Application Methods and Systems for Calculating GNSS Satellite Clock Error Parameters

Abstract

This invention discloses a method and system for parametric calculation of GNSS satellite clock bias, belonging to the field of satellite navigation and positioning. It includes constructing a parametric estimation function model for GNSS satellite clock bias based on commonly used GNSS satellite clock bias models and GNSS ionospheric-free observation models; linearizing this model to form a linearized parametric estimation equation for GNSS satellite clock bias; selecting the GNSS observation length for estimating the model coefficients based on the performance of different GNSS satellite clock bias models; subsequently, selecting constraints to solve the GNSS satellite clock bias model coefficients; and constructing broadcast ephemeris services and high-precision real-time satellite clock bias services based on the estimated GNSS satellite clock bias model coefficients. This invention simplifies the GNSS satellite clock bias calculation and service process and mode, ensures the timeliness of service parameters, maintains high-precision services, improves service performance, reduces the calculation pressure on the real-time satellite clock bias service terminal, and ensures the stable and continuous high-precision positioning needs of real-time precise positioning users.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation, and in particular to a method and system for calculating and applying GNSS satellite clock bias parameters. Background Technology

[0002] Currently, GNSS satellite clock bias estimation and service utilizes GNSS pseudorange and phase observations, and performs single-epoch estimation based on the white noise characteristics of GNSS satellite clock bias. The estimated values ​​are time-series values ​​corresponding to each epoch. The estimated GNSS satellite clock bias time-series values ​​are then used to fit satellite clock bias model coefficients to construct broadcast ephemeris and high-precision real-time service (RTS). This process is time-consuming and cumbersome, severely reducing the timeliness of GNSS satellite clock bias corrections and the accuracy of GNSS satellite clock bias services in positioning applications.

[0003] With the continuous improvement of GNSS spaceborne atomic clock performance, its stability has become increasingly significant, and it can be represented with high precision using model functions. Therefore, to enhance the performance of GNSS satellite clock bias services, simplify its calculation process, ensure the timeliness of GNSS satellite clock bias service parameters, and maintain high-precision positioning, a method for parametric calculation and application of GNSS satellite clock bias has been invented. This method directly estimates the satellite clock bias model coefficients using GNSS pseudorange and phase observations and broadcasts them directly to real-time users. This simplifies the GNSS satellite clock bias estimation and service process, further improving the timeliness of GNSS satellite clock bias service parameters while ensuring service accuracy. This is of great significance for improving the service performance and high-precision application of GNSS precision satellite clock bias products. Summary of the Invention

[0004] This invention is proposed in view of the problems existing in GNSS satellite clock bias estimation and services.

[0005] Therefore, the technical problem solved by this invention is: how to simplify the data processing flow in GNSS satellite clock bias service, save data processing time, ensure the timeliness of service parameters, and maintain its positioning accuracy.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, this invention provides a method for the parameterization and application of GNSS satellite clock bias, comprising: constructing a parameterized estimation function model of GNSS satellite clock bias based on commonly used GNSS satellite clock bias models and GNSS ionospheric-free observation models; linearizing the constructed parameterized estimation function model of GNSS satellite clock bias to form a linearized parameterized estimation equation of GNSS satellite clock bias; selecting the GNSS observation length for estimating the model coefficients based on the performance of different GNSS satellite clock bias models; selecting constraints to solve the coefficients of the GNSS satellite clock bias model based on the GNSS satellite clock bias model, the linearized parameterized estimation equation of GNSS satellite clock bias, and the used GNSS observation length; and constructing a broadcast ephemeris service and a high-precision real-time satellite clock bias service based on the estimated coefficients.

[0008] As an application method for parameterizing GNSS satellite clock bias described in this invention, the GNSS satellite clock bias model includes a linear model, a quadratic polynomial model, a linear model with a fourth harmonic function, a quadratic polynomial model with a fourth harmonic function, a linear model with an eighth harmonic function, and a quadratic polynomial model with an eighth harmonic function. The unified function model is represented as follows:

[0009]

[0010] Where n1 is the highest order of the polynomial model, n1 = 2, n2 is the highest order of the harmonic function model, n2 = 8, t k For the time required to calculate the GNSS satellite clock bias, δ g,s (t) represents the satellite clock difference at time t, a k Let A be the polynomial coefficient. m1 T m1 and Φ m1 These represent the amplitude, period, and phase of the harmonic function model, respectively.

[0011] As an application method for the parameterization of GNSS satellite clock bias described in this invention, the GNSS ionospheric-free observation model is expressed as follows:

[0012]

[0013] in, and These are the ionospherically unsaturated delay combined phase and pseudorange observations for reference station r and satellite s at time t, respectively. Let be the geometric distance between satellite s and receiver r at time t. and δ g,s (t) represents the receiver clock bias and satellite clock bias of reference station r at time t. Let be the phase ambiguity corresponding to reference station r satellite s at time t. Let r be the tropospheric delay corresponding to reference station r at time t. and This refers to phase and pseudorange observation noise.

[0014] As an application method for GNSS satellite clock bias parameterization calculation described in this invention, the GNSS satellite clock bias parameterization estimation function model is constructed based on commonly used GNSS satellite clock bias models and GNSS ionospheric-free observation models. The GNSS satellite clock bias parameterization estimation function model is expressed as follows:

[0015]

[0016]

[0017] As an application method for GNSS satellite clock bias parameterization described in this invention, the constructed GNSS satellite clock bias parameterization estimation function model is linearized to form a linearized GNSS satellite clock bias parameterization estimation equation. This linearization process uses precise coordinates, precise satellite orbit products to fix station coordinates and satellite orbits. The linearized GNSS satellite clock bias parameterization estimation equation is expressed as follows:

[0018]

[0019] in, and These represent the ionospheric delay phase and pseudorange observation residuals for reference station r and satellite s at time t, respectively. and δ' g,s (t) represents the receiver clock bias and linearized satellite clock bias of reference station r at time t. Let be the phase ambiguity corresponding to reference station r satellite s at time t. δ' is the tropospheric delay corresponding to reference station r at time t; g,s (t) represents the linearized satellite clock error at time t, expressed as:

[0020]

[0021] Formula (4) can be rewritten as:

[0022] AX + BY = l (6)

[0023] in,

[0024]

[0025]

[0026] X = […, [(A0)] s …(a k )s (A1) s …(A n1 ) s (Φ1) s …(Φ n1 ) s ],…] T ;

[0027]

[0028]

[0029]

[0030] Where n and m are the number of satellites and stations, respectively, A is the coefficient matrix of the linearized satellite clock error model used for GNSS satellite clock error parameterization estimation, and e 1×n Represents a 1xn matrix with all elements equal to 1, e m×1 Let a be an m x 1 matrix with all elements equal to 1, where the coefficient matrix a represents the order of a k-polynomial. and Let n1 and n2 represent the amplitude and phase approximations of the harmonic function linearization, respectively; let n1 represent the order of the harmonic function expression; X represents the parameters to be estimated in the parameterization estimation of GNSS satellite clock bias, including polynomial coefficients and harmonic function coefficients, (a k ) s Let A be the polynomial coefficients of the clock error model for satellite s, and (A) n1 ) s and (Φ n1 ) s Let I be the amplitude and phase coefficient corrections of the harmonic function of the clock error model for satellite s; B is the linearized coefficient matrix of the corresponding parameter Y to be estimated; I is the amplitude and phase coefficient corrections of the harmonic function of satellite s. n×n Let I represent an n×n identity matrix. (m×n)×(m×n) It is an identity matrix with (m×n) rows and (m×n) columns. Y is the mapping function for tropospheric delay; Y represents other unknown parameters estimated along with the GNSS satellite clock error model coefficients, including receiver clock error, phase ambiguity, and tropospheric delay. These are the combined residuals of the ionospheric delay phase and pseudorange for reference station r and satellite s at time t, respectively.

[0031] As an application method for GNSS satellite clock bias parameter calculation described in this invention, the GNSS observation length for estimating the model coefficients is selected based on the performance of different GNSS satellite clock bias models, specifically the dual-frequency observation length of GNSS.

[0032] As an application method for GNSS satellite clock bias parameterization described in this invention, the process of solving the GNSS satellite clock bias model coefficients includes estimating the GNSS satellite clock bias parameterization equation based on linearization and estimating the GNSS satellite clock bias model coefficients, receiver clock bias, tropospheric delay, and ambiguity parameters by selecting the GNSS dual-frequency observation length. The estimation method is least squares, and the formula is as follows:

[0033] [X,Y] T =([AB]'·[AB]) -1 [AB]'·l (7)

[0034] The construction of broadcast ephemeris service and high-precision real-time satellite clock bias service based on the estimated GNSS satellite clock bias model coefficients involves directly broadcasting the coefficients to GNSS users at certain sampling intervals using satellite messages or networks.

[0035] Secondly, embodiments of the present invention provide a GNSS satellite clock bias parameterization application system, comprising: a function model establishment module, which establishes a function model for GNSS satellite clock bias parameterization based on the GNSS satellite clock bias sequence; an estimation module, which performs parameterization based on the function model and its constraints to obtain estimated values ​​of the coefficients of the GNSS satellite clock bias model, receiver clock bias, tropospheric delay, and ambiguity parameters; and an application module, which constructs broadcast ephemeris service and high-precision real-time satellite clock bias service based on the GNSS satellite clock bias model coefficients.

[0036] In a third aspect, embodiments of the present invention provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement any step of the GNSS satellite clock bias parameter calculation and application method.

[0037] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the GNSS satellite clock bias parameter calculation and application method. Attached Figure Description

[0038] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0039] Figure 1 This is an overall flowchart of a GNSS satellite clock bias parameter calculation and application method and system provided in one embodiment of the present invention;

[0040] Figure 2 This is a diagram illustrating the calculation results of GNSS satellite clock bias parameters with different arc lengths provided in one embodiment of the present invention;

[0041] Figure 3 The broadcast ephemeris satellite clock bias service accuracy is constructed by decomposing GNSS satellite clock bias parameters and coefficients according to one embodiment of the present invention.

[0042] Figure 4 The real-time satellite clock bias parameterization coefficient service accuracy is provided by constructing the GPS, BDS, and Galileo satellite clock bias parameterization coefficients according to one embodiment of the present invention. Detailed Implementation

[0043] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0044] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0045] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0046] Example 1

[0047] Reference Figure 1 This is one embodiment of the present invention, which provides a specific process for the calculation and application of GNSS satellite clock bias parameters, including:

[0048] S1: Construct a parameterized estimation function model for GNSS satellite clock bias based on commonly used GNSS satellite clock bias models and GNSS ionospheric-free observation models;

[0049] GNSS satellite clock bias models include linear models, quadratic polynomial models, linear models with fourth-order harmonic functions, quadratic polynomial models with fourth-order harmonic functions, linear models with eighth-order harmonic functions, and quadratic polynomial models with eighth-order harmonic functions. The principal periodic terms in the harmonic functions are determined based on existing results. The polynomial function coefficients, amplitude, and phase parameters in the harmonic functions are estimated as parameters to be estimated in the satellite clock bias models. A unified function model is expressed as follows:

[0050]

[0051] Where n1 is the highest order of the polynomial model, n1 = 2, n2 is the highest order of the harmonic function model, n2 = 8, t k For the time required to calculate the GNSS satellite clock bias, δ g,s (t) represents the satellite clock difference at time t, a k Let A be the polynomial coefficient. m1 T m1 and Φ m1 The values ​​represent the amplitude, period, and phase of the harmonic function model, respectively, with the period shown in the table below:

[0052] cycle <![CDATA[T1]]> <![CDATA[T2]]> <![CDATA[T3]]> <![CDATA[T4]]> <![CDATA[T5]]> <![CDATA[T6]]> <![CDATA[T7]]> <![CDATA[T8]]> GPS 12 8 6 4.8 4 3.4 3 2.7 BDS-3 12 8 6 4.8 4 3.4 3 2.7 Galileo 12 8 6 4.8 4 3.4 3 2.7

[0053] The GNSS observation model is represented as follows:

[0054]

[0055] in, and These are the ionospherically unsaturated delay combined phase and pseudorange observations for reference station r and satellite s at time t, respectively. Let be the geometric distance between satellite s and receiver r at time t. Other errors, such as phase entanglement, receiver and satellite antenna phase center correction, solid tides, phase entanglement, and Earth rotation correction, are corrected using a model. and δ g,s (t) represents the receiver clock bias and satellite clock bias of reference station r at time t. Let be the phase ambiguity corresponding to reference station r satellite s at time t. Let r be the tropospheric delay corresponding to reference station r at time t. and This refers to phase and pseudorange observation noise.

[0056] Based on the established GNSS satellite clock bias model and GNSS ionospheric-free observation model, a parameterized estimation function model for GNSS satellite clock bias is constructed, which is expressed as follows:

[0057]

[0058]

[0059] S2. Linearize the constructed GNSS satellite clock bias parameter estimation function model to form a linearized GNSS satellite clock bias parameter estimation equation;

[0060] The constructed GNSS satellite clock bias parameter estimation function model is linearized to form a linearized GNSS satellite clock bias parameter estimation equation. This linearization process uses precise coordinates, precise satellite orbit products to fix station coordinates and satellite orbits. The linearized GNSS satellite clock bias parameter estimation equation is expressed as follows:

[0061]

[0062] in, and These represent the ionospheric delay phase and pseudorange observation residuals for reference station r and satellite s at time t, respectively. and δ' g,s (t) represents the receiver clock bias and linearized satellite clock bias of reference station r at time t. Let be the phase ambiguity corresponding to reference station r satellite s at time t. δ' is the tropospheric delay corresponding to reference station r at time t; g,s (t) represents the linearized satellite clock error at time t, expressed as:

[0063]

[0064] Formula (4) can be rewritten as:

[0065] AX + BY = l (6)

[0066] in,

[0067]

[0068]

[0069] X = […, [(a0)] s …(a k ) s (A1) s …(A n1 ) s (Φ1) s …(Φ n1 ) s ],…] T ;

[0070]

[0071]

[0072]

[0073] Where n and m are the number of satellites and stations, respectively, A is the coefficient matrix of the linearized satellite clock error model used for GNSS satellite clock error parameterization estimation, and e1×n Represents a 1xn matrix with all elements equal to 1, e m×1 Let a be an m x 1 matrix with all elements equal to 1, where the coefficient matrix a represents the order of a k-polynomial. and Let n1 and n2 represent the amplitude and phase approximations of the harmonic function linearization, respectively; let n1 represent the order of the harmonic function expression; X represents the parameters to be estimated in the parameterization estimation of GNSS satellite clock bias, including polynomial coefficients and harmonic function coefficients, (a k ) s Let A be the polynomial coefficients of the clock error model for satellite s, and (A) n1 ) s and (Φ n1 ) s Let I be the amplitude and phase coefficient corrections of the harmonic function of the clock error model for satellite s; B is the linearized coefficient matrix of the corresponding parameter Y to be estimated; I is the amplitude and phase coefficient corrections of the harmonic function of satellite s. n×n Let I represent an n×n identity matrix. (m×n)×(m×n) It is an identity matrix with (m×n) rows and (m×n) columns. Y is the mapping function for tropospheric delay; Y represents other unknown parameters estimated along with the GNSS satellite clock error model coefficients, including receiver clock error, phase ambiguity, and tropospheric delay. These are the combined residuals of the ionospheric delay phase and pseudorange for reference station r and satellite s at time t, respectively.

[0074] S3. Select the GNSS observation length for estimating its model coefficients based on the performance of different GNSS satellite clock error models;

[0075] The GNSS observation length used to estimate the model coefficients is selected based on the performance of different GNSS satellite clock bias models, specifically the dual-frequency observation length of GNSS.

[0076] S4. Based on the GNSS satellite clock bias model, the linearized GNSS satellite clock bias parameterization estimation equation, and the GNSS observation length used, the constraints are selected to solve the coefficients of the GNSS satellite clock bias model;

[0077] The process of solving the GNSS satellite clock bias model coefficients includes estimating the GNSS satellite clock bias parameterization equations based on linearization and estimating the GNSS satellite clock bias model coefficients, receiver clock bias, tropospheric delay, and ambiguity parameters by selecting the GNSS dual-frequency observation length. The estimation method is least squares, and the formula is as follows:

[0078] [X,Y] T =([AB]'·[AB]) -1 [AB]'·l (7)

[0079] S5: Construct broadcast ephemeris service and high-precision real-time satellite clock bias service based on the estimated GNSS satellite clock bias model coefficients;

[0080] The broadcast ephemeris service and high-precision real-time satellite clock bias service are constructed based on the estimated GNSS satellite clock bias model coefficients. These coefficients are directly broadcast to GNSS users at certain sampling intervals using satellite messages or networks.

[0081] Furthermore, this embodiment also provides a GNSS satellite clock bias parameter calculation application system, including:

[0082] The function model building module establishes a function model for parametric calculation of GNSS satellite clock errors based on the GNSS satellite clock error sequence.

[0083] The estimation module performs parametric decomposition based on the function model and its constraints to obtain estimated values ​​of the coefficients of the GNSS satellite clock error model, receiver clock error, tropospheric delay, and ambiguity parameters.

[0084] The application module constructs broadcast ephemeris services and high-precision real-time satellite clock bias services based on GNSS satellite clock bias model coefficients.

[0085] This embodiment also provides a computer device applicable to the GNSS satellite clock bias parameterization application method, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the GNSS satellite clock bias parameterization application method proposed in the above embodiment.

[0086] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0087] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the GNSS satellite clock bias parameter calculation application method proposed in the above embodiments.

[0088] The storage medium proposed in this embodiment and the data storage method proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0089] In summary, this invention addresses the issue of GNSS precise satellite clock bias estimation and service by first estimating the time series of GNSS satellite clock bias based on its white noise characteristic, and then fitting service parameters. However, this approach neglects the stable variation characteristics of high-performance GNSS atomic clocks, which restricts the service performance of high-precision satellite clock bias, weakens the timeliness of service parameters, and reduces GNSS positioning accuracy. The invention proposes a parameterized solution and application method for GNSS satellite clock bias. This method directly estimates the satellite clock bias model coefficients and uses them to construct parameterized precise clock bias products, broadcast ephemeris services, and real-time satellite clock bias services. It omits the step of fitting parameters using estimated discrete clock bias sequences, simplifying the solution process, reducing the computational burden on the server side, and ensuring the timeliness of service parameters and high-precision positioning performance.

[0090] Example 2

[0091] Reference Figures 2-4 This is one embodiment of the present invention. In order to further verify the beneficial effects in Embodiment 1, this embodiment uses real data for scientific demonstration.

[0092] First, such as Figure 2 As shown, taking GPS as an example, the parameterized estimation results of GPS satellite clock bias for different arc lengths are compared with the modeling results of precise satellite clock bias products (F1, F2, F3, F4, F5, and F6 represent the results of establishing satellite clock bias parameterized models and performing GNSS satellite clock bias parameterization using linear polynomials, quadratic polynomials, linear polynomials plus fourth-order harmonic functions, quadratic polynomials plus fourth-order harmonic functions, linear polynomials plus eighth-order harmonic functions, and quadratic polynomials plus eighth-order harmonic functions, respectively). Figure 3 As shown, taking GPS as an example, the accuracy of broadcast ephemeris satellite clock extrapolation constructed from the parameterized coefficients of GPS satellite clock errors estimated with different arc lengths is illustrated; Figure 4 As shown, the accuracy of real-time satellite clock bias services constructed from the estimated GPS, BDS, and Galileo satellite clock bias parameterization coefficients for the 1-hour arc is compared (1#, 2#, 3#, and 4# represent real-time satellite clock bias parameterization coefficient products with broadcast intervals of 1, 2, 5, and 10 minutes, respectively; CNES is a real-time satellite clock bias archive product provided by the French National Centre for Space Studies).

[0093] Secondly, this experiment presents the application method and system for calculating GNSS satellite clock bias parameters over a three-day period from March 2nd to March 4th, 2023. The specific steps are as follows:

[0094] (1) Based on the commonly used GNSS satellite clock error model, linear polynomial, quadratic polynomial, linear polynomial plus fourth harmonic function, quadratic polynomial plus fourth harmonic function, linear polynomial plus eighth harmonic function, and quadratic polynomial plus eighth harmonic function are proposed to establish the clock error model in the parameterized estimation function model of GNSS satellite clock error.

[0095] (2) Based on the selected GNSS satellite clock error model and GNSS ionospheric-free observation model, construct the GNSS satellite clock error parameter estimation function model, and linearize it to form the GNSS satellite clock error parameter estimation equation. During the linearization process, use precise coordinate products and precise satellite orbit products to fix the station coordinates and satellite orbit, and correct other modelable errors such as phase winding, receiver and satellite antenna phase center correction, solid tide, phase winding, and Earth rotation correction according to the error model.

[0096] (3) Based on the performance of different GNSS satellite clock error models, the length of GNSS dual-frequency observations used to estimate the model coefficients was determined, and the selected lengths were 1, 2, 4, 6, 12, and 24 hours, respectively.

[0097] (4) Based on the GNSS observation length and GNSS satellite clock bias model used, and using the linearized phase and pseudorange observation equations, the least squares method is employed to estimate the GNSS satellite clock bias model coefficients, receiver clock bias, tropospheric delay, and ambiguity parameters. By using six satellite clock bias models to perform GNSS satellite clock bias parameterization, the calculated arc lengths are 1, 2, 4, 6, 12, and 24 hours, respectively. The observation length used is 24 hours. The parameterization estimation results show that the quadratic polynomial plus eight-period harmonic function model has the highest parameterization estimation accuracy, corresponding to an arc length of 1 hour.

[0098] (5) Constructing broadcast ephemeris service and high-precision real-time satellite clock bias service: The estimated GNSS satellite clock bias model coefficients are broadcast directly to GNSS users at certain time intervals via navigation messages or networks, constructing broadcast ephemeris satellite clock bias and real-time high-precision satellite clock bias services. Users can calculate the satellite clock bias at any time based on the received satellite clock bias model coefficients and the corresponding clock bias model. The broadcast ephemeris service update interval includes four types: 1, 2, 3, and 4 hours, and the real-time satellite clock bias service broadcast interval includes four types: 1, 2, 5, and 10 minutes.

[0099] In the above examples, by applying methods and systems for the parameterization of GNSS satellite clock bias, the advantages of the stable periodicity of high-performance satellite atomic clocks are fully utilized. The model parameters are directly estimated, omitting the steps of fitting the satellite clock bias sequence estimated epoch by epoch to obtain the satellite clock bias model coefficients and then broadcasting the coefficients to users. This simplifies the GNSS satellite clock bias estimation and service solution process, ensuring the timeliness of GNSS satellite clock bias service parameters and maintaining its high-precision positioning performance.

[0100] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating and applying GNSS satellite clock bias parameters, characterized in that, include: A parameterized estimation function model for GNSS satellite clock bias is constructed based on the GNSS satellite clock bias model and the GNSS ionospheric-free observation model. The constructed GNSS satellite clock bias parameter estimation function model is linearized to form a linearized GNSS satellite clock bias parameter estimation equation; The GNSS observation length used to estimate the model coefficients is selected based on the performance of different GNSS satellite clock error models. Based on the aforementioned GNSS satellite clock bias model, the linearized GNSS satellite clock bias parameterization estimation equation, and the GNSS observation length used, constraints are selected to solve the coefficients of the GNSS satellite clock bias model. Broadcast ephemeris service and high-precision real-time satellite clock bias service are constructed based on the estimated GNSS satellite clock bias model coefficients.

2. The GNSS satellite clock bias parameter calculation and application method as described in claim 1, characterized in that: The GNSS satellite clock error model includes a linear model, a quadratic polynomial model, a linear model with a fourth harmonic function, a quadratic polynomial model with a fourth harmonic function, a linear model with an eighth harmonic function, and a quadratic polynomial model with an eighth harmonic function. The unified function model is represented as follows: Where n1 is the highest order of the polynomial model, n1 = 2, n2 is the highest order of the harmonic function model, n2 = 8, t k For the time required to calculate the GNSS satellite clock bias, δ g,s (t) represents the satellite clock difference at time t, a k Let A be the polynomial coefficient. m1 T m1 and Φ m1 These represent the amplitude, period, and phase of the harmonic function model, respectively.

3. The GNSS satellite clock bias parameter calculation and application method as described in claim 1, characterized in that: The GNSS ionospheric-free observation model is expressed as follows: in, and These are the ionospherically unsaturated delay combined phase and pseudorange observations for reference station r and satellite s at time t, respectively. Let be the geometric distance between satellite s and receiver r at time t. and δ g,s (t) represents the receiver clock bias and satellite clock bias of reference station r at time t. Let r be the phase ambiguity corresponding to reference station r and satellite s at time t. Let r be the tropospheric delay corresponding to reference station r at time t. and This refers to phase and pseudorange observation noise.

4. The GNSS satellite clock bias parameter calculation and application method as described in any one of claims 1 to 3, characterized in that: A parameterized estimation function model for GNSS satellite clock bias is constructed based on the GNSS satellite clock bias model and the GNSS ionospheric-free observation model. The parameterized estimation function model for GNSS satellite clock bias is expressed as follows:

5. The GNSS satellite clock bias parameter calculation and application method as described in claim 1, characterized in that: The linearization process of the constructed GNSS satellite clock bias parameter estimation function model to form a linearized GNSS satellite clock bias parameter estimation equation includes using precise coordinates, precise satellite orbit products to fix station coordinates and satellite orbits during the linearization process. The linearized GNSS satellite clock bias parameter estimation equation is expressed as follows: in, and These represent the ionospheric delay phase and pseudorange observation residuals for reference station r and satellite s at time t, respectively. and δ′ g,s (t) represents the receiver clock bias and linearized satellite clock bias of reference station r at time t. Let r be the phase ambiguity corresponding to reference station r and satellite s at time t. δ represents the tropospheric delay corresponding to reference station r at time t; ′ g,s (t) represents the linearized satellite clock error at time t, expressed as: Formula (4) can be rewritten as: AX + BY = l (6) in, X=[[(a0) s ,(a1) s ,(a2) s ,(A1) s ,(Φ1) s ,…,(TO n1 ) s ,(Φ n1 ) s ]] T ; Where n and m are the number of satellites and stations, respectively, A is the coefficient matrix of the linearized satellite clock error model used for GNSS satellite clock error parameterization estimation, and e 1×n Represents a 1xn matrix with all elements equal to 1, e m×1 Let a be an m x 1 matrix with all elements equal to 1, where the coefficient matrix a represents the order of a k-polynomial. and Let n1 and n2 represent the amplitude and phase approximations of the harmonic function linearization, respectively; let n1 represent the order of the harmonic function expression; X represents the parameters to be estimated in the parameterization estimation of GNSS satellite clock bias, including polynomial coefficients and harmonic function coefficients, (a k ) s Let A be the polynomial coefficients of the clock error model for satellite s, and (A) n1 ) s and (Φ n1 ) s Let I be the amplitude and phase coefficient corrections of the harmonic function of the clock error model for satellite s; B is the linearized coefficient matrix of the corresponding parameter Y to be estimated; I is the amplitude and phase coefficient corrections of the harmonic function of satellite s. n×n Let I represent an n×n identity matrix. (m×n)×(m×n) It is an m×n row m×n column identity matrix. Y is the mapping function for tropospheric delay; Y represents other unknown parameters estimated along with the GNSS satellite clock error model coefficients, including receiver clock error, phase ambiguity, and tropospheric delay. These are the combined residuals of the ionospheric delay phase and pseudorange for reference station r and satellite s at time t, respectively.

6. The GNSS satellite clock bias parameter calculation and application method as described in claim 1, characterized in that: The dual-frequency observation length of GNSS is selected based on the performance of different GNSS satellite clock error models, using the estimated model coefficients.

7. The GNSS satellite clock bias parameter calculation and application method as described in claim 1, characterized in that: The process of solving the GNSS satellite clock bias model coefficients includes estimating the GNSS satellite clock bias parameterization equations based on linearization and estimating the GNSS satellite clock bias model coefficients, receiver clock bias, tropospheric delay, and ambiguity parameters by selecting the GNSS dual-frequency observation length. The estimation method is least squares, and the formula is as follows: [X,Y] T =([A B]′·[A B]) -1 [A B]′·l (7) The construction of broadcast ephemeris service and high-precision real-time satellite clock bias service based on the estimated GNSS satellite clock bias model coefficients involves directly broadcasting the coefficients to GNSS users at certain sampling intervals using satellite messages or networks.

8. A GNSS satellite clock bias parameter calculation and application system, based on the GNSS satellite clock bias parameter calculation and application method according to any one of claims 1 to 7, characterized in that, include: The function model building module establishes a function model for parametric calculation of GNSS satellite clock errors based on the GNSS satellite clock error sequence. The estimation module performs parametric decomposition based on the function model and its constraints to obtain estimated values ​​of the coefficients of the GNSS satellite clock error model, receiver clock error, tropospheric delay, and ambiguity parameters. The application module constructs broadcast ephemeris services and high-precision real-time satellite clock bias services based on GNSS satellite clock bias model coefficients.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the GNSS satellite clock bias parameter calculation and application method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the GNSS satellite clock bias parameter calculation and application method according to any one of claims 1 to 7.

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