Satellite orbit deviation correction estimation method based on broadcast ephemeris of wide area network PPP-RTK

Abstract

A method for ephemeris satellite orbit deviation correction estimation based on wide area network (WAN) PPP-RTK includes the following steps: first, calculating the satellite position; then, linearizing the GNSS non-differenced observation equations based on the satellite position; and finally, eliminating rank deficiency to obtain a full-rank estimable observation model. Based on the full-rank estimable observation model, broadcast ephemeris orbit deviation correction parameters are introduced, transforming the full-rank estimable observation model into a WAN multi-epoch measurement model. Based on the WAN multi-epoch observation model, the time-varying characteristics of each parameter to be estimated are introduced, and dynamic models corresponding to these time-varying characteristics are constructed. First, a full-rank equation set is constructed based on the WAN multi-epoch observation model and the dynamic model, and then the full-rank equation set is initialized to obtain orbit deviation correction information. This invention does not rely on external infrastructure for wide-area high-precision positioning.

Description

Technical Field

[0001] This invention relates to an improvement in high-precision data processing technology for global navigation satellite systems, belonging to the field of satellite precision data processing, and particularly to a method for ephemeris satellite orbit deviation correction estimation based on wide area network PPP-RTK. Background Technology

[0002] PPP-RTK is a key technology for high-precision GNSS positioning, mainly consisting of two parts: a reference network and a user terminal. The network generates correction information such as satellite orbit, clock bias, phase deviation, and atmospheric delay. The user terminal uses this information to achieve high-precision positioning and integer ambiguity fixation. Among these, the accuracy of the satellite orbit directly determines the positioning accuracy, convergence speed, and service range of PPP-RTK.

[0003] Existing PPP-RTK satellite orbit processing methods rely on globally distributed GNSS stations to directly estimate precise orbits in order to ensure continuous satellite visibility and sufficient geometric strength. However, this method is highly dependent on infrastructure, complex to implement, and costly to deploy, making it difficult to meet the application requirements of autonomous and independent high-precision services. When using this fixed orbit strategy, commonly used orbit information includes broadcast ephemeris and precise orbit products. Broadcast ephemeris has limited accuracy, and under wide-area reference network conditions, orbit errors are difficult to be effectively absorbed by clock bias parameters, resulting in a particularly prominent problem of insufficient accuracy. This also fails to meet the requirements for stable operation of wide-area PPP-RTK.

[0004] Patent application CN202410154469.4, filed on February 2, 2024, discloses a precise point positioning method based on accurate modeling of broadcast ephemeris errors, relating to the field of satellite navigation technology, specifically to the field of precise point positioning. The method theoretically and precisely models the orbital errors and clock errors of individual satellites within different satellite systems based on their broadcast ephemeris error characteristics. Then, based on actual positioning calculations, it selects a combination of orbital error and clock error models from different systems for positioning calculations, converting the broadcast ephemeris parameters into the same parameter form as the precise ephemeris. Following the traditional ionospheric PPP positioning calculation steps, it uses a BE-PPP model that incorporates orbital error and clock error constraint correction models, substituting the converted broadcast ephemeris parameters into the model for positioning calculations, thus obtaining the final high-precision positioning solution. While this solution addresses the problem that the satellite orbital and clock error parameters of the broadcast ephemeris cannot be effectively constrained, affecting positioning accuracy, it does not solve the problem of relying on external infrastructure for wide-area high-precision positioning.

[0005] The information disclosed in this background section is intended only to enhance the understanding of the overall background of this patent application and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to overcome the problem that existing technologies require external infrastructure for wide-area high-precision positioning, and to provide a wide-area network PPP-RTK-based broadcast ephemeris satellite orbit deviation correction estimation method that does not require external infrastructure for wide-area high-precision positioning.

[0007] To achieve the above objectives, the technical solution of the present invention is: a method for ephemeris satellite orbital deviation correction estimation based on wide area network PPP-RTK, wherein the method for ephemeris satellite orbital deviation correction estimation based on wide area network PPP-RTK includes the following steps:

[0008] The first step is to calculate the satellite position based on the continuous observation data from the reference station by broadcasting ephemeris. Then, based on the satellite position, the GNSS non-differential observation equation is linearized. Finally, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated to obtain a full-rank estimable observation model.

[0009] The second step is to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model by introducing broadcast ephemeris orbital deviation correction parameters based on the full-rank estimable observation model.

[0010] The third step is to introduce the time-varying characteristics of each parameter to be estimated into the multi-epoch observation model based on the wide area network, and construct dynamic models corresponding to the time-varying characteristics respectively.

[0011] The fourth step is to first construct a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initialize the full-rank equation system to obtain orbital deviation correction information.

[0012] In the first step, the satellite position is calculated using broadcast ephemeris data based on continuous observation data from the reference station. Then, the GNSS non-differenced observation equation is linearized based on this satellite position, specifically as follows:

[0013] In a wide area reference network, a reference station is set up. For satellite In frequency Continuous observations are conducted on the reference station, whose three-dimensional coordinate vector is known. ,satellite Location Calculated from broadcast ephemeris, denoted as Since the broadcast ephemeris position vector is affected by bias, it is corrected by estimating its corresponding orbital bias. ,assumed dimensional vector and Each contains phase and pseudorange observations The linearized model of this observation method is expressed as:

[0014] ;

[0015] in, and These represent the carrier phase observation minus the calculated value and the pseudorange observation minus the calculated value, respectively, after calculation using broadcast ephemeris orbits, representing the satellite-to-Earth distance. Calculated from the broadcast ephemeris orbit ;

[0016] This represents the unit vector indicating the line-of-sight direction between the satellite and the receiver;

[0017] express 1-dimensional unit column vector; and These represent the clock biases of the satellite and receiver, respectively. This indicates the first-order ionospheric slack delay at the first frequency;

[0018] dimensional vector From coefficients constitute;

[0019] and These represent receiver and satellite code offsets, respectively.

[0020] express A diagonal matrix with diagonal elements of ;

[0021] Represents a real-valued ambiguity vector;

[0022] Expressed as ,in The ambiguity is in integer form. and These represent non-integer receiver and satellite phase offsets, respectively.

[0023] Tropospheric delay corrected by prior model to and middle.

[0024] In the first step, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated. Specifically, the rank deficiency of the equation is eliminated by applying minimum constraints to the S-basis reference, restoring the rank-deficient GNSS non-differential observation equation to a full-rank estimable model, and determining the estimable forms of orbital deviation correction, clock error, ionospheric delay, phase deviation, code deviation, and ambiguity.

[0025] The full-rank estimable observation model is as follows:

[0026] ;

[0027] in, .

[0028] In the second step, based on the full-rank estimable observation model, a broadcast ephemeris orbital bias correction parameter is introduced to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model. Specifically, the following symbols are defined first:

[0029] The observation model is represented as:

[0030] ;

[0031] in, Indicates the GNSS reference network in consecutive epochs The sequence of collected observations.

[0032] In the third step, the parameters to be estimated include orbital deviation correction, satellite clock error, receiver clock error, ionospheric delay, satellite-receiver phase deviation, satellite-receiver code deviation, and ambiguity parameters.

[0033] The third step, the dynamic model, is as follows:

[0034] ;

[0035] in, express of First-order time derivative; The sampling interval represents the observation values, and the highest order of the polynomial dynamic model is... , and These are spurious observations with zero mean.

[0036] The dynamic model further includes: using ionospheric delay as a time-varying floating-point parameter and instrument bias as a time-dependent parameter, whereby instrument bias includes code bias and phase bias at the receiver and satellite ends.

[0037] The fourth step involves first constructing a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initializing the full-rank equation system to obtain orbital deviation correction information. Specifically, this involves combining the multi-epoch observation model and the parameter dynamic model to perform orbital and clock corrections. constant velocity model The full-rank system of equations is constructed as follows:

[0038] .

[0039] After generating the orbital deviation correction information, the generated orbital deviation correction information, along with satellite clock error correction, ionospheric correction, and phase deviation correction, is broadcast to the user terminal for use in fixing integer ambiguity and high-precision positioning at the user terminal.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] 1. In this invention, a method for ephemeris satellite orbital deviation correction estimation based on wide area network (WAN) PPP-RTK, the satellite position is first calculated using broadcast ephemeris data from a reference station. Then, the GNSS non-differential observation equations are linearized based on these satellite positions. Finally, the rank deficiency of the linearized GNSS non-differential observation equations is eliminated to obtain a full-rank estimable observation model. Based on this full-rank estimable observation model, broadcast ephemeris orbital deviation correction parameters are introduced, transforming the full-rank estimable observation model into a WAN multi-epoch observation model. Based on the WAN multi-epoch observation model, the time-varying characteristics of each parameter to be estimated are introduced, and dynamic models corresponding to these time-varying characteristics are constructed. First, a full-rank equation set is constructed based on the WAN multi-epoch observation model and the dynamic model. Then, the full-rank equation set is initialized to obtain orbital deviation correction information. The advantages of this design are as follows:

[0042] First, by using the broadcast ephemeris orbit as a benchmark, the deviation correction parameters of the satellite's actual orbit relative to the broadcast ephemeris orbit are estimated using observation data from the wide area reference network. This eliminates the need to rely on a globally distributed tracking network for precise satellite orbit determination and also eliminates the need to rely entirely on external precise orbit products. This reduces the dependence of the wide area network PPP-RTK service on external infrastructure and improves the autonomy and feasibility of wide area high-precision services.

[0043] Secondly, by calculating satellite positions through broadcast ephemeris and linearizing the GNSS non-differenced observation equations, the rank deficiency is eliminated to obtain a full-rank estimable observation model. This solves the problem that the clock error, orbit, and ambiguity parameters of the non-differenced model are strongly correlated and cannot be directly solved, ensuring that all parameters are mathematically estimable and providing a stable and reliable mathematical foundation for subsequent orbital deviation estimation.

[0044] Thirdly, an orbital deviation correction parameter relative to the broadcast ephemeris is introduced to construct a multi-epoch observation model. Instead of directly using the broadcast ephemeris with limited accuracy, the orbital error is explicitly expressed as an estimable parameter, which can accurately separate and compensate for the orbital error of the broadcast ephemeris itself, significantly improving the actual accuracy of satellite orbit use. The multi-epoch joint observation model is adopted to unify the modeling of observations at multiple times, making full use of the redundant information of the time series, suppressing observation noise and random errors, and making the estimation of orbital deviation parameters smoother and more stable.

[0045] Fourth, construct corresponding dynamic models for different parameters to be estimated, so that various parameters change reasonably according to their own physical characteristics, avoiding overfitting or abnormal fluctuations, and improving the robustness of the overall solution.

[0046] Fifth, the final generation of high-precision orbital deviation correction information can significantly improve the positioning accuracy of the user terminal, accelerate the ambiguity fixing speed, expand the PPP-RTK service range, and at the same time ensure the system's autonomy, stability and practicality.

[0047] Therefore, this invention does not require external infrastructure when performing wide-area high-precision positioning.

[0048] 2. In this invention, a method for ephemeris satellite orbit deviation correction estimation based on wide area network (WAN) PPP-RTK is proposed. Different dynamic models are constructed for the temporal variation characteristics of different parameters in the full-rank observation model, and a multi-epoch recursive filtering model for the wide-area reference network is established. This effectively describes the temporal evolution of satellite orbit deviation correction parameters and related parameters, thereby improving the problems of weak estimability of orbit deviation correction parameters, near-rank deficiency of the model, and unstable initialization under WAN conditions. This enhances the stability and reliability of parameter estimation. The broadcast ephemeris orbit deviation is modeled using low-order polynomial dynamics, which conforms to the physical characteristics of slow and smooth changes in orbit deviation, avoiding the misestimation of high-frequency noise as true orbit deviation, and improving the accuracy and reliability of correction information. A constant constraint is applied to the orbit correction and satellite clock error change rate, effectively suppressing rapid parameter jumps, reducing parameter estimation variance, and making orbit and clock error corrections more continuous and smooth. Therefore, this invention improves the problems of weak estimability of orbit deviation correction parameters, near-rank deficiency of the model, and unstable initialization under WAN conditions.

[0049] 3. In the wide-area network PPP-RTK-based method for ephemeris satellite orbital deviation estimation, this invention enables the joint estimation of ephemeris satellite orbital deviation correction parameters and related parameters based on multi-epoch continuous observation data from a wide-area reference network. This provides a reliable foundation for the generation of wide-area network PPP-RTK correction information and is beneficial for improving the application capabilities of wide-area high-precision navigation, positioning, and timing services. Therefore, this invention enhances the application capabilities of wide-area high-precision navigation, positioning, and timing services. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the structure of the present invention.

[0051] Figure 2 This is a geographical distribution map of the GNSS stations used in this invention.

[0052] Figure 3 This is a time series and a local sequence diagram of the first-order linear fitting of satellite orbit deviation correction in the x, y, and z directions in this invention.

[0053] Figure 4 This is a schematic diagram of the standard deviation of the double-difference orbital deviation correction based on the ambiguity floating-point solution in this invention.

[0054] Figure 5 This is a schematic diagram of the standard deviation of the double-difference orbital deviation correction based on the fixed ambiguity solution in this invention.

[0055] Figure 6 This is a user positioning performance diagram of the GOP6 station in this invention.

[0056] Figure 7 This is a user positioning performance diagram of the PASA station in this invention. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] See Figures 1 to 7 A method for ephemeris satellite orbital deviation correction estimation based on wide area network PPP-RTK, comprising the following steps:

[0059] The first step is to calculate the satellite position based on the continuous observation data from the reference station by broadcasting ephemeris. Then, based on the satellite position, the GNSS non-differential observation equation is linearized. Finally, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated to obtain a full-rank estimable observation model.

[0060] The second step is to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model by introducing broadcast ephemeris orbital deviation correction parameters based on the full-rank estimable observation model.

[0061] The third step is to introduce the time-varying characteristics of each parameter to be estimated into the multi-epoch observation model based on the wide area network, and construct dynamic models corresponding to the time-varying characteristics respectively.

[0062] The fourth step is to first construct a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initialize the full-rank equation system to obtain orbital deviation correction information.

[0063] In the first step, the satellite position is calculated using broadcast ephemeris data based on continuous observation data from the reference station. Then, the GNSS non-differenced observation equation is linearized based on this satellite position, specifically as follows:

[0064] In a wide area reference network, a reference station is set up. For satellite In frequency Continuous observations are conducted on the reference station, whose three-dimensional coordinate vector is known. ,satellite Location Calculated from broadcast ephemeris, denoted as Since the broadcast ephemeris position vector is affected by bias, it is corrected by estimating its corresponding orbital bias. ,assumed dimensional vector and Each contains phase and pseudorange observations The linearized model of this observation method is expressed as:

[0065] ;

[0066] in, and These represent the carrier phase observation minus the calculated value and the pseudorange observation minus the calculated value, respectively, after calculation using broadcast ephemeris orbits, representing the satellite-to-Earth distance. Calculated from the broadcast ephemeris orbit ;

[0067] This represents the unit vector indicating the line-of-sight direction between the satellite and the receiver;

[0068] express 1-dimensional unit column vector; and These represent the clock biases of the satellite and receiver, respectively. This indicates the first-order ionospheric slack delay at the first frequency;

[0069] dimensional vector From coefficients constitute;

[0070] and These represent receiver and satellite code offsets, respectively.

[0071] express A diagonal matrix with diagonal elements of ;

[0072] Represents a real-valued ambiguity vector;

[0073] Expressed as ,in The ambiguity is in integer form. and These represent non-integer receiver and satellite phase offsets, respectively.

[0074] Tropospheric delay corrected by prior model to and middle.

[0075] In the first step, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated. Specifically, the rank deficiency of the equation is eliminated by applying minimum constraints to the S-basis reference, restoring the rank-deficient GNSS non-differential observation equation to a full-rank estimable model, and determining the estimable forms of orbital deviation correction, clock error, ionospheric delay, phase deviation, code deviation, and ambiguity.

[0076] The full-rank estimable observation model is as follows:

[0077] ;

[0078] in, .

[0079] In the second step, based on the full-rank estimable observation model, a broadcast ephemeris orbital bias correction parameter is introduced to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model. Specifically, the following symbols are defined first:

[0080] The observation model is represented as:

[0081] ;

[0082] in, Indicates the GNSS reference network in consecutive epochs The sequence of collected observations.

[0083] In the third step, the parameters to be estimated include orbital deviation correction, satellite clock error, receiver clock error, ionospheric delay, satellite-receiver phase deviation, satellite-receiver code deviation, and ambiguity parameters.

[0084] The third step, the dynamic model, is as follows:

[0085] ;

[0086] in, express of First-order time derivative; The sampling interval represents the observation values, and the highest order of the polynomial dynamic model is... , and These are spurious observations with zero mean.

[0087] The dynamic model further includes: using ionospheric delay as a time-varying floating-point parameter and instrument bias as a time-dependent parameter, whereby instrument bias includes code bias and phase bias at the receiver and satellite ends.

[0088] The fourth step involves first constructing a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initializing the full-rank equation system to obtain orbital deviation correction information. Specifically, this involves combining the multi-epoch observation model and the parameter dynamic model to perform orbital and clock corrections. constant velocity model The full-rank system of equations is constructed as follows:

[0089] .

[0090] After generating the orbital deviation correction information, the generated orbital deviation correction information, along with satellite clock error correction, ionospheric correction, and phase deviation correction, is broadcast to the user terminal for use in fixing integer ambiguity and high-precision positioning at the user terminal.

[0091] The supplementary technical features of this design are as follows:

[0092] This invention obtains high-precision satellite orbit deviation correction information that can be used for PPP-RTK services by utilizing only wide-area reference network observation data and broadcast ephemeris data without relying on precision orbit products and global stations, thereby improving the autonomy, stability and practicality of wide-area high-precision positioning services.

[0093] Example 1:

[0094] A method for ephemeris satellite orbital deviation correction estimation based on PPP-RTK over wide area networks, comprising the following steps:

[0095] The first step is to calculate the satellite position based on the continuous observation data from the reference station by broadcasting ephemeris. Then, based on the satellite position, the GNSS non-differential observation equation is linearized. Finally, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated to obtain a full-rank estimable observation model.

[0096] The second step is to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model by introducing broadcast ephemeris orbital deviation correction parameters based on the full-rank estimable observation model.

[0097] The third step is to introduce the time-varying characteristics of each parameter to be estimated into the multi-epoch observation model based on the wide area network, and construct dynamic models corresponding to the time-varying characteristics respectively.

[0098] The fourth step is to first construct a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initialize the full-rank equation system to obtain orbital deviation correction information.

[0099] Example 2:

[0100] Example 2 is basically the same as Example 1, except that:

[0101] In a wide area reference network, a reference station is set up. For satellite In frequency Continuous observations are conducted on the reference station, whose three-dimensional coordinate vector is known. ,satellite Location Calculated from broadcast ephemeris, denoted as Since the broadcast ephemeris position vector is affected by bias, it is corrected by estimating its corresponding orbital bias. This data, along with its corrections, is then broadcast to the PPP-RTK user terminal. To achieve this, the corresponding GNSS observation equations first need to be linearized, assuming... dimensional vector and Each contains phase and pseudorange observations The linearized model of this observation method is expressed as:

[0102] ;

[0103] in, and These represent the carrier phase observation minus the calculated value and the pseudorange observation minus the calculated value, respectively, after calculation using broadcast ephemeris orbits, representing the satellite-to-Earth distance. Calculated from the broadcast ephemeris orbit ;

[0104] This represents the unit vector indicating the line-of-sight direction between the satellite and the receiver;

[0105] express 1-dimensional unit column vector; and These represent the clock biases of the satellite and receiver, respectively. This indicates the first-order ionospheric slack delay at the first frequency;

[0106] dimensional vector From coefficients constitute;

[0107] and These represent receiver and satellite code offsets, respectively.

[0108] express A diagonal matrix with diagonal elements of ;

[0109] Represents a real-valued ambiguity vector;

[0110] Expressed as ,in The ambiguity is in integer form. and These represent non-integer receiver and satellite phase offsets, respectively.

[0111] Tropospheric delay corrected by prior model to and In, excluding the ambiguity term , , The unit is weeks, and the unit for the rest is meters.

[0112] To select the S-basis and determine the corresponding estimable parameters, assumptions must first be made regarding the time-varying characteristics of the parameters in the linearized model. It is assumed that time-stable parameters, namely phase / code bias and orbital bias corrections, follow a constant-state stochastic process, while the more rapidly time-varying satellite clock bias is modeled using a constant-velocity process. In the absence of phase cycle slips, the integer ambiguity vector... Treated as a time-invariant parameter, while the receiver clock bias... and ionospheric delay Treating the parameters as time-independent, and given the above assumptions, choosing a commonly used S-basis yields the following full-rank estimable observation model:

[0113] ;

[0114] in, Unlike the original parameters, the full-rank model contains parameters derived from... The estimable parameters, represented by symbols, are detailed in Table 1 below. The parameters in the table... Indicates an epochal index;

[0115] Table 1 shows the estimable parameters under a given Kalman filter model and associated S-basis, with the time interval of consecutive epochs represented by... It means that the first Epoch satellite clock speed express:

[0116]

[0117]

[0118] .

[0119] Example 3:

[0120] Example 3 is basically the same as Example 1, except that:

[0121] Although individual orbital deviation corrections are not precise enough, their combination with other corrections is sufficient to fix integer ambiguities at the user end. Furthermore, to ensure sufficient accuracy of the time-delayed combined corrections in the presence of correction delays, the central portion of the orbital deviation correction needs to be packaged and transmitted to the user along with the satellite clock error correction. This optimized transmission strategy is based on orbital deviation corrections obtained from multi-epoch joint calculations and relies on the assumption that the orbital deviation corrections are time-dependent. Therefore, it is necessary to focus on the time-varying characteristics of the orbital deviation corrections in the dynamic model and propose a wide-area reference network multi-epoch joint processing model. First, the following notations are defined:

[0122] The observation model is represented as:

[0123] ;

[0124] in, Indicates the GNSS reference network in consecutive epochs The sequence of collected observations.

[0125] Through the above steps, the orbital deviation correction parameters of the broadcast ephemeris satellites are introduced into the original observation equations, and the rank deficiency of the model is eliminated to construct an observation model suitable for multi-epoch joint estimation of the wide-area reference network, thus providing a foundation for the subsequent establishment of a parameter dynamic model and a wide-area network filtering solution model.

[0126] After the observation model is constructed, the dynamic model of the parameters needs to be determined. First, the orbital deviation correction parameters need to be considered. The orbital deviation correction parameter depends on the position of the broadcast ephemeris satellite, which itself is uncertain. Therefore, the time variation of the orbital deviation correction parameter is affected by both the actual satellite orbital dynamics and the time-varying error of the broadcast ephemeris satellite position. For consecutive epochs within the same set of broadcast ephemeris valid intervals, the satellite orbital deviation correction parameter usually exhibits a smooth and continuous variation characteristic. However, at the time of broadcast ephemeris update switching, the orbital deviation correction parameter may jump. Therefore, within the valid time period of a single set of broadcast ephemeris, the satellite orbital deviation correction parameter is modeled as a low-order polynomial process that varies continuously with time.

[0127] The dynamic model is:

[0128] ;

[0129] in, express of First-order time derivative; The sampling interval represents the observation values, and the highest order of the polynomial dynamic model is... , and These are spurious observations with zero mean.

[0130] Zero-mean pseudo-observation and Temporal consistency is imposed across parameters in consecutive epochs, where the strength of this consistency is controlled by the assumed process noise variance. Smaller variance imposes stronger temporal stability, effectively controlling parameters to change slowly over time, while larger variance allows for more flexible temporal variations.

[0131] This invention employs an ionospheric floating-point model, where the complete ionospheric delay is treated as a time-varying variable. Instrument biases, including code and phase biases at the receiver and satellite ends, are also modeled as time-dependent parameters with associated uncertainties, as they may vary over time. Regarding orbital corrections and satellite clock offsets, with respect to their first-order time derivatives, for example, Apply constraints, assuming they are constants.

[0132] Example 4:

[0133] Example 4 is basically the same as Example 1, except that:

[0134] Combining multi-epoch observation models and parameter dynamic models, orbit and clock correction constant velocity model The full-rank system of equations is constructed as follows:

[0135] .

[0136] Because the orbital deviation correction parameters are poorly estimable, the basic model approaches rank deficiency. Therefore, filter initialization requires additional constraints on the orbital deviation correction parameters. Due to the boundedness of the orbital deviation correction, spurious observations are introduced. Initialize the data, setting its empirical variance to 3m. 2 , The processing noise variance is set to 1×10. −2 m 2 / s.

[0137] Example 5:

[0138] Example 5 is basically the same as Example 1, except that:

[0139] The geographical distribution of the selected GNSS stations in this invention is shown in the figure. Figure 2 The blue triangles represent reference stations that constitute the wide-area GNSS reference network, the blue pentagrams represent the center position of the reference network, and the red dots are the user stations selected by this invention.

[0140] This embodiment is used to illustrate the accuracy of orbit deviation correction parameter estimation under wide-area GNSS reference network conditions, as well as its time-varying characteristics and modeling analysis, using two user stations, GOP6 (approximately 500 km from the main station) and PASA (approximately 1000 km from the main station), as representatives.

[0141] Figure 3 The time series of satellite orbital deviation corrections in the x, y, and z directions, as well as the local sequences of the first-order linear fit, are presented. The left figure shows the time series of satellite orbital deviation corrections in the x, y, and z directions, while the right figure shows the first-order linear fit applied to model the time variation of orbital deviation corrections. The black-framed wide-area data is selected as an example, and the red dashed line represents the fitting residuals. Data was collected in 2025 (DoY182), using the G25 satellite as a representative example. Figure 5 As shown on the left, the converted orbital deviation correction changes smoothly within the effective interval of IODE. For GPS, IODE is typically updated every two hours. However, during IODE switching periods, all directional components of the orbital correction exhibit discontinuities, accompanied by corresponding changes in their temporal trends. Further magnifying the wide area within the black box shown on the right, the results of simulating orbital deviation correction using first-order linear fitting show that while the linear model captures the overall trend well, centimeter-level fitting residuals still exist. This indicates that orbital deviation correction can be accurately modeled using polynomial functions within the validity period of a single ephemeris dataset.

[0142] Figure 4 The standard deviation of the double-difference orbital deviation correction based on ambiguity floating-point solutions is presented. The selected G29 satellite is highlighted in blue. The left and right figures show the ambiguity floating-point solution results for GOP6 and PASA, located approximately 500 km and 1000 km from the master station, respectively. It can be seen that the double-difference orbital deviation correction for GOP6 exhibits significantly higher accuracy than that for PASA. However, even for GOP6, achieving a high level of accuracy, such as one to two centimeters, requires several hours of convergence time.

[0143] Figure 5The standard deviations of double-difference orbital deviation corrections based on ambiguity-fixed solutions are presented. Blue dots highlight the selected G29 satellite. The left and right figures show the ambiguity fixing results for GOP6 and PASA, located approximately 500 km and 1000 km from the master station, respectively. Compared to floating-point solutions, double-difference orbital deviation corrections converge rapidly to very high accuracy once ambiguities are fixed. The standard deviation for PASA reaches one to two centimeters, while the standard deviation for GOP6 even reaches millimeter-level accuracy. However, this performance is highly dependent on a high success rate of ambiguity fixing.

[0144] Example 6:

[0145] Example 6 is basically the same as Example 1, except that:

[0146] This embodiment illustrates the application effect of the satellite orbit deviation correction parameters estimated by the present invention in wide area network PPP-RTK user positioning. The reference network consists of 11 reference stations, with the orbit fixed solution using a precision orbit product as the benchmark.

[0147] Figure 6 The user positioning performance of GOP6 station, located approximately 500 kilometers from the reference network center, is presented. The left and right panels represent floating-point and fixed solutions, respectively. The green line represents the baseline results using the orbital fixed model, while the blue line represents the results obtained in this invention. By comparing the user positioning results obtained in this invention with the baseline results, it can be observed that the floating-point and fixed solutions for the user station are almost identical to the baseline results.

[0148] Figure 7 The positioning performance of a PASA station approximately 1000 km from the reference network center is presented. The left and right panels represent floating-point and fixed-point solutions, respectively. The green line represents the baseline results using the orbital fixed model, while the blue line represents the results of this invention. Although individual orbital deviation correction parameters are not precise enough, they become sufficiently accurate when combined with other corrections, and the accuracy depends on the distance from the network center. Therefore, this embodiment includes a PASA station approximately 1000 km from the network center. Analysis Figure 7 It can be seen that both the ambiguity floating-point solution and the ambiguity fixed solution obtained using this invention remain close to the benchmark results. Although the results of this invention exhibit slightly larger perturbations than the benchmark results, especially for the floating-point solution, the fixed solution has the same first positioning time (TTFF) and only shows a small deviation shortly after TTFF, which is obviously acceptable.

[0149] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.

Claims

1. A method for estimating satellite orbital deviation corrections based on PPP-RTK over wide area networks, characterized in that: The method for ephemeris satellite orbital bias correction estimation based on wide area network PPP-RTK includes the following steps: The first step is to calculate the satellite position based on the continuous observation data from the reference station using broadcast ephemeris data. Then, based on the satellite position, the GNSS non-differential observation equation is linearized. Finally, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated to obtain a full-rank estimable observation model. In the first step, the satellite position is calculated using broadcast ephemeris data based on continuous observation data from the reference station. Then, the GNSS non-differenced observation equation is linearized based on this satellite position, specifically as follows: In a wide area reference network, a reference station is set up. , For satellites , In frequency , Continuous observations are conducted on the reference station, whose three-dimensional coordinate vector is known. ,satellite Location Calculated from broadcast ephemeris, denoted as Since the broadcast ephemeris position vector is affected by bias, it is corrected by estimating its corresponding orbital bias. ,assumed dimensional vector and Each contains phase and pseudorange observations The observation equation is: ； in, and These represent the carrier phase observation minus the calculated value and the pseudorange observation minus the calculated value, respectively, after calculation using broadcast ephemeris orbits, representing the satellite-to-Earth distance. Calculated from the broadcast ephemeris orbit ; This represents the unit vector indicating the line-of-sight direction between the satellite and the receiver; express 1-dimensional unit column vector; and These represent the clock biases of the satellite and receiver, respectively. This indicates the first-order ionospheric slack delay at the first frequency; dimensional vector From coefficients constitute; and These represent receiver and satellite code offsets, respectively. express A diagonal matrix with diagonal elements of , ; Represents a real-valued ambiguity vector; Expressed as ,in The ambiguity is in integer form. and These represent non-integer receiver and satellite phase offsets, respectively. Tropospheric delay corrected by prior model to and middle; The second step is to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model by introducing broadcast ephemeris orbital deviation correction parameters based on the full-rank estimable observation model. The third step is to introduce the time-varying characteristics of each parameter to be estimated into the multi-epoch observation model based on the wide area network, and construct dynamic models corresponding to the time-varying characteristics respectively. The fourth step is to first construct a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initialize the full-rank equation system to obtain orbital deviation correction information.

2. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 1, characterized in that: In the first step, the rank deficiency of the linearized GNSS non-differential observation equation is eliminated. Specifically, the rank deficiency of the equation is eliminated by applying minimum constraints by selecting the S-basis reference, restoring the rank-deficient GNSS non-differential observation equation to a full-rank estimable model, and determining the estimable forms of orbital deviation correction, clock error, ionospheric delay, phase deviation, code deviation, and ambiguity.

3. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 2, characterized in that: The full-rank estimable observation model is as follows: ； in, .

4. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 1, characterized in that: In the second step, based on the full-rank estimable observation model, a broadcast ephemeris orbital bias correction parameter is introduced to transform the full-rank estimable observation model into a wide-area network multi-epoch observation model. Specifically, the following symbols are defined first: The observation model is represented as: ； in, Indicates the GNSS reference network in consecutive epochs The sequence of collected observations.

5. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 1, characterized in that: In the third step, the parameters to be estimated include orbital deviation correction, satellite clock error, receiver clock error, ionospheric delay, satellite-receiver phase deviation, satellite-receiver code deviation, and ambiguity parameters.

6. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 5, characterized in that: The third step, the dynamic model, is as follows: ； in, express of First-order time derivative; The sampling interval represents the observation values, and the highest order of the polynomial dynamic model is... , and These are spurious observations with zero mean.

7. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 6, characterized in that: The dynamic model further includes: using ionospheric delay as a time-varying floating-point parameter and instrument bias as a time-dependent parameter, whereby instrument bias includes code bias and phase bias at the receiver and satellite ends.

8. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 1, characterized in that: The fourth step involves first constructing a full-rank equation system based on the multi-epoch observation model and dynamic model of the wide area network, and then initializing the full-rank equation system to obtain orbital deviation correction information. Specifically, this involves combining the multi-epoch observation model and dynamic model to perform orbital and clock corrections. constant velocity model The full-rank system of equations is constructed as follows: ； in, ; ； ； in, .

9. The method for estimating satellite orbital deviation correction based on PPP-RTK over a wide area network according to claim 8, characterized in that: After obtaining the orbital deviation correction information, the generated orbital deviation correction information, along with satellite clock correction, ionospheric correction, and phase deviation correction, is broadcast to the user terminal for use in fixing integer ambiguity and high-precision positioning at the user terminal.

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