A method for joint calculation of Earth rotation parameters and short-term forecasting by regional network satellite-ground inter-satellite systems
By using a regional network-ground-satellite joint solution method, and utilizing a small amount of ground-satellite and inter-satellite measurement data from domestic stations, combined with forecast values from the International Earth Rotation Service, high-precision calculation and real-time short-term forecasts of Earth rotation parameters were achieved. This solved the problem of insufficient global station data in existing technologies and improved the accuracy and autonomy of the satellite navigation system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI ASTRONOMICAL OBSERVATORY CHINESE ACAD OF SCI
- Filing Date
- 2026-02-04
- Publication Date
- 2026-06-02
AI Technical Summary
Existing technologies struggle to accurately calculate Earth's rotation parameters and make real-time forecasts using regional station ground-to-ground measurement data and inter-satellite measurement data, and the method relying on globally distributed stations suffers from insufficient observation data.
The regional network satellite-ground-satellite joint solution method is adopted. It uses a small amount of satellite-ground observation data and inter-satellite measurement data from domestic stations, combined with the forecast values from the International Earth Rotation Service as initial values, and forecasts Earth rotation parameters through least squares batch processing and linear relationships to achieve real-time short-term forecasts.
It enables high-precision calculation of Earth's rotation parameters with limited data, reduces accumulated errors, and improves the service accuracy and autonomous maintenance capability of satellite navigation systems.
Smart Images
Figure CN122131348A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of satellite navigation technology, and in particular relates to a method for joint calculation of Earth rotation parameters and short-term forecasting between regional network satellites and ground stations. Background Technology
[0002] In the field of satellite navigation, precise satellite orbit determination is handled within a celestial reference frame, while ground monitoring stations and users operate within an terrestrial reference frame. Therefore, satellite navigation systems require real-time conversion between the celestial and terrestrial reference frames during operation. Earth rotation parameters (ERPs) are essential for this conversion and significantly impact the navigation system's service accuracy and autonomous maintenance capabilities. ERPs include polar motion (x, y), UT1-UTC, and length of day variation (LOD). Due to the characteristics of GNSS technology, only polar motion and LOD can be calculated; UT1-UTC is then obtained by integrating the LOD.
[0003] Currently, there are various methods for calculating and forecasting EOP parameters using GNSS technology. These methods all use satellite-to-ground GNSS measurement data from globally distributed stations for calculation and then use long-term historical data for EOP forecasting. However, there has been no research on methods that consider using only regional station satellite-to-ground measurement data and inter-satellite measurement data to determine highly reliable ERP parameters and make real-time forecasts.
[0004] VLBI technology directly uses distant extragalactic radio sources as a reference to determine all parameters of Earth's rotation. However, VLBI stations are less distributed globally, resulting in less observational data compared to GNSS. GNSS and SLR technologies, due to the strong correlation between satellite orbital elements and parameters such as UT1-UTC and nutation, can measure polar motion with high precision, but they cannot independently measure UT1-UTC. They can only measure diurnal variation (ΔLOD), and UT1-UTC is obtained through integration, thus introducing cumulative errors. SLR equipment is large and expensive, and there are fewer stations globally compared to GNSS, resulting in less observational data. GNSS technology can conduct all-weather, high-precision, continuous observations, and its stations are evenly distributed globally, providing ample high-precision observational data to compensate for the discontinuity of VLBI and SLR data. To leverage the advantages of each technology and compensate for their disadvantages, the international approach currently relies on a combination of high-precision measurement techniques (GNSS, SLR, and VLBI) to obtain Earth's rotation parameters; this method depends on globally distributed stations. Summary of the Invention
[0005] Currently, methods for calculating polar motion and diurnal variation using GNSS technology mainly rely on satellite-ground GNSS observation data from globally distributed stations. To address this technological limitation, this invention proposes a regional network-based satellite-ground-satellite joint method for calculating Earth rotation parameters and short-term forecasts. This method utilizes satellite-ground observation data and inter-satellite measurement data from a limited number of domestic stations to jointly calculate ERP parameters and achieve real-time short-term forecasts even with limited data accumulation.
[0006] This invention discloses a method for joint calculation of Earth rotation parameters and short-term forecasting using a regional network satellite-ground inter-satellite system. The method includes: S1. Using the forecast value from the International Earth Rotation and Retirement Service (IERS) as the initial value for the Earth Orientation Parameter (EOP), perform calculations for satellite orbit, clock error, and Earth Rotation Parameter (ERP) based on satellite-to-ground observation data and inter-satellite link measurement data; S2. Perform short-term ERP forecasts based on the Earth's rotation parameters (ERP) of historical and current epochs; use the forecasted ERP as the initial value for the next epoch calculation; and evaluate the accuracy of the calculated and forecasted ERP.
[0007] In S1, satellite-to-ground measurement equations are constructed using satellite-to-ground observation data, where: pseudorange data and phase data The measurement model is as follows: in, The wavelength corresponding to the phase data. and These are the position vectors of the satellite and the receiver, respectively, where c is the speed of light. and These are receiver clock bias and satellite clock bias, respectively. This is due to the phase center deviation of the satellite antenna. The delay is due to relativistic effects. For tropospheric delay, For ionospheric delay, To correct the eccentricity of the station, For tidal correction at the station, The distance measurement deviation is caused by the displacement of the measuring station. For phase data ambiguity, and These represent multipath and noise, respectively, for pseudorange and phase.
[0008] In S1, inter-satellite measurement equations are constructed using inter-satellite link measurement data, where: The inter-satellite link uses a time-division measurement system to obtain ranging observations in both directions, including ranging information between satellites and relative clock differences; satellite A receives the ranging signal transmitted by satellite B at time t1 on its own clock face. Satellite B receives the ranging signal transmitted by Satellite A at time t2. Then the inter-satellite measurement equation is: in, , These are the three-dimensional positions of satellite A and satellite B, respectively. , The satellite clock biases for satellite A and satellite B are respectively. It's the speed of light. 1 and 2 represents the time of light travel. and These are the satellite's transmission delay and reception delay, respectively. and This is the error correction term in distance measurement.
[0009] In S1, calculations for satellite orbit, clock bias, and Earth rotation parameter ERP are performed based on satellite-to-ground observation data and inter-satellite link measurement data, including: Adding simultaneous two-way ranging measurements eliminates satellite clock bias, leaving only satellite distance information; subtracting simultaneous two-way ranging measurements eliminates satellite orbit bias, leaving only satellite clock bias; due to the different times of mutual transmission and reception ranging, single and two-way observations are reclassified to an intermediate epoch. The expression is: in, and The expressions for satellite position and satellite clock bias corrections are: and By adding the satellite clock errors to eliminate them, the relative distances between the satellites are obtained, which are used for precise orbit determination. Decouple satellite orbits and clock biases in inter-satellite two-way pseudorange measurements for use in orbit calculations.
[0010] In S1, calculations for satellite orbit, clock bias, and Earth rotation parameter ERP are performed based on satellite-to-ground observation data and inter-satellite link measurement data, including: The satellite's equations of motion and their corresponding initial conditions are as follows: The process of establishing observation equations for satellite orbit determination is a process of linearizing the orbit determination observation equations. The nonlinear satellite orbit determination observation equations are as follows: in, It is observation data The corresponding truth value, For the observation time, The vector of parameters to be estimated includes satellite orbital elements, dynamic model parameters, satellite clock bias, station coordinates, and receiver clock bias. For observation purposes, This is the observation error; The nonlinear satellite orbit determination and observation equations are applied in... Satellite reference position at time Expand here: Mapping the observation equations to the reference time, the satellite orbit determination observation equations become: Includes state transition matrix and sensitivity matrix Obtained through orbital integration. For parameter correction values; Using astro-terrestrial observations as the data source, the measurement equation is characterized as follows: in, For common parameters, for , These are non-common parameters. For the corresponding partial derivatives; Inter-satellite observations use inter-satellite distance measurement as the observable quantity, then: in This is the correction value for the sum of the satellite's transmit and receive delays; Perform data fusion between satellite, ground, and inter-satellite observations: The satellite orbit and Earth rotation parameters were obtained by using least squares batch processing.
[0011] In S2: Given a small number of historical epochs and the current solution epoch, with the linear relationship represented by y = a + bt, and obtaining the optimal solutions for a and b using the least squares method, the P-value of the predicted ERP parameters for the next epoch is: P=a+b (t-t0) Where t is the end epoch and t0 is the start epoch; The first calculation epoch uses the international IERS forecast product as the initial value for satellite orbit determination and ERP parameter calculation. Using the international IERS forecast product as the standard, the accuracy of the calculated ERP parameters is evaluated and short-term forecasts are made. The predicted ERP parameters for the next epoch are used as the initial value for satellite orbit determination and ERP parameter calculation for the next epoch, and so on.
[0012] In S2: The EOPs provided by the International Earth Rotation and Reference Systems Service (IERS) include VLBI, GNSS, SLR, and DORIS; IERS CO4 is obtained by collecting single-technology EOP sequences from multiple technologies and analysis centers; the accuracy is evaluated by comparing the calculated ERP parameters and the predicted ERP with IERS CO4.
[0013] This invention utilizes a limited number of regional stations to perform joint orbit determination and ERP parameter calculation using ground-to-satellite observation data and inter-satellite link measurement data. Furthermore, considering the limited amount of accumulated ERP data, a real-time short-term ERP forecasting method based on historical calculations is employed for forecasting, and its accuracy is compared and evaluated with the international IERS CO4 product. Attached Figure Description
[0014] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0015] Figure 1 This is a schematic flowchart of a regional network-based inter-satellite joint solution method for Earth rotation parameters and short-term forecasting, according to an embodiment of the present invention. Figure 2This is a schematic diagram illustrating how, according to an embodiment of the present invention, the IERS precise ERP product, the IERS predicted ERP product, and the predicted ERP value of the present invention are used as initial ERP values for joint orbit determination to estimate the ERP. Detailed Implementation
[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0017] This invention proposes a method for joint calculation of Earth rotation parameters and short-term forecasting using a regional network satellite-ground inter-satellite system, such as... Figure 1 As shown, the main steps for ERP calculation and forecasting using joint regional station satellite-to-ground and inter-satellite measurement data are as follows: The initial calculation uses IERS forecast values as the initial values, and performs joint orbit determination and ERP parameter calculation using both satellite-to-ground and inter-satellite measurement data from regional stations; short-term forecasts are made based on historical and current epoch ERP parameters; the forecasted ERP values are used as the initial values for the next epoch calculation, and joint satellite-to-ground and inter-satellite orbit determination and ERP calculation are performed for the next epoch, and so on, with daily EOP forecast updates; the daily calculated and forecasted ERP parameters are compared with IERS C04 for accuracy evaluation.
[0018] 1. ERP parameter calculation (1) Equation for Star-to-Ground Measurement Pseudorange phase data is a crucial data source for precise orbit determination of navigation satellites. and phase data The measurement model is as follows (the following formulas are formula (1) and formula (2) respectively): in, The wavelength corresponding to the phase data. and These are the position vectors of the satellite and the receiver, respectively, where c is the speed of light. and These are receiver clock bias and satellite clock bias, respectively. This is due to the phase center deviation of the satellite antenna. The delay is due to relativistic effects. For tropospheric delay, For ionospheric delay, To correct the eccentricity of the station, For tidal correction at the station, The distance measurement deviation is caused by the displacement of the measuring station. For phase data ambiguity, and These represent multipath and noise, respectively, for pseudorange and phase.
[0019] (2) Interstellar measurement equations Inter-satellite links employ a time-division measurement system to obtain ranging observations in both directions, including ranging information between satellites and relative clock differences. Satellite A receives the ranging signal transmitted by satellite B at time t1 on its own clock face. Satellite B receives the ranging signal transmitted by Satellite A at time t2. The observation equation is: (3) (4) in, , These are the three-dimensional positions of satellites A and B, respectively. , The satellite clock biases for satellites A and B are respectively. It's the speed of light. 1 and 2 represents the time of light travel. and These represent the satellite's launch delay and reception delay, respectively. and These are error correction terms that can be accurately modeled in ranging.
[0020] Simultaneous addition of two-way ranging measurements eliminates satellite clock bias, containing only satellite distance information; simultaneous subtraction of two-way ranging measurements eliminates satellite orbit bias, containing only satellite clock bias. Because the timing of mutual transmission and reception ranging measurements differs, it is necessary to revert the single- and two-way observations to an intermediate epoch. The formula is: (4) (5) in and For satellite position and satellite clock bias corrections: (6) (7) Adding formulas (6) and (7) can eliminate satellite clock errors and obtain the relative distance between satellites, which is used for precise orbit determination. (8) Formula (8) can decouple the satellite orbit and clock error in inter-satellite two-way pseudorange measurement, and can be directly used in subsequent orbit calculations.
[0021] (3) Joint solution of satellite-to-ground / inter-satellite link equations The satellite's equations of motion and their corresponding initial conditions are as follows: ; .
[0022] The process of establishing observation equations for satellite orbit determination is essentially the process of linearizing these equations. Assume the nonlinear satellite orbit determination observation equations are as follows:
[0023] in, It is observation data The corresponding truth value, For the observation time, The vector of parameters to be estimated includes satellite orbital elements, dynamic model parameters, satellite clock bias, station coordinates, receiver clock bias, etc. Observations This represents the observation error.
[0024] Equation (9) is in Satellite reference position at time Expand here:
[0025] Mapping the observation equations to the reference time, the satellite orbit determination observation equations become:
[0026] and Includes state transition matrix and sensitivity matrix The two parts can be obtained through orbital integration. This is the parameter correction value.
[0027] Using astro-terrestrial observations as the data source, observation equations (1) and (2) can be written in the following form according to the method of equation (11):
[0028] in For common parameters, for , These are non-common parameters. is the corresponding partial derivative.
[0029] Inter-satellite observation uses inter-satellite distance measurement as the observation method, and the observation equation is formula (8). Formula (11) can be written in the following form: (13) in This is the correction value for the satellite's transmission and reception delays.
[0030] The fusion of ground-to-satellite and inter-satellite observation data is achieved through the superposition of normal equations. Combining equations (12) and (13), we get:
[0031] The satellite's orbit and Earth's rotation parameters (polar motion and diurnal variation) can be obtained by using least squares batch processing to solve equation (14).
[0032] 2. ERP parameter forecasting Using the ERP parameters calculated before the epoch, assuming a series of observations ti, yi (i=1,2,3,4,5), and assuming they have a linear relationship, which can be represented by y=a+bt, and obtaining the optimal solutions for a and b through the least squares method, the predicted ERP parameter P is: P=a+b (t-t0) (15) Where t is the end epoch and t0 is the start epoch.
[0033] The first calculation epoch uses the international IERS forecast product as the initial value to perform satellite orbit determination and ERP parameter calculation. The accuracy of the calculated ERP parameters is evaluated using the international IERS product as the standard. Then, short-term forecasts are made based on the formula (15) and a small number of historical cumulative ERP values. The predicted ERP parameters of the next epoch are used as the initial value. Step 1 is repeated to perform satellite orbit determination and ERP parameter calculation for the next epoch. This process is repeated daily to update the forecast calculation.
[0034] 3. ERP Parameter Accuracy Assessment The EOP (Earth Optimization Program) product provided by the International Earth Rotation and Reference Systems Service (IERS) is a comprehensive result of four technologies: VLBI, GNSS, SLR, and DORIS. By collecting single-technology EOP sequences from multiple technologies and analysis centers, and performing comprehensive processing, the final EOP product is obtained, which is currently the most accurate internationally, with the latest version being IERS C04. Therefore, this scheme evaluates accuracy by comparing the calculated ERP parameters with IERS C04.
[0035] ERP parameter calculation and real-time short-term forecasting are performed using satellite-to-ground observation data from regional stations and inter-satellite measurement data. For example... Figure 2As shown, fixed regional network station coordinates are used, and broadcast ephemeris satellite orbits are adopted as the initial state values for joint orbit determination. Precise orbit determination is performed using inter-satellite observation data, and ERP parameters (polar motion, diurnal variation) are estimated and short-term forecasts are made, with cross-difference comparisons performed with IERS C04. The IERS precise ERP product, the IERS forecast ERP product, and the ERP value predicted by this scheme are used as the initial ERP values for joint orbit determination, respectively, to estimate the ERP. The blue curve represents the difference between the ERP value calculated using the IERS precise ERP product as the initial value and IERS C04; the red curve represents the difference between the ERP value calculated using the IERS forecast ERP product as the initial value and IERS C04; the pink curve represents the difference between the ERP value calculated using the ERP parameters predicted by this scheme as the initial value and IERS C04; and the green curve represents the difference between the IERS forecast ERP product and the precise ERP product. Figure 2 As can be seen, when using the IERS-predicted ERP as the initial value, the ERP estimation error (red) is smaller than the IERS-predicted ERP error (green), indicating that joint calculation of star-ground-satellite data can yield a more accurate ERP. Using the ERP measurements and ERP prediction algorithm of this scheme, the obtained ERP values have relatively stable accuracy (pink), with a polar shift of approximately 2 mas and a day length of approximately 0.6 ms.
[0036] This invention utilizes limited regional station observation data and inter-satellite link measurement data to perform joint orbit determination and ERP parameter calculation. Considering the limited amount of accumulated ERP data, a real-time short-term ERP forecasting method based on historical calculations is employed, and the forecasts are compared and their accuracy evaluated with the international IERS CO4 product.
[0037] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.
Claims
1. A method for joint calculation of Earth rotation parameters and short-term forecasting using a regional network satellite-ground inter-satellite system, characterized in that, The method includes: S1. Using the forecast value from the International Earth Rotation and Retirement Service (IERS) as the initial value for the Earth Orientation Parameter (EOP), perform calculations for satellite orbit, clock error, and Earth Rotation Parameter (ERP) based on satellite-to-ground observation data and inter-satellite link measurement data; S2. Perform short-term ERP forecasts based on the Earth's rotation parameters (ERP) of historical and current epochs; use the forecasted ERP as the initial value for the next epoch calculation; and evaluate the accuracy of the calculated and forecasted ERP.
2. The method for joint calculation of Earth rotation parameters and short-term forecasting by a regional network satellite-ground inter-satellite network according to claim 1, characterized in that, In S1, satellite-to-ground measurement equations are constructed using satellite-to-ground observation data, where: pseudorange data and phase data The measurement model is as follows: in, The wavelength corresponding to the phase data. and These are the position vectors of the satellite and the receiver, respectively, where c is the speed of light. and These are receiver clock bias and satellite clock bias, respectively. This is due to the phase center deviation of the satellite antenna. The delay is due to relativistic effects. For tropospheric delay, For ionospheric delay, To correct the eccentricity of the station, For tidal correction at the station, The distance measurement deviation is caused by the displacement of the measuring station. For phase data ambiguity, and These represent multipath and noise, respectively, for pseudorange and phase.
3. The method for joint calculation of Earth rotation parameters and short-term forecasting by a regional network satellite-ground inter-satellite network according to claim 2, characterized in that, In S1, inter-satellite measurement equations are constructed using inter-satellite link measurement data, where: The inter-satellite link uses a time-division measurement system to obtain ranging observations in both directions, including ranging information between satellites and relative clock differences; satellite A receives the ranging signal transmitted by satellite B at time t1 on its own clock face. Satellite B receives the ranging signal transmitted by Satellite A at time t2. Then the inter-satellite measurement equation is: in, , These are the three-dimensional positions of satellite A and satellite B, respectively. , The satellite clock biases for satellite A and satellite B are respectively. It's the speed of light. 1 and 2 represents the time of light travel. and These are the satellite's transmission delay and reception delay, respectively. and This is the error correction term in distance measurement.
4. The method for joint calculation of Earth rotation parameters and short-term forecasting by a regional network satellite-ground inter-satellite network according to claim 3, characterized in that, In S1, calculations for satellite orbit, clock bias, and Earth rotation parameter ERP are performed based on satellite-to-ground observation data and inter-satellite link measurement data, including: Adding simultaneous two-way ranging measurements eliminates satellite clock bias, leaving only satellite distance information; subtracting simultaneous two-way ranging measurements eliminates satellite orbit bias, leaving only satellite clock bias; due to the different times of mutual transmission and reception ranging, single and two-way observations are reclassified to an intermediate epoch. The expression is: in, and The expressions for satellite position and satellite clock bias corrections are: and By adding the satellite clock errors to eliminate them, the relative distances between the satellites are obtained, which are used for precise orbit determination. Decouple satellite orbits and clock biases in inter-satellite two-way pseudorange measurements for use in orbit calculations.
5. The method for joint calculation of Earth rotation parameters and short-term forecasting by a regional network satellite-ground inter-satellite network according to claim 4, characterized in that, In S1, calculations for satellite orbit, clock bias, and Earth rotation parameter ERP are performed based on satellite-to-ground observation data and inter-satellite link measurement data, including: The satellite's equations of motion and their corresponding initial conditions are as follows: The process of establishing observation equations for satellite orbit determination is a process of linearizing the orbit determination observation equations. The nonlinear satellite orbit determination observation equations are as follows: in, It is observation data The corresponding truth value, For the observation time, The vector of parameters to be estimated includes satellite orbital elements, dynamic model parameters, satellite clock bias, station coordinates, and receiver clock bias. For observation purposes, This is the observation error; The nonlinear satellite orbit determination and observation equations are applied in... Satellite reference position at time Expand here: Mapping the observation equations to the reference time, the satellite orbit determination observation equations become: Includes state transition matrix and sensitivity matrix Obtained through orbital integration. For parameter correction values; Using astro-terrestrial observations as the data source, the measurement equation is characterized as follows: in, For common parameters, for , These are non-common parameters. For the corresponding partial derivatives; Inter-satellite observations use inter-satellite distance measurement as the observable quantity, then: in This is the correction value for the sum of the satellite's transmit and receive delays; Perform data fusion between satellite, ground, and inter-satellite observations: The satellite orbit and Earth rotation parameters were obtained by using least squares batch processing.
6. The method for joint calculation of Earth rotation parameters and short-term forecasting by regional network satellite-ground inter-satellite networks according to claim 5, characterized in that, In S2: Given a small number of historical epochs and the current solution epoch, with the linear relationship represented by y = a + bt, and obtaining the optimal solutions for a and b using the least squares method, the P-value of the predicted ERP parameters for the next epoch is: P=a+b (t-t0) Where t is the end epoch and t0 is the start epoch; The first calculation epoch uses the international IERS forecast product as the initial value for satellite orbit determination and ERP parameter calculation. Using the international IERS forecast product as the standard, the accuracy of the calculated ERP parameters is evaluated and short-term forecasts are made. The predicted ERP parameters for the next epoch are used as the initial value for satellite orbit determination and ERP parameter calculation for the next epoch, and so on.
7. The method for joint calculation of Earth rotation parameters and short-term forecasting by a regional network satellite-ground inter-satellite network according to claim 6, characterized in that, In S2: The EOPs provided by the International Earth Rotation and Reference Systems Service (IERS) include VLBI, GNSS, SLR, and DORIS; IERS CO4 is obtained by collecting single-technology EOP sequences from multiple technologies and analysis centers; the accuracy is evaluated by comparing the calculated ERP parameters and the predicted ERP with IERS CO4.