observes.

[0040] For any sample terminal C, an ionospherically independent combined observation equation can be constructed based on the observation equation set of the i-th satellite observed by it, as shown in expression (4).

[0041]

[0042] in, and As shown in expression (5).

[0043] Substituting expressions (2) and (3) into expression (4), the coefficient of the first-order ionospheric delay term is reduced to zero, thus eliminating the ionospheric delay term. Therefore, the ionospherically independent combined observation equation can be understood as an observation equation with ionospheric delay eliminated.

[0044] By transforming expression (4), we can obtain the ionosphere-independent combined linearized observation equation shown in expression (6).

[0045]

[0046] in, for and difference, This represents the approximate geometric distance calculated based on satellite coordinates and the rough initial coordinates of the sample terminal. The equivalent wavelength corresponding to the ionosphere-independent combined observation equation. This represents the equivalent carrier phase ambiguity corresponding to the ionosphere-independent combined observation equation. Let i be the row vector of the design matrix for the i-th satellite. The parameters to be estimated only include the coordinate corrections for the sample terminal C. Let be the posterior residual of sample terminal C.

[0047] In expression (6) for , The expression, for , The expression is as follows. After the carrier phase ambiguity is fixed at the sample terminal C, the fixed carrier phase ambiguity can be substituted into expression (6). In this way, the left side of expression (6) is all known quantities, and the right side is... and This is an unknown quantity. When the carrier phase ambiguity is known, residual interference caused by floating-point offset of the carrier phase ambiguity can be eliminated. Simultaneously, based on the precise satellite orbit, satellite clock bias, and receiver clock bias corrections sent by the server, the observed values ​​can be pre-processed. , After completing the orbit and clock error compensation, the satellite orbit deviation and clock error can be omitted in expression (6).

[0048] Based on the above, after eliminating the ionospheric delay, the posterior residual The data only includes zenith tropospheric modeling variance, terminal observation noise, multipath error, and other incompletely modeled errors. Among these, terminal observation noise, multipath error, and other incompletely modeled errors account for a relatively small proportion; therefore, the posterior residuals can be considered... It is approximated as the variance of the zenith troposphere modeling.

[0049] In summary, a single sample terminal can observe multiple satellites, each with its own corresponding ionospherically independent combined linearized observation equation. For any given sample terminal and all its observed satellites, by minimizing the weighted sum of squared posterior residuals of all satellites, a joint least-squares solution is performed on the multiple ionospherically independent combined linearized observation equations corresponding to the sample terminal. This yields the coordinate correction amount for that sample terminal. Adjust the coordinates. Substituting back into the ionospherically independent combined linearized observation equations corresponding to each satellite, we can obtain the posterior residuals for each satellite. That is, each sample terminal can obtain multiple posterior residuals corresponding to the observed satellites.

[0050] Specifically, multiple ionosphere-independent linearized observation equations corresponding to the same sample terminal can be integrated into the form shown in expression (7).

[0051]

[0052] in, For all satellites observed by this sample terminal and The vector formed by the difference between them For the equivalent wavelength matrix, This is the equivalent carrier phase ambiguity vector. The design matrix rows after back-substituting carrier phase ambiguity. The parameter matrix to be estimated, Let be the posterior residual vector.

[0053] S102, based on the posterior residual, determine the zenith tropospheric modeling variance at the location of the sample terminal.

[0054] Specifically, based on expression (8), multiple posterior residuals of the same sample terminal can be statistically analyzed to obtain the variance of the unit weight posterior residual at the location of the corresponding sample terminal.

[0055]

[0056] in, The posterior residual vector in expression (7); is the observation weight matrix, which stores the weights of the observation equations corresponding to each satellite; n is the number of observation equations. Since each satellite corresponds to one observation equation, n can also be regarded as the number of satellites; m is the number of parameters to be estimated in expression (5). Since the number of parameters to be estimated x in expression (5) only includes the coordinate correction of the sample terminal C, m takes the value of 3, that is, Δx, Δy, Δz. nm is the degree of freedom of observation; The variance of the unit-weighted posterior residual is used to characterize the level of random noise in the overall observation.

[0057] Furthermore, the zenith tropospheric modeling variance at the location of each sample terminal can be determined based on the unit weight posterior residual variance, the tropospheric projection function, and the elevation angle of each satellite.

[0058] Specifically, the relationship between the unit weight posterior residual variance, the tropospheric projection function, and the elevation angle of each satellite is shown in expression (9).

[0059]

[0060] in, This represents the elevation angle of the i-th satellite observed by sample terminal C. This represents the tropospheric projection function, where n represents the number of satellites observed by sample terminal C. This represents the combined variance of terminal observation noise, multipath error, and other residual errors at sample terminal C. Model the variance of the zenith troposphere at the location of sample terminal C.

[0061] Furthermore, due to The value of is small and can be ignored. Therefore, expression (9) can be transformed into expression (10), and the variance of zenith tropospheric modeling can be obtained based on expression (10).

[0062]

[0063] For each sample terminal, the zenith tropospheric modeling variance of the corresponding sample terminal can be obtained based on expressions (9) to (10). Variance of zenith tropospheric modeling This can be viewed as the accuracy of the tropospheric model at the location of each sample terminal. When A larger value indicates lower accuracy of the tropospheric model. A smaller value indicates higher accuracy of the tropospheric model.

[0064] S103, based on the coordinates of the sample terminal's location and the variance of the zenith troposphere modeling, constructs a precision function.

[0065] In this embodiment, the precision function is shown in expression (11).

[0066]

[0067] in, , This represents the horizontal coordinate of the r-th sample terminal. This represents the height coordinates of the r-th sample terminal. This represents the spatial distance between the r-th sample terminal and the k-th sample terminal. This represents the radial basis function value between the r-th and k-th sample terminals, where N represents the number of sample terminals. Model the variance of the zenith troposphere for the r-th sample terminal predicted by the accuracy function. ~ Let be the coefficients of the polynomial to be solved. These are the coefficients of the radial basis function to be solved. The accuracy function can also be called a prediction model based on three-dimensional thin-plate spline function interpolation.

[0068] In practical applications, the spatial distance between two sample terminals can be determined based on the coordinates of any two sample terminals. . Each spatial distance Substitute the radial basis functions of the thin plate spline respectively The radial basis function values ​​can be obtained. Based on radial basis function values The coordinates of the sample terminal location and the variance of the r-th zenith troposphere modeling calculated in step S102. (i.e., using the zenith troposphere to model variance) Replace the precision function The coefficients of the precision function can be determined by solving for these coefficients. Furthermore, based on these coefficients, the precision function can be constructed.

[0069] Furthermore, based on the coordinates of any two sample terminals, the difference between their horizontal coordinates and their height coordinates can be calculated. The height coordinate difference is then weighted by a weighted coefficient to obtain the weighted height coordinate difference. Finally, based on the difference in horizontal coordinates and the weighted height coordinate difference, the spatial distance between the two sample terminals can be determined. Specifically, as shown in expression (12):

[0070] in, , This represents the horizontal coordinate of the r-th sample terminal. This represents the height coordinates of the r-th sample terminal. , This represents the horizontal coordinate of the k-th sample terminal. This represents the height coordinates of the k-th sample terminal. This represents the elevation difference weighting coefficient. This represents the spatial distance between the r-th sample terminal and the k-th sample terminal.

[0071] Then, Substituting the radial basis function of the thin plate spline as shown in expression (13) (That is, replacing the d variable in the radial basis function of the thin plate spline with...) The radial basis function values ​​can be obtained. .

[0072]

[0073] in, It represents a small positive number and is used to avoid the singularity of the logarithmic term when d=0.

[0074] Furthermore, a matrix expression as shown in expression (14) can be constructed based on the interpolation conditions of multiple sample points and the thin plate spline constraint conditions.

[0075]

[0076] in, The kernel matrix is ​​composed of the radial basis function values ​​between each sample terminal. Let be a polynomial matrix consisting of the three-dimensional coordinates of the sample terminal. , For the polynomial coefficient vector and radial basis function coefficient vector in expression (11).

[0077] Solving expression (14) yields the polynomial coefficients and radial basis function coefficients. Substituting the obtained polynomial coefficients and radial basis function coefficients into expression (11) allows us to construct the precision function.

[0078] S104. Based on the accuracy function and the coordinates of the terminal to be located, determine the zenith tropospheric modeling variance at the location of the terminal to be located, and send the zenith tropospheric modeling variance to the terminal to be located so that the terminal to be located can evaluate the accuracy of the tropospheric delay parameters sent by the tropospheric model based on the zenith tropospheric modeling variance.

[0079] Specifically, the spatial distance between the terminal to be located and each sample terminal can be determined based on expression (15).

[0080]

[0081] in, , This represents the horizontal coordinates of the terminal to be located. This indicates the height coordinates of the terminal to be located. , This represents the horizontal coordinate of the k-th sample terminal. This represents the height coordinates of the k-th sample terminal. This represents the elevation difference weighting coefficient. This represents the spatial distance between the terminal to be located and the k-th sample terminal.

[0082] spatial distance Substituting the radial basis function of the thin plate spline shown in expression (13), we obtain the radial basis function values. .

[0083] spatial distance Coordinates of the terminal to be located , , Substitute the values ​​into the precision function shown in expression (16). Since the coefficients in the precision function are already known, the zenith tropospheric modeling variance at the location of the terminal to be located can be obtained. .

[0084]

[0085] Combined with the reference expression (15), this application introduces an elevation difference weighting coefficient, which can not only consider the planar distance between the sample terminal and the terminal to be located, but also the influence of elevation difference on the accuracy of tropospheric delay modeling, thus making it suitable for the construction of tropospheric accuracy fields in river basins, mountain valleys and areas with obvious topographic relief.

[0086] Corresponding to the tropospheric modeling accuracy calibration method, this application also provides a positioning method based on the variance of zenith tropospheric modeling. This positioning method can be applied to the terminal to be positioned, such as... Figure 2 As shown, the positioning method includes the following steps: S201, receive the tropospheric delay parameters and zenith tropospheric modeling variance sent by the server.

[0087] Specifically, the zenith tropospheric modeling variance characterizes the accuracy of the tropospheric delay parameter. The zenith tropospheric modeling variance received by the terminal being located at at least some locations may differ.

[0088] S202, based on observation data from the Global Navigation Satellite System, constructs the observation equations of the Global Navigation Satellite System, and based on the tropospheric delay parameter, constructs the pseudo-observation constraint equations of the troposphere.

[0089] Specifically, the observation equations of the global navigation satellite system and the tropospheric pseudo-observation constraint equations can be combined into a joint equation, as shown in expression (17).

[0090]

[0091] in, The observations of all satellites observed by the terminal to be positioned and The matrix formed by the difference between them This represents the approximate geometric distance matrix calculated based on satellite coordinates and the rough initial coordinates of the terminal to be positioned. The design matrix for all satellites observed by the terminal to be positioned. For the posterior residual vector, A vector composed of zenith tropospheric delay parameters. The matrix of parameters to be estimated, This is the residual vector of the tropospheric pseudo-observation. Unlike expressions (6) and (7), in expression (17)... In addition to the coordinate correction of the terminal to be located, it also includes the zenith tropospheric delay parameter. Used from the parameter matrix to be estimated Extract the zenith tropospheric delay parameters.

[0092] In expression (17), , , The observation equations of the global navigation satellite system are constituted. , This constitutes the tropospheric pseudo-observation constraint equations. In the process of solving the observation equations of the Global Navigation Satellite System, the tropospheric pseudo-observation constraint equations are used to constrain the solution process.

[0093] S203, based on the variance of zenith tropospheric modeling, determines the weights of tropospheric pseudo-observations, and constructs an extended weight matrix based on the weights of tropospheric pseudo-observations and the weight matrix of global navigation satellite system observation data.

[0094] In this embodiment, the variance of zenith tropospheric modeling can be adjusted based on a preset accuracy adjustment coefficient, and the preset baseline accuracy can be added to the adjusted variance of zenith tropospheric modeling to obtain the variance of tropospheric pseudo-observations. Then, based on the variance of tropospheric pseudo-observations, the weight of tropospheric pseudo-observations can be determined. Specifically, as shown in expressions (18) and (19).

[0095]

[0096]

[0097] Specifically, in expression (18), Model the variance of the zenith troposphere issued by the server. This is the precision adjustment coefficient. For reference accuracy, For tropospheric pseudo-observation variance, This represents the weighting of pseudo-observations in the troposphere.

[0098] The extended weight matrix is ​​shown in expression (20).

[0099]

[0100] in, This is a weight matrix for global navigation satellite system observation data. The meaning and acquisition method of this weight matrix are similar to those of conventional techniques, and will not be elaborated here.

[0101] S204, based on the extended weight matrix, uses weighted least squares to solve the observation equations of the global navigation satellite system and the tropospheric pseudo-observation constraint equations to obtain the coordinates at the location.

[0102] Specifically, the tropospheric pseudo-observation constraint equation is used to constrain the solution process of the global navigation satellite system observation equation. The extended weight matrix is ​​used to control the constraint strength of the tropospheric pseudo-observation constraint equation. It can be seen from expression (19) that the tropospheric pseudo-observation weight... variance of tropospheric pseudo-observations Inversely proportional. Thus, in the tropospheric pseudo-observation variance... When the value is large (i.e., when the accuracy of the zenith tropospheric delay parameter is low), the weight of tropospheric pseudo-observations is increased. The variance of tropospheric pseudo-observations is relatively small, resulting in weaker constraint strength in the tropospheric pseudo-observation constraint equations during the solution of the global navigation satellite system observation equations. This reduces the risk of systematic bias and improves the positioning accuracy and robustness of the global navigation satellite system in complex tropospheric environments. When the value is small (i.e., when the accuracy of the zenith tropospheric delay parameter is high), the weight of tropospheric pseudo-observations is... The variance of zenith tropospheric observations is relatively large, resulting in strong constraints on the tropospheric pseudo-observation constraint equations during the solution of the global navigation satellite system observation equations. This application introduces zenith tropospheric modeling variance to dynamically adjust the constraint strength of the tropospheric pseudo-observation constraint equations, thereby improving solution stability and convergence efficiency.

[0103] Based on the above description, in some embodiments of this application, the zenith tropospheric modeling variance at the location of the sample terminal is determined based on the posterior residual of the sample terminal, and a precision function is constructed based on the coordinates of the sample terminal's location and the zenith tropospheric modeling variance. The precision function constructed using this method can accurately reflect the spatial differences in tropospheric modeling precision in complex environments such as river basins and mountain valleys. During terminal positioning, the zenith tropospheric modeling variance can be generated using this precision function based on the actual location of each terminal to be positioned. After the zenith tropospheric modeling variance is sent to the terminal to be positioned, the terminal can determine the reliability of the tropospheric model based on this variance. This allows for dynamic adjustment of the constraint strength of the tropospheric pseudo-observation constraint equations. When the reliability of the tropospheric model is high, the constraint strength of the pseudo-observation constraint equations can be increased, thereby improving solution efficiency. Conversely, when the reliability of the tropospheric model is low, the constraint strength of the pseudo-observation constraint equations can be decreased, thereby reducing the risk of systematic bias and improving the positioning accuracy and robustness of the global navigation satellite system in complex tropospheric environments.

[0104] Furthermore, this application provides a device for calibrating the accuracy of tropospheric modeling based on a posteriori residuals, such as... Figure 3 As shown, the tropospheric modeling accuracy calibration device includes: The equation construction module 301 is used to construct ionospherically independent combined observation equations based on the observation data of the Global Navigation Satellite System uploaded by the sample terminal, and to substitute the fixed carrier phase ambiguity of the sample terminal into the ionospherically independent combined observation equations to determine the posterior residual of the sample terminal. The first variance determination module 302 is used to determine the zenith tropospheric modeling variance at the location of the sample terminal based on the posterior residual. The precision function construction module 303 is used to construct a precision function based on the coordinates of the sample terminal's location and the variance of the zenith troposphere modeling. The second variance determination module 304 is used to determine the zenith tropospheric modeling variance at the location of the terminal to be located based on the accuracy function and the coordinates of the terminal to be located, and to send the zenith tropospheric modeling variance to the terminal to be located so that the terminal to be located can evaluate the accuracy of the tropospheric delay parameters sent by the tropospheric model based on the zenith tropospheric modeling variance.

[0105] In some embodiments, each sample terminal has an observation link with multiple satellites, and each sample terminal can obtain multiple posterior residuals corresponding one-to-one with the observed satellites; the first variance determination module 302 is specifically used for: By statistically analyzing multiple posterior residuals of the same sample terminal, the variance of the unit-weighted posterior residual at the location of the corresponding sample terminal is obtained. Based on the unit-weighted posterior residual variance, the tropospheric projection function, and the elevation angle of each satellite, the zenith tropospheric modeling variance at the location of each sample terminal is determined.

[0106] In some embodiments, the precision function construction module 303 is specifically used for: Determine the spatial distance between two sample terminals based on their coordinates. Substitute each spatial distance into the radial basis function of the thin plate spline to obtain the radial basis function value; Based on the radial basis function values, the coordinates of the sample terminal location, and the variance of the zenith troposphere modeling, the coefficients of the accuracy function are solved, and the accuracy function is constructed based on the solved coefficients.

[0107] In some embodiments, the coordinates of the sample terminal include horizontal and vertical coordinates; the precision function construction module 303 is specifically used for: Calculate the difference between the horizontal coordinates and the difference between the height coordinates of the two sample terminals; The difference in elevation coordinates is weighted by the elevation difference weighting coefficient to obtain the weighted difference in elevation coordinates; The spatial distance between the two sample terminals is determined based on the difference in their horizontal coordinates and the difference in their weighted vertical coordinates.

[0108] Furthermore, this application also provides a positioning device based on the variance of zenith tropospheric modeling. For example... Figure 4 As shown, the positioning device includes: Data receiving module 401 is used to receive tropospheric delay parameters and zenith tropospheric modeling variance sent by the server; Equation construction module 402 is used to construct global navigation satellite system observation equations based on global navigation satellite system observation data, and to construct tropospheric pseudo-observation constraint equations based on the tropospheric delay parameters; The weight determination module 403 is used to determine the pseudo-observation weights of the troposphere based on the variance of the zenith troposphere modeling, and to construct an extended weight matrix based on the pseudo-observation weights of the troposphere and the weight matrix of the observation data of the global navigation satellite system. The positioning module 404 is used to perform a weighted least squares joint solution on the observation equation of the global navigation satellite system and the tropospheric pseudo-observation constraint equation based on the extended weight matrix to obtain the coordinates of the current location.

[0109] In some embodiments, the weight determination module 403 is specifically used for: The variance of the zenith troposphere modeling is adjusted based on a preset accuracy adjustment coefficient. The pseudo-observation variance of the troposphere is obtained by adding the preset baseline accuracy to the adjusted zenith tropospheric modeling variance. The weights of tropospheric pseudo-observations are determined based on the variance of tropospheric pseudo-observations.

[0110] Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0111] In this embodiment, the tropospheric modeling accuracy calibration device based on a posteriori residuals and the positioning device based on zenith tropospheric modeling variance are presented in the form of functional units. Here, a unit refers to an ASIC (Application-Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0112] like Figure 5 The diagram shown is a structural schematic of a computer device provided in an embodiment of this application. Figure 5 As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 5 Take a processor 10 as an example.

[0113] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0114] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0115] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0116] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0117] This application provides a computer program product including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the method of any embodiment of this application.

[0118] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for calibrating the accuracy of tropospheric modeling based on posterior residuals, characterized in that, include: The server performs a tropospheric modeling accuracy calibration step, which includes: The observation data uploaded by the sample terminal is obtained, and an ionospherically independent combined observation equation is constructed based on the observation data. The fixed carrier phase ambiguity is then substituted into the ionospherically independent combined observation equation to determine the posterior residual. Based on the posterior residuals, statistical processing is performed, and combined with the tropospheric projection function and satellite elevation angle, the zenith tropospheric modeling variance at the location of the sample terminal is determined; Based on the variance and location information of zenith tropospheric modeling from multiple sample terminals, a three-dimensional thin-plate spline radial basis function interpolation method with elevation difference weighting coefficients is used to construct a tropospheric modeling accuracy function. Based on the location coordinates of the terminal to be located, the zenith tropospheric modeling variance of the location of the terminal to be located is predicted using the tropospheric modeling accuracy function, and the predicted zenith tropospheric modeling variance and the tropospheric delay parameter are sent to the terminal to be located. The terminal performs an adaptive positioning step, which includes: Receive the tropospheric delay parameters and zenith tropospheric modeling variance sent by the server; Based on the tropospheric delay parameters, GNSS observation equations and tropospheric pseudo-observation constraint equations are constructed. Based on the received zenith tropospheric modeling variance, the tropospheric pseudo-observation weights are determined, and an extended weight matrix containing the tropospheric pseudo-observation weights is constructed. The extended weight matrix is ​​used to solve the GNSS observation equation and the tropospheric pseudo-observation constraint equation using weighted least squares to obtain the positioning result of the terminal to be positioned.

2. The method for calibrating the accuracy of tropospheric modeling based on posterior residuals according to claim 1, characterized in that, In the tropospheric modeling accuracy calibration step performed by the server, the specific process of determining the posterior residual includes: Based on the carrier phase observations and pseudorange observations uploaded by the sample terminal, an ionospherically independent combined observation equation that eliminates the influence of first-order ionospheric delay is constructed. The integer ambiguity obtained by the fixed solution of the sample terminal is substituted into the ionosphere-independent combined observation equation as a known quantity to eliminate the influence of ambiguity floating-point deviation on the residual. Based on the ionospherically independent combined observation equation after substituting integer ambiguity, the difference between the observed value and the model prediction value is calculated to obtain the posterior residual.

3. The method for calibrating the accuracy of tropospheric modeling based on posterior residuals according to claim 1, characterized in that, The specific process for determining the zenith tropospheric modeling variance in the server-side tropospheric modeling accuracy calibration step includes: Statistical analysis is performed on multiple posterior residuals of the same sample terminal within a preset time window, and the variance of the unit-weighted posterior residual is calculated. Obtain the tropospheric projection function values ​​and satellite elevation angles when the sample terminal observes each satellite; Based on the unit-weighted posterior residual variance, the tropospheric projection function value, and the satellite elevation angle, the effects of observation noise and multipath error are separated, and the zenith tropospheric modeling variance at the location of the sample terminal is obtained by inversion.

4. The method for calibrating the accuracy of tropospheric modeling based on posterior residuals according to claim 1, characterized in that, The method of constructing the tropospheric modeling accuracy function using a three-dimensional thin-plate spline radial basis function interpolation method that incorporates an elevation difference weighting coefficient specifically includes: Using the three-dimensional position coordinates of multiple sample terminals as nodes and the corresponding zenith troposphere modeling variance as node values, a three-dimensional thin-plate spline radial basis function model is constructed. When calculating the spatial distance between any two sample terminal nodes, the horizontal Euclidean distance and the elevation difference are multiplied by preset weighting coefficients and then combined to obtain the weighted spatial distance. Based on the weighted spatial distance, the coefficients of the radial basis function model of the three-dimensional thin plate spline are solved to obtain the tropospheric modeling accuracy function, which can characterize the spatial distribution characteristics of tropospheric modeling accuracy in terrain undulation areas.

5. The method for calibrating the accuracy of tropospheric modeling based on posterior residuals according to claim 1, characterized in that, In the adaptive positioning step performed on the terminal side, the tropospheric pseudo-observation weights are determined based on the received zenith tropospheric modeling variance, specifically including: The reciprocal of the received zenith tropospheric modeling variance is used as the initial weight of the tropospheric pseudo-observations; When the variance of the zenith tropospheric modeling is greater than a preset variance threshold, the initial weights are reduced according to a preset attenuation factor to obtain the final tropospheric pseudo-observation weights. When the variance of the zenith tropospheric modeling is less than or equal to a preset variance threshold, the initial weights are directly used as the final tropospheric pseudo-observation weights.

6. The method for calibrating the accuracy of tropospheric modeling based on posterior residuals according to claim 1, characterized in that, In the adaptive positioning step performed on the terminal side, the extended weight matrix is ​​used to perform a weighted least squares joint solution of the GNSS observation equation and the tropospheric pseudo-observation constraint equation, specifically including: Based on the extended weight matrix, the GNSS observation equations and the tropospheric pseudo-observation constraint equations are combined into a joint observation equation set; The normal equations of the joint observation equation set are constructed to obtain a normal equation matrix that includes the weights of tropospheric pseudo-observations; The normal equation matrix is ​​solved to simultaneously estimate the position parameters and tropospheric wet delay residual parameters of the terminal to be located, which are used as the positioning result.

7. The method for calibrating the accuracy of tropospheric modeling based on posterior residuals according to claim 1, characterized in that, The sample terminal is a crowdsourced terminal that has completed carrier phase ambiguity fixing and whose positioning results meet a preset accuracy threshold; the method further includes: The server continuously receives new observation data and location information uploaded by sample terminals according to a preset update cycle; The nodes and coefficients of the tropospheric modeling accuracy function are dynamically updated based on the newly received data to reflect the spatiotemporal variation characteristics of the tropospheric modeling accuracy in real time.

8. A tropospheric modeling accuracy calibration system based on posterior residuals, applicable to the tropospheric modeling accuracy calibration method based on posterior residuals as described in any one of claims 1-7, characterized in that, Including both the server and the terminal side; The server includes: The posterior residual calculation module is used to acquire the observation data uploaded by the sample terminal, construct the ionosphere-independent combined observation equation based on the observation data, and substitute the fixed carrier phase ambiguity into the ionosphere-independent combined observation equation to determine the posterior residual. The modeling variance inversion module is used to perform statistical processing based on the posterior residuals and, in conjunction with the tropospheric projection function and the satellite elevation angle, determine the zenith tropospheric modeling variance at the location of the sample terminal. The accuracy function construction module is used to model the variance and location information of the zenith troposphere based on multiple sample terminals. It uses a three-dimensional thin-plate spline radial basis function interpolation method with elevation difference weighting coefficients to construct the troposphere modeling accuracy function. The accuracy prediction and distribution module is used to predict the zenith tropospheric modeling variance of the location of the terminal to be located based on the location coordinates of the terminal to be located using the tropospheric modeling accuracy function, and then distribute the predicted zenith tropospheric modeling variance and the tropospheric delay parameter to the terminal to be located. The terminal side includes: The data receiving module is used to receive the tropospheric delay parameters and zenith tropospheric modeling variance sent by the server. The equation construction module is used to construct GNSS observation equations and tropospheric pseudo-observation constraint equations based on the tropospheric delay parameters. The weight adaptive module is used to determine the tropospheric pseudo-observation weights based on the received zenith tropospheric modeling variance, and to construct an extended weight matrix containing the tropospheric pseudo-observation weights. The joint solution module is used to perform weighted least squares joint solution of the GNSS observation equation and the tropospheric pseudo-observation constraint equation using the extended weight matrix to obtain the positioning result of the terminal to be positioned.

9. A computer device, characterized in that, include: The system includes a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform the tropospheric modeling accuracy calibration method based on posterior residuals as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the tropospheric modeling accuracy calibration method based on a posteriori residuals as described in any one of claims 1 to 7.

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