A method for estimating the earth motion based on the clock difference random model constraint of a spaceborne receiver

Abstract

The application provides a method for estimating the earth motion based on a clock difference random model constraint of a spaceborne receiver, comprising: obtaining an effective sequence of a low-orbit satellite clock difference; constructing a clock difference model containing a switchable order polynomial term and a random term; integrating the clock difference random model as a constraint into a parameter estimation model to jointly solve the earth motion and clock difference parameters; and combining multi-orbit plane low-orbit satellite data to uniformly solve the earth motion time sequence. The method significantly improves the earth motion estimation accuracy, reduces the Z-component form error, weakens the parameter correlation, reduces the system error pollution, suppresses the false signal, makes the annual and semi-annual cycle signals clearer, enhances the reliability of the solution, improves the integer solution success rate, is highly universal, is suitable for various low-orbit satellites carrying high-precision oscillators, and provides a core technology for high-precision monitoring of the earth motion by using multi-source low-orbit satellite data.

Description

Technical Field

[0001] This invention relates to the fields of geodesy and satellite navigation and positioning technology, specifically providing a geocentric motion estimation method based on a random model constraint of a spaceborne receiver clock bias. Background Technology

[0002] Global Navigation Satellite System (GNSS) possesses advantages such as global coverage and high sampling rates, making it a crucial technological means for monitoring geocentric motion. Compared to navigation satellites, low-Earth orbit (LEO) satellites orbit the Earth at higher speeds and lower altitudes, making them more sensitive to the Earth's center. With the continuous development and maturation of spaceborne GNSS technology, combining it with LEO satellite observations has become an important direction for geocentric motion estimation. Research indicates that the strong correlation between geocentric parameters and parameters such as clock bias and tropospheric delay is one of the main reasons for the low quality of GNSS-estimated geocentric motion. Current LEO satellite geocentric motion estimation primarily relies on GNSS tracking data, treating satellite clock bias as a white noise process for parameter estimation, objectively ignoring the correlation of satellite clock bias between epochs. Furthermore, since satellite orbit and satellite clock bias are estimated simultaneously, the satellite clock bias will inevitably be affected by orbital errors. Theoretically, introducing a reasonable clock bias model to constrain satellite clock bias can improve the estimation accuracy of satellite orbit and satellite clock bias, thereby improving the accuracy and reliability of geocentric motion estimation.

[0003] Existing technologies suffer from the following problems: strong parameter correlation leads to low accuracy in geocentric motion parameter estimation: 1. Geocentric motion parameters are strongly correlated with satellite clock errors, especially significantly affecting the geocentric Z-component. In traditional methods, satellite clock errors are typically treated as white noise processes for epoch-level independent estimation during precise orbit determination of low-Earth orbit (LEO) GNSS satellites, ignoring the physical correlation of clock errors between epochs. This further exacerbates the coupling between geocentric motion parameters and clock errors, resulting in low accuracy in geocentric motion estimation. 2. Coupling between satellite clock errors and orbital errors: Satellite clock errors and orbital parameters need to be estimated synchronously. Orbital errors (such as solar radiation pressure modeling errors) are transmitted to the clock error estimation results through the observation equations, resulting in periodic errors in satellite clock error products related to the satellite orbital period. These errors further contaminate the geocentric motion time series, causing serious deviations from the true geocentric motion. 3. LEO satellite advantages are not fully utilized: Due to their low orbital altitude, LEO satellites are significantly more sensitive to geocentric motion than medium- and high-Earth orbit (MEO) GNSS satellites. Furthermore, combining multiple LEO satellites with different orbital configurations can enhance the geometric diversity of observations. However, existing methods for estimating geocentric motion of low-Earth orbit (LEO) satellites do not have dedicated constraint models for LEO satellite clock bias characteristics, nor do they effectively combine the geometric advantages of multiple LEO satellites to decouple geocentric motion from orbit and clock bias parameters, resulting in the LEO satellite's potential for geocentric motion detection not being fully realized.

[0004] Therefore, there is an urgent need for a geocentric motion estimation method based on the constraints of a stochastic model of spaceborne receiver clock bias to solve the above problems. Summary of the Invention

[0005] To address the problems in existing low-Earth orbit (LEO) satellite geocentric motion estimation, such as severe parameter coupling due to clock bias being treated as white noise, clock bias being contaminated by orbital errors, and the underutilization of the advantages of LEO satellites, this invention is proposed to provide solutions or partial solutions to the above problems.

[0006] This invention provides a geocentric motion estimation method based on a stochastic model constraint of a spaceborne receiver clock bias, comprising: S1, calculating the precise orbit and original clock bias of a low-Earth orbit satellite using a simplified dynamic precise orbit determination method based on collected relevant data, removing outliers from the original clock bias to obtain an effective clock bias sequence; the data includes at least: the spaceborne GNSS data of the low-Earth orbit satellite. The data includes: S1) Dual-frequency pseudorange and carrier phase observation data, precise ephemeris and clock bias products of GNSS navigation satellites, prior orbits of low-Earth orbit (LEO) satellites, prior model parameters of LEO satellite solar radiation pressure, and Earth rotation parameters; S2) Based on the effective clock bias sequence, calculate the clock bias random term after fitting the polynomial term, and construct a clock bias random model for the random term. The polynomial term is a time polynomial with switchable order, and the random term is a process noise term characterizing the random characteristics of the clock bias. The clock bias random model is used to describe the variation law of the clock bias of the LEO satellite's onboard receiver with epochs; fit the polynomial term to the effective clock bias sequence to obtain the clock bias residual; calculate the variability function based on the clock bias residual, and then determine the process noise of the random term; S3) Use the clock bias random model as a constraint and integrate it into a parameter estimation model containing the LEO satellite dynamics equation and observation equation, and jointly solve the geocentric motion parameters and clock bias model parameters; S4) Combine the observation data of one or more LEO satellites and the clock bias random model to perform a unified solution to obtain the time series of geocentric motion parameters.

[0007] In one technical solution of the geocentric motion estimation method based on the constraints of the stochastic model of the spaceborne receiver clock bias, the expression of the clock bias model is: Where clk(t) is the low-Earth orbit satellite clock bias at epoch t; a0 is the clock bias at the reference time; a1 is the frequency offset; a2 is the frequency drift; and β is the optional model coefficient. This is a clock bias random term.

[0008] In one of the above-mentioned technical solutions for geocentric motion estimation methods based on the random model constraint of spaceborne receiver clock bias, β=0 for linear models and β=1 for quadratic polynomial models.

[0009] In one technical solution of the geocentric motion estimation method based on the constraints of the random model of the spaceborne receiver clock bias, the random term of the clock bias... Process noise The following is obtained through estimation using the variogram function: This noise is used as a constraint for the stochastic model in subsequent parameter estimation.

[0010] In one technical solution of the geocentric motion estimation method based on the constraints of the stochastic model of the spaceborne receiver clock bias, the variogram is calculated as follows: a polynomial model is fitted to the preprocessed clock bias time series to obtain the clock bias residuals, and the variogram of the residuals is calculated based on a robust method, as shown in the formula: ,in, The epoch interval (consistent with the observation sampling interval); To meet The set of epoch pairs; The variation function represents the number of elements in the set and reflects the clock-related random terms at different time intervals. The changing characteristics under the following conditions.

[0011] In one technical solution of the geocentric motion estimation method based on the constraints of the random model of the spaceborne receiver clock bias, during the geocentric motion estimation process, the parameters a0, a1, and a2 of the polynomial terms are estimated as constant parameters throughout the entire processing arc, and the random clock bias terms are estimated as random process parameters in each estimation epoch.

[0012] In one technical solution of the geocentric motion estimation method based on the random model constraint of the satellite receiver clock bias, the outlier removal method includes: using the median absolute deviation method to detect and remove clock bias outliers, and combining visual inspection methods to remove clock jump data.

[0013] In one technical solution of the geocentric motion estimation method based on the random model constraint of the satellite receiver clock bias, after step S3, there is also a solution optimization step: the carrier phase ambiguity is fixed to an integer using a single-station ambiguity fixing technique.

[0014] In one technical solution of the geocentric motion estimation method based on the random model constraint of the spaceborne receiver clock bias, in step S3, the parameter estimation model is a least squares model or a Kalman filter model.

[0015] The beneficial effects of the geocentric motion estimation method based on a random model constraint of satellite receiver clock bias provided by this invention are as follows: 1. Significantly improves the accuracy of geocentric motion estimation: By modeling the clock bias of low-star receivers and applying reasonable random constraints, the prior statistical characteristics of clock bias between epochs are effectively utilized, avoiding the information loss caused by simply treating it as white noise. This method can significantly reduce the formal error of geocentric motion parameters, especially the Z component.

[0016] 2. Reduced Parameter Correlation: The introduction of the clock bias model alters the structure of parameter estimation, effectively reducing the strong correlation between receiver clock bias and geocentric motion parameters (especially the Z component) as well as with other force model parameters (such as SRP empirical parameters). This reduces the contamination of geocentric motion estimation by systematic errors such as force model errors through parameter correlation.

[0017] 3. Suppressing spurious signals: By weakening the clock error related to the orbital period, this invention can effectively suppress spurious signals related to the satellite orbital period (such as the annual cycle of satellite intersections) in the geocentric motion time series, making the geocentric motion signals, especially the annual and semi-annual cycle signals, clearer and more reliable.

[0018] 4. Enhanced solution reliability: By combining single-station ambiguity fixation and multi-satellite joint solution, this invention can further improve the success rate and strength of integer solutions for geocentric motion estimation, and the output results have better consistency with the results of independent techniques such as SLR.

[0019] 5. High versatility: This method is applicable to various low-Earth orbit satellites equipped with high-precision oscillators (such as USO, rubidium clocks, etc.), such as gravity measurement satellites (GRACE, GRACE-FO), ocean altimetry satellites (Sentinel-3, Jason), and future large-scale low-Earth orbit constellations, providing core technology for high-precision monitoring of geocentric motion using multi-source low-Earth orbit satellite data. Attached Figure Description

[0020] The disclosure of this invention will become more readily understood with reference to the accompanying drawings. It will be readily understood by those skilled in the art that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Furthermore, similar numbers in the drawings are used to denote similar components, wherein: Figure 1 This is a schematic flowchart of a geocentric motion estimation method based on a random model constraint of a spaceborne receiver clock bias according to an embodiment of the present invention. Figure 2 This is a flowchart for determining the noise of the clock bias random term process according to an embodiment of the present invention. Detailed Implementation

[0021] Some embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0022] Example like Figure 1-2 As shown, this invention provides a geocentric motion estimation method based on a stochastic model constrained by a spaceborne receiver clock bias, comprising: Step S1: Data Preprocessing We collect onboard GNSS dual-frequency pseudorange and carrier phase observation data from low-Earth orbit (LEO) satellites (such as GRACE-FO, Swarm, and Sentinel-3), precise ephemeris and clock bias products from GNSS navigation satellites, prior orbits of LEO satellites, prior model parameters of LEO satellite solar radiation pressure (such as box wing model geometric parameters), and Earth rotation parameters (ERP). Using the precise orbits of GNSS satellites, we employ a simplified dynamic precise orbit determination method to calculate the precise orbits and clock biases of LEO satellites. We use the median absolute deviation (MAD) method to detect and remove clock bias anomalous values, and combine this with visual inspection methods to remove clock jump data (such as observations with single-epoch clock bias variations exceeding 5 times the RMS).

[0023] Step S2: Construct a stochastic clock bias model for low-Earth orbit satellites Based on the type of clock carried by the low-Earth orbit satellite, a satellite clock bias model consisting of a polynomial and a random term is constructed, as follows: (1) Where clk(t) is the low-Earth orbit satellite clock bias at epoch t (unit: m, converted by time difference multiplied by speed of light); a0 is the clock bias at the reference time; a1 is the frequency offset (clock speed); a2 is the frequency drift (clock drift); β is an optional model coefficient, β=0 for linear models and β=1 for quadratic polynomial models. The clock bias random term has its process noise estimated by the variogram. In the geocentric motion estimation process, the polynomial components (a0, a1, and a2) are estimated as constant parameters throughout the entire processing arc, while the random term... Then, it is used as a parameter of the stochastic process and estimated at each estimation epoch.

[0024] Specifically, step S2.1, clock error residual calculation: For the preprocessed low-Earth orbit satellite clock error time series, fit the above polynomial model to obtain the clock error residual. , For the observation epoch).

[0025] Step S2.2, Variance function estimation: Calculate residuals based on robust methods. The variogram is given by the following formula: (2) in, The epoch interval (consistent with the observation sampling interval); To meet The set of epoch pairs; The number of elements in the set. The variogram reflects the clock-related random term at different time intervals. The changing characteristics under the following conditions.

[0026] Step S2.3, Noise Determination: Random Items Process noise Calculated using different functions: (3) This noise is used as a constraint for the stochastic model in subsequent parameter estimation.

[0027] Step S3: Joint parameter estimation based on clock bias constraints A parameter estimation model is constructed, including the dynamic equations and observation equations of the low-Earth orbit satellite (usually using the least squares method or Kalman filter). In the estimation model, the geocentric motion parameters, the initial orbital state of the low-Earth orbit satellite, the force model parameters (such as the SRP scale factor and atmospheric drag coefficient), and the carrier phase ambiguity are used as parameters to be estimated. At the same time, the clock bias of the low-Earth orbit satellite receiver is parameterized according to the model established by formulas (1) and (3) and incorporated into the overall normal equation for joint solution. The clock bias polynomial coefficients are estimated as constant parameters, and the random terms are estimated as constant parameters. Then the process noise variance determined by formula (3) is constrained.

[0028] Step S4, Ambiguity Fixing and Solution Optimization: Building upon step 3, a single-station ambiguity fixing technique is employed to fix the carrier phase ambiguity to an integer value. This significantly strengthens the geometric constraints between low-Earth orbit satellites and GNSS satellites, reduces the estimation error of geocentric motion parameters, and further improves the accuracy and stability of the solution.

[0029] Step S5: Multi-star joint solution to enhance solution strength: A unified solution is obtained by combining observation data from multiple low-Earth orbit satellites (with different orbital planes, inclinations, and altitudes) and clock bias models. Multi-satellite observations can greatly improve the geometric structure of parameter estimation and effectively reduce the correlation between geocentric motion parameters and the unique force model parameters of each satellite (such as the SRP scale factor), thereby obtaining a more robust and reliable geocentric motion time series.

[0030] Step S6, Output Results The final solution yields time series of the three components of geocentric motion (X, Y, Z), precise orbits of low-Earth orbit satellites, and clock error parameters, among other products.

[0031] Single-star calculation and comparison: Comparative Example: A traditional low-Earth orbit satellite precise orbit determination and geocentric motion estimation model is constructed, in which the GRACE-C receiver clock error is estimated as an independent white noise parameter for each epoch. The force model adopts a box-wing model and estimates the constant SRP scale factor and atmospheric drag coefficient. Simultaneously, geocentric motion parameters, initial orbit, carrier phase ambiguity, etc., are estimated. The target period data is processed to obtain the geocentric motion time series TS_white.

[0032] Example of this invention: Under the same force model and parameter settings, the receiver clock bias estimation strategy is replaced with the "polynomial + stochastic process" model proposed in this invention. The polynomial coefficients are used as arc segment constant parameters for estimation, and the stochastic term is estimated according to the process noise constraints determined in step 2. The contemporaneous data is then processed to obtain the geocentric motion time series TS_model.

[0033] Performance Validation: Comparison of TS_white and TS_model. It is expected that the geocentric motion sequence from the TS_model, especially the Z component, will have a smaller estimation error, and high-frequency fluctuations and obvious orbital-related periodic patterns in the time series will be effectively suppressed. The goodness of fit between the two and the SLR geocentric motion sequence is calculated; the goodness of fit from the TS_model is expected to be higher, with annual average amplitude and phase closer to the SLR results.

[0034] Multi-satellite co-processing and ambiguity fixation: Observational data from both GRACE-C and GRACE-D satellites are combined, and single-station ambiguity fixation techniques are applied for recalculation (clock errors are all calculated using the model of this invention), resulting in the joint solution TS_combined. The correlation between the geocentric motion Z-component and the SRP scale factor of the GRACE-C satellite in TS_combined is analyzed, and its value is expected to be significantly lower than the correlation in the single-satellite solution TS_model. The TS_combined sequence should exhibit optimal stability and reliability.

[0035] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions resulting from these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A geocentric motion estimation method based on a stochastic model constrained by a spaceborne receiver clock bias, characterized in that, include: S1. Based on the collected relevant data, the precise orbit and original clock bias of the low-Earth orbit satellite are calculated using a simplified dynamic precision orbit determination method. Outliers are removed from the original clock bias to obtain an effective clock bias sequence. The data includes at least: onboard GNSS dual-frequency pseudorange and carrier phase observation data of the low-Earth orbit satellite, precise ephemeris and clock bias products of the GNSS navigation satellite, the prior orbit of the low-Earth orbit satellite, the prior model parameters of the solar radiation pressure of the low-Earth orbit satellite, and the Earth rotation parameters. S2. Based on the effective clock bias sequence, calculate the clock bias random term after fitting the polynomial term, and construct a clock bias random model for the random term. The polynomial term is a time polynomial with switchable order, and the random term is a process noise term characterizing the random characteristics of the clock bias. The clock bias random model is used to describe the variation law of the clock bias of the low-Earth orbit satellite onboard receiver with epochs. Fit the polynomial term to the effective clock bias sequence to obtain the clock bias residual. Calculate the variability function based on the clock bias residual, and then determine the process noise of the random term. S3. Using the clock bias stochastic model as a constraint, integrate it into a parameter estimation model that includes the low-orbit satellite dynamics equation and the observation equation, and jointly solve the geocentric motion parameters and clock bias model parameters. S4. Combining the observation data from one or more low-orbit satellites and the clock bias stochastic model, a unified solution is performed to obtain the time series of geocentric motion parameters.

2. The method according to claim 1, characterized in that, The expression for the clock error model is: ； Where clk(t) is the low-Earth orbit satellite clock bias at epoch t; a0 is the clock bias at the reference time; a1 is the frequency offset; a2 is the frequency drift; and β is the optional model coefficient. This is a clock bias random term.

3. The method according to claim 2, characterized in that, For the linear model, β=0; for the quadratic polynomial model, β=1.

4. The method according to claim 2, characterized in that, The clock difference random term Process noise The following is obtained through estimation using the variogram function: ； This noise is used as a constraint for the stochastic model in subsequent parameter estimation.

5. The method according to claim 4, characterized in that, The variogram function is calculated as follows: a polynomial model is fitted to the preprocessed clock error time series to obtain the clock error residuals, and the variogram function of the residuals is calculated based on a robust method, using the following formula: ； in, The epoch interval (consistent with the observation sampling interval); To meet The set of epoch pairs; The variation function represents the number of elements in the set and reflects the clock-related random terms at different time intervals. The changing characteristics under the following conditions.

6. The method according to claim 2, characterized in that, In the geocentric motion estimation process, the parameters a0, a1, and a2 of the polynomial terms are estimated as constant parameters throughout the entire processing arc, and the clock error random term is estimated as a random process parameter at each estimation epoch.

7. The method according to claim 1, characterized in that, The outlier removal methods include: using the median absolute deviation method to detect and remove clock jump outliers, and combining visual inspection methods to remove clock jump data.

8. The method according to claim 1, characterized in that, The step S3 is followed by a solution optimization step: the carrier phase ambiguity is fixed to an integer using a single-station ambiguity fixing technique.

9. The method according to claim 1, characterized in that, In step S3, the parameter estimation model is either a least squares model or a Kalman filter model.

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