Autonomous measurement and control orbit determination method and system for high-orbit satellite

Abstract

The invention relates to an autonomous measurement and control orbit determination method and system for a high-orbit satellite. The method comprises the following steps: acquiring satellite-borne GNSS broadcast ephemeris data and single-frequency pseudo-range observation data of a high-orbit satellite; based on the GNSS broadcast ephemeris data and the single-frequency pseudo-range observation data, coarse orbit data of the high-orbit satellite are generated through a dynamic pseudo-range orbit determination algorithm; performing outlier elimination preprocessing on the coarse orbit data to obtain orbit data after outlier elimination; performing smooth fitting and equal-interval sampling on the orbit data after outlier elimination to obtain smooth orbit data; determining an orbit determination arc section according to the scheduling time and the orbit maneuvering time; and using the motion equation and the state transition matrix of the high-orbit satellite to process least square iteration in batches to obtain optimal orbit data, and executing orbit forecasting. The method provided by the invention does not depend on information transmission of ground measurement and control resources, realizes on-satellite autonomous orbit determination, reduces the complexity of data fusion calculation, and is small in calculation amount.

Description

Technical Field

[0001] The present invention relates to the field of satellite measurement and control technology, and in particular to a method and system for autonomous measurement, control and orbit determination of a high-orbit satellite. Background Art

[0002] The onboard autonomous measurement, control and orbit determination technology generally involves equipping a global satellite navigation system receiver for positioning and timing. This method has strong autonomy, high positioning accuracy, and low volume and power consumption, and has been used for precise orbit determination in low-orbit orbits. High-orbit satellites generally refer to geosynchronous orbit satellites with an orbit height of 35,786 km above the ground. However, since the satellite navigation signal transmitting antenna is directed toward the ground, high-orbit satellites can only receive leakage signals from the opposite side of the earth, resulting in low signal strength, poor observation quality, and a small number of visible navigation satellites [1]. When performing data transmission and communication tasks, high-orbit satellites need to adjust the communication antenna to align with the relay satellite, which also affects the quality of the high-orbit satellite-borne receiver tracking satellite signals. Therefore, directly using the original observation data for orbit determination will result in large errors. At the same time, the high-orbit satellite control system regularly unloads momentum wheels, and frequent orbital maneuvers will also affect the orbit determination results. The onboard thrust during the orbital maneuver also makes it difficult to predict the orbit across the arc segment.

[0003] The measurement, control and orbit determination of high-orbit satellites is crucial for the normal operation of satellites and the completion of their missions. Accurate measurement, control and orbit determination technology can monitor the orbital position of satellites in real time, ensure that satellites operate in predetermined orbits, and avoid collisions with other satellites or deviations from their mission orbits. By accurately measuring the orbital parameters of satellites, the attitude and orbit of satellites can be adjusted in a timely manner to ensure that satellites can complete complex tasks such as communications, weather monitoring, and navigation. In addition, the measurement, control and orbit determination technology of high-orbit satellites can also effectively prevent possible orbital decay or external disturbances of satellites. Because satellites in high orbits are affected by factors such as the earth's gravity, solar radiation pressure, and gas friction, their orbits may change slightly. Regular orbital measurements and adjustments ensure that satellites are always in the optimal orbital position, which plays an important role in the life of the satellite, data accuracy, and reliability. To date, there has been little research on the problems existing in high-orbit measurement, control and orbit determination technology. The existing high-orbit measurement, control and orbit determination solutions are as follows:

[0004] Solution 1 provides a batch processing method for autonomous satellite orbit determination in short arc segments. This method uses GNSS (Global Navigation Satellite System) observation data within the current arc segment for inter-satellite single difference, and uses the previous arc segment's integrated prediction of satellite status information at all observation times in the current arc segment to eliminate gross errors in the inter-satellite single difference data. Using the inter-satellite single difference observation data without gross errors and the integrated predicted satellite status information, batch processing is used to iteratively estimate the satellite state. The posterior residual is used to determine the convergence of the estimate. If convergence is determined, the next arc segment is integrated, and the original GNSS data is used to calculate the statistical characteristics of the receiver clock error to predict the receiver clock error at the starting point of the next arc segment to correct the clock of the GNSS receiver tracking loop. This solution performs inter-satellite single difference on a smaller amount of missed signal GNSS data, resulting in reduced data redundancy, while the difference in observation data increases the observation noise. Furthermore, this scheme uses the state information of the previous arc segment to predict the current state of the orbit and eliminate gross errors in the observation data of the current arc segment. It does not take into account the fact that orbit predictions are inaccurate during orbital maneuvers. Therefore, gross error elimination may lead to serious errors and eliminate useful data. Moreover, during periods without orbit control, as the orbit prediction time increases, the predicted orbit accuracy decreases, which also affects gross error elimination. Using raw GNSS observation data to calculate the receiver clock error at each sampling time will make the receiver clock error calculation and the predicted clock error unreliable due to the observation quality issues of the raw data.

[0005] A second solution provides a method for autonomous orbit determination of high-orbit satellites based on fused information. The method includes: establishing an orbital dynamics model based on a differential representation of position and velocity vectors; applying the orbital dynamics model to perform extrapolation calculations based on GNSS navigation data and celestial navigation data, respectively, to obtain a first extrapolated result based on the GNSS navigation data and a second extrapolated result based on the celestial navigation data; correcting the first and second extrapolated results using valid new GNSS navigation data; and outputting an autonomous orbit determination result based on the currently selected extrapolated calculation result. This solution relies on information fusion to maintain two independent systems, without collaborative orbit determination to enhance system robustness. In this solution, astronomical data is limited by celestial visibility and the positioning accuracy of the corrected celestial navigation is only better than 5 km. Therefore, it can only be used for rough verification of results. The autonomous orbit determination results provided when GNSS is unavailable are of low accuracy. This solution uses filtering correction, which relies on a priori known system noise variance and measurement noise variance. This is unsuitable for real-world satellite operating environments, where satellites are subject to various perturbations and where the quality of astronomical data and onboard GNSS data is poor and highly variable, resulting in noise uncertainty and unstable results. In addition, the onboard autonomous orbit determination of this scheme does not take into account orbital maneuvers.

[0006] Solution 3 provides a high-precision autonomous orbit determination method for high-orbit satellites based on GNSS broadcast ephemeris. This method uses only GNSS broadcast ephemeris and GNSS observations to achieve high-precision autonomous orbit determination for high-orbit satellites. Using an onboard enhanced extended Kalman filter (AEKF), GNSS observations are tightly coupled with the orbital dynamics model, achieving the advantages of high short-term accuracy in the recursive orbital dynamics model and stable long-term GNSS observation divergence. Furthermore, the slowly varying GNSS satellite orbit and clock errors introduced by the broadcast ephemeris are jointly estimated during the filtering process and subtracted from the raw GNSS observations to mitigate their impact on the orbit determination results. This solution does not account for the poor quality of missed signal observations and the potential for filter divergence caused by noise variance selection in actual satellite operating environments, which is affected by multiple perturbations. Including broadcast ephemeris errors in the equations increases computational complexity and workload. Furthermore, when a high-orbit satellite receives a small number of observations, this approach can lead to rank deficiency, making the calculation impossible. Furthermore, frequent orbital maneuvers by high-orbit satellites can also lead to low accuracy in the recursive dynamics model.

[0007] Existing autonomous tracking, control, and orbit determination solutions for high-orbit satellites suffer from numerous shortcomings, including inter-satellite single-difference reduction, which reduces data redundancy and amplifies noise; low astronomical navigation accuracy; unstable noise statistics; unresolved issues with poor signal quality; and computationally complex errors in ephemeris broadcast estimation. Therefore, a method that effectively addresses these issues is urgently needed. Summary of the Invention

[0008] In order to solve some or all of the problems in the prior art, the present invention provides a method for autonomous measurement, control and orbit determination of a high-orbit satellite, which comprises the following steps:

[0009] Obtain onboard GNSS broadcast ephemeris data and single-frequency pseudorange observation data of high-orbit satellites;

[0010] Based on the GNSS broadcast ephemeris data and the single-frequency pseudorange observation data, a dynamic pseudorange orbit determination algorithm is used to generate coarse orbit data of the high-orbit satellite;

[0011] Performing outlier elimination preprocessing on the coarse orbit data to obtain orbit data after outlier elimination;

[0012] Performing smooth fitting and equally spaced sampling on the orbital data after outliers are removed to obtain smoothed orbital data;

[0013] Determine the orbit arc based on the scheduling time and orbit maneuvering time; and

[0014] Based on the orbit determination arc and the smoothed orbit data, the motion equation of the high-orbit satellite and the state transfer matrix are used to perform batch least squares iteration to obtain the optimal orbit data and perform orbit prediction.

[0015] Furthermore, the dynamic pseudorange orbit determination algorithm uses the least squares method to calculate the minimum norm of the difference between the pseudorange observation value and the error model value;

[0016] The pseudo-range observation equation of the satellite receiver is as follows:

[0017]

[0018] Where s and T represent satellite and satellite system respectively, c represents the speed of light, and subscripts r and j represent reception and frequency respectively. is the pseudorange observation value obtained from the receiver, is the geometric distance between the high-orbit satellite and the satellite transmitting the leaked signal; dt r and dt s,T represent the satellite clock error and receiver clock error respectively. The satellite clock error is corrected using the broadcast ephemeris clock error parameters, and the receiver clock error is used as the parameter to be estimated. represents the frequency-dependent ionospheric delay amplification factor; represents the slant ionospheric delay corresponding to frequency f1, which is corrected using the ionospheric model published in the broadcast ephemeris; and They represent the receiver-side pseudorange hardware delay and the satellite-side pseudorange hardware delay, respectively. The receiver-side pseudorange hardware delay is estimated together with the receiver clock error, and the satellite-side pseudorange hardware delay is corrected using the TGD parameter in the broadcast ephemeris. represents the sum of pseudo-observation noise, multipath effects, and other unmodeled errors;

[0019] The estimated equation after model modification and linearization is:

[0020]

[0021] in, Pseudorange observation value The difference from the error model value, u represents the direction cosine, and x represents the three-dimensional increment relative to the initial coordinate The parameters to be estimated are recorded as The parameters to be estimated include four estimation parameters: three-dimensional coordinate increment and parameterized receiver clock error; therefore, the minimum number of satellites required is 4, and the satellite coordinates are obtained using the least squares estimation method.

[0022] Furthermore, the outlier removal preprocessing includes:

[0023] When the geometric dilution of precision of the coarse orbit data is greater than 20, the corresponding orbit point is eliminated; or

[0024] When the number of satellite observations used in dynamic pseudorange orbit determination is less than or equal to 5, the corresponding orbit point is eliminated.

[0025] Further, perform smooth fitting and equidistant sampling on the orbit data after outlier rejection to obtain smooth orbit data, including:

[0026] Use a sliding window to perform quadratic polynomial fitting on the orbit data after outlier rejection. The quadratic polynomial fitting formula is

[0027] y(t) = a0 + a1t + a2t 2

[0028] where a0, a1, and a2 represent the parameters to be fitted;

[0029] The goal of fitting is to minimize the error function J(a0, a1, a2),

[0030]

[0031] where t i represents time, y i represents the orbit point, and n represents the number of points used for fitting the parameters;

[0032] After data fitting, use the following formula to reject outliers

[0033] |v i | > 3σ or v i > 50

[0034] where v i is the fitting residual, and σ is the standard deviation of the fitting residual, which is expressed by the following formula

[0035]

[0036] where represents the average value of v i ;

[0037] Remove outliers and calculate the polynomial parameters a0, a1, a2 to generate equidistant sampling points of the orbit. Set the sampling time, and use the equidistant sampling points as the smooth orbit data.

[0038] Further, determine the orbit determination arc segment according to the scheduling time and the orbit maneuvering time, including:

[0039] Determine the orbit determination arc segment according to the following conditions:

[0040] When t1 > tm2, the orbit determination arc segment for batch processing is from t1 to t2;

[0041] When tm1 < t1 < tm2 and t2 > tm2, the orbit determination arc segment for batch processing is from tm2 to t2;

[0042] When tm1 < t1 < tm2 and t2 < tm2, the orbit determination integration point is t1 = t2;

[0043] When t1 < tm1 and tm1 < t2 < tm2, the orbit determination integration point is t1 = t2;

[0044] Where, t1 is the start time of the orbit determination arc segment, t2 is the end time of the orbit determination arc segment, tm1 is the start time of the orbit maneuver, tm2 is the end time of the orbit maneuver, and the orbit determination integration point is the start moment of the orbit integration;

[0045] The initial orbit is obtained according to the start moment of the orbit determination arc segment and the fitting formula, and each scheduling of orbit determination is separated by a set time.

[0046] Further, the sampling time is 30 seconds; and / or

[0047] Each scheduling of orbit determination is separated by a set time of 10 minutes or 30 minutes.

[0048] Further, based on the orbit determination arc segment and the smooth orbit data, the optimal orbit data is obtained by using the motion equation and state transition matrix of the geostationary satellite for batch least squares iteration. The orbit prediction includes:

[0049] During the non-maneuvering period of the satellite, the motion equation of the geostationary satellite in the inertial system is

[0050]

[0051] Where, r, respectively represent the position, velocity, and acceleration vectors of the satellite's center of mass; P represents the dynamic parameters to be estimated; GM e represents the gravitational constant of the earth; the first term f0 on the right end represents the central gravitational force of the two-body motion, and the second term f1 represents the sum of the orbital perturbation forces acting on the satellite other than the central gravitational force;

[0052] The motion equation is transformed into the following differential equation

[0053]

[0054] Set the state vector of the geostationary satellite as Set the right function vector

[0055] Then the differential equation is transformed into

[0056]

[0057] By integrating the initial state vector at time t0, the state vector X at time t is obtained t, we get the general solution of the above formula,

[0058] X(t)=φ(t,t0)X(t0)

[0059] Among them, φ(t,t0) represents the state transfer matrix;

[0060] The state transfer matrix of the high-orbit satellite is:

[0061]

[0062] Among them, X GNSSi Indicates the GNSS satellite at time t i The state vector of Represents the state vector of the GNSS satellite at the initial moment;

[0063] According to the above state transfer matrix, the orbit state of each sampling point in the orbit arc can be obtained: And get the satellite status X at time i i , the error equation at time i is,

[0064]

[0065] Among them, ΔX0 represents the initial state correction amount, and Δp0 represents the initial parameter correction amount;

[0066] The data in the entire arc segment is used to perform batch least squares iteration to obtain the optimal orbit data;

[0067] The orbit prediction is obtained by performing the above-mentioned state transition using the smoothed orbit data and the solved parameters;

[0068] During the satellite maneuver, the motion equation of the high-orbit satellite in the inertial system is:

[0069]

[0070] The magnitude of the acceleration generated by the satellite thrust f2 is,

[0071]

[0072] Where m1 and m2 represent the satellite mass at the time of satellite ignition and shutdown, respectively; w represents the total ignition pulse width; and T represents the pulse period.

[0073] Based on the above motion equations and transfer matrices, orbit prediction during satellite maneuvers is achieved.

[0074] The present invention also provides a system for the above-mentioned high-orbit satellite autonomous measurement, control and orbit determination method, the system comprising:

[0075] The ephemeris and observation data acquisition module is configured to obtain the onboard GNSS broadcast ephemeris data and single-frequency pseudo-range observation data of the high-orbit satellite;

[0076] a coarse orbit data generation module configured to generate coarse orbit data of a high-orbit satellite using a dynamic pseudorange orbit determination algorithm based on the GNSS broadcast ephemeris data and the single-frequency pseudorange observation data;

[0077] a preprocessing module configured to perform outlier removal preprocessing on the coarse track data to obtain track data after outlier removal;

[0078] A fitting module is configured to perform smooth fitting and equally spaced sampling on the orbital data after outliers are removed to obtain smoothed orbital data;

[0079] An orbit determination arc segment determination module is configured to determine the orbit determination arc segment according to the scheduling time and the orbit maneuvering time; and

[0080] The optimal orbit data and orbit prediction module is configured to obtain the optimal orbit data and perform orbit prediction based on the orbit determination arc and the smoothed orbit data using the motion equation of the high-orbit satellite and the state transfer matrix batch least squares iteration.

[0081] The present invention further provides an electronic device, comprising:

[0082] a processor configured to execute machine-readable instructions;

[0083] A graphics card with an artificial intelligence chip, configured to train the high-orbit satellite autonomous measurement, control and orbit determination method; and

[0084] The memory is configured to store machine-readable instructions, which, when executed by the processor and / or graphics card, perform the steps of the high-orbit satellite autonomous measurement, control and orbit determination method.

[0085] The present invention also provides a computer-readable storage medium, characterized in that machine-readable instructions are stored thereon, and when the machine-readable instructions are executed by a processor, the steps of the high-orbit satellite autonomous measurement, control and orbit determination method are executed.

[0086] The technical solution provided by the present invention has the following advantages:

[0087] 1. The proposed method for autonomous measurement, control, and orbit determination of high-orbit satellites uses only onboard single-frequency GNSS data, broadcast ephemeris, orbit maneuver-related information, and model files related to dynamic orbit determination. It does not rely on information transmission from ground-based measurement and control resources, enabling autonomous orbit determination onboard without increasing the load on other onboard sensors. This reduces the complexity of data fusion calculations, minimizes computational effort, and saves time.

[0088] 2. The autonomous measurement, control and orbit determination method for high-orbit satellites proposed in this invention addresses the problems of frequent maneuvers of high-orbit satellites, the need for autonomous orbit determination, and signal quality loss. It proposes a dynamic orbit determination and prediction scheme based on single-frequency GNSS orbit determination data preprocessing and considering maneuvering forces.

[0089] 3. The high-orbit satellite autonomous measurement, control and orbit determination method proposed in this invention proposes a relatively complete data preprocessing method, which uses the number of satellites and the geometric precision factor to eliminate outliers, and then uses quadratic fitting based on a sliding window, and uses three times the mean square error and the fitting residual threshold to eliminate outliers, thereby obtaining equally spaced orbit data without outliers.

[0090] 4. The autonomous measurement, control and orbit determination method for high-orbit satellites proposed in this invention uses maneuvering time and real-time scheduling of orbit determination arc time to determine the final orbit determination arc and orbit prediction time, solving the problem of decreased orbit determination and orbit prediction accuracy caused by frequent maneuvers in high orbits, and has the characteristics of real-time and high precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] To further illustrate the above and other advantages and features of various embodiments of the present invention, a more detailed description of various embodiments of the present invention will be presented with reference to the accompanying drawings. It will be understood that these drawings depict only typical embodiments of the present invention and are not to be considered as limiting the scope thereof. In the drawings, for clarity, identical or corresponding components will be represented by the same or similar reference numerals.

[0092] Figure 1 A schematic diagram showing a flow chart of a method for autonomous measurement, control and orbit determination of a high-orbit satellite according to an embodiment of the present invention; and

[0093] Figure 2 A schematic diagram of an autonomous measurement, control and orbit determination system for a high-orbit satellite according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0094] In the following description, the present invention is described with reference to various embodiments. However, those skilled in the art will recognize that the embodiments may be implemented without one or more of the specific details or with other alternative and / or additional methods or components. In other cases, well-known structures or operations are not shown or described in detail to avoid obscuring the inventive aspects of the present invention. Similarly, specific numbers and configurations are set forth for illustrative purposes in order to provide a comprehensive understanding of the embodiments of the present invention. However, the present invention is not limited to these specific details.

[0095] In this specification, reference to "one embodiment" or "the embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. The appearances of the phrase "in one embodiment" in various places in this specification are not necessarily all referring to the same embodiment.

[0096] It should be noted that the embodiments of the present invention describe the method steps in a specific order, but this is only for the purpose of illustrating the specific embodiment and does not limit the order of the steps. On the contrary, in different embodiments of the present invention, the order of the steps can be adjusted according to actual needs.

[0097] Traditional orbit measurement and control methods use a single ground-based measurement, or astronomical observation and inertial combined navigation autonomous orbit determination technology, or a combination of several methods. Due to the small geometric changes and poor structure of high-orbit satellites relative to ground stations, it is difficult for ground measurement and control methods to provide sufficiently accurate orbit determination data. In addition, the real-time transmission time of ground station data and the limited resources of ground measurement and control stations also make this method have certain limitations. Astronomical data is limited by the visibility of celestial bodies and requires various sensor corrections, which makes the implementation complex and the accuracy cannot be guaranteed. Inertial navigation has a high information output frequency and occupies a large amount of space. If a high-orbit satellite performs long-term continuous orbital maneuvers, the errors in the data obtained by integrating the orbital dynamics model will accumulate, seriously affecting the orbit determination accuracy. Since more complex algorithms cannot be used on board, the use of multiple fusion technologies will also bring a large load. Therefore, how to use single GNSS onboard data with poor observation quality to perform autonomous orbit control of high-orbit satellites and ensure the real-time and accuracy of orbit determination is a technical problem that the present invention needs to solve.

[0098] Current real-time orbit determination algorithms based on space-based GNSS are based on Kalman filtering. However, Kalman filters rely on both system noise variance and measurement noise variance, making the data quality of GNSS signals with leaky signals extremely unstable, leading to uncertain measurement noise. Furthermore, during actual high-orbit satellite operations, satellites are subject to various perturbations, such as the Earth's non-spherical gravity and solar pressure. The geometric changes in position observations caused by satellite maneuvers also lead to uncertainty in the statistical characteristics of the system noise variance. Therefore, achieving both stability and real-time performance is a challenge addressed by the present invention.

[0099] High-orbit satellites often undergo frequent orbital maneuvers, which cause changes in both the satellite's attitude and orbital position. Propulsion systems are generally divided into chemical and electric propulsion. Chemical propulsion's main advantages are high thrust and rapid response, enabling rapid changes in the spacecraft's speed and orbit. Ion electric propulsion boasts wide-range, continuous, fine-tuned adjustments and low noise. Satellite maneuvers can complicate orbit determination. A complete orbital arc is divided into three parts: pre-control, inter-control, and post-control. Producing reliable, high-precision orbit determination in real time across these three parts, while ensuring the accuracy and reliability of orbit determination and prediction, is a challenging task.

[0100] The present invention proposes a method for autonomous measurement, control and orbit determination of high-orbit satellites. In order to solve the problems of data transmission burden, low precision, complex calculation, sensor correction and high requirements for on-board equipment in traditional ground-based and space-based single and fusion technologies, it is proposed to use satellite-borne GNSS single-frequency pseudo-range observation data for preliminary dynamic pseudo-range orbit determination. Pure kinematic orbit determination does not need to consider the influence of perturbation force. In order to solve the problem of outliers in the orbit caused by the quality of leaked signal data, it is further proposed to use the PDOP value of the satellite geometric configuration and the number of observed satellites for preliminary elimination. Then, the high-orbit satellite is used to satisfy the quadratic polynomial in the short term to perform sliding window smoothing fitting on the orbit within the orbit determination arc segment and use triple mean error to further remove noise. In order to make the integrator of batch orbit determination more effective, the orbit within the arc segment is fitted into equally spaced orbit data.

[0101] To address the problem of unreliable orbit determination results caused by unclear statistical characteristics of measurement noise and system noise on the satellite in filtered orbit determination, the present invention uses a method of least squares batch processing of real-time scheduling of short-arc segment orbit data to meet the real-time requirements and the accuracy of orbit determination results. It can adapt to poor observation conditions and has the characteristics of wide application range and stability.

[0102] To address the problem of frequent maneuvers of high-orbit satellites, the present invention uses maneuvering time to divide orbital arcs to meet the requirements of orbit determination and prediction during maneuvers. By dividing the orbital arcs, the real-time scheduled orbit determination task can be divided into three parts: orbit determination and prediction before control, orbit determination and prediction during control, and orbit determination and prediction after control. This can meet the real-time high-precision orbit determination and prediction needs during maneuvers, as well as the problem of rapid orbit recovery after maneuvers.

[0103] Figure 1 The following is a flow chart showing a method for autonomous measurement, control and orbit determination of a high-orbit satellite according to an embodiment of the present invention. Figure 1 , the high-orbit satellite autonomous measurement, control and orbit determination method proposed by the present invention is described. In one embodiment of the present invention, the high-orbit satellite autonomous measurement, control and orbit determination method can be executed by a computer. Figure 1 As shown, the high-orbit satellite autonomous measurement, control and orbit determination method includes the following steps:

[0104] First, obtain onboard GNSS broadcast ephemeris data and single-frequency pseudorange observation data from high-orbit satellites. In one embodiment of the present invention, this also includes obtaining satellite attitude related to orbital maneuvers, thrust time, thrust magnitude, pulse period, and satellite mass information before and after the maneuver related to orbital control forces; and preparing batch orbit determination data files, such as various model files. In one embodiment of the present invention, single-frequency pseudorange observation data typically refers to single-frequency pseudorange observation data from four or more satellites.

[0105] Next, based on the GNSS broadcast ephemeris data and single-frequency pseudorange observation data, the coarse orbit data of the high-orbit satellite is generated by the dynamic pseudorange orbit determination algorithm. The dynamic pseudorange orbit determination algorithm uses the least squares method to calculate the minimum norm of the difference between the pseudorange observation value and the error model value. The pseudorange observation value is calculated by the pseudorange observation equation of the onboard receiver.

[0106]

[0107] Where s and T represent satellite and satellite system respectively, c represents the speed of light, and subscripts r and j represent reception and frequency respectively. is the pseudorange observation value obtained from the receiver, is the geometric distance between the high-orbit satellite and the satellite transmitting the leaked signal; dt r and dt s,T represent the satellite clock error and receiver clock error respectively. The satellite clock error is corrected using the broadcast ephemeris clock error parameters, and the receiver clock error is used as the parameter to be estimated. represents the frequency-dependent ionospheric delay amplification factor; represents the slant ionospheric delay corresponding to frequency f1, which is corrected using the ionospheric model published in the broadcast ephemeris; and They represent the receiver-side pseudorange hardware delay and the satellite-side pseudorange hardware delay, respectively. The receiver-side pseudorange hardware delay is estimated together with the receiver clock error, and the satellite-side pseudorange hardware delay is corrected using the TGD (Timing Group Delay) parameter in the broadcast ephemeris. represents the sum of pseudo-observation noise, multipath effects, and other unmodeled errors without additional correction.

[0108] The above-mentioned satellite receiver pseudorange observation equation represents the original pseudorange of the receiver The relationship between the error model value and the error model value. The error model value includes ionospheric delay, hardware delay parameters, etc.

[0109] According to the above model correction method and because the satellite coordinates and pseudorange observation values ​​in the pseudorange observation equation of the satellite receiver are nonlinear, the estimation equation after model correction and linearization is:

[0110]

[0111] in, Pseudorange observation value The difference from the error model value, u represents the direction cosine, and x represents the three-dimensional increment relative to the initial coordinate The parameters to be estimated are recorded as The parameters to be estimated include four estimation parameters: three-dimensional coordinate increment and parameterized receiver clock error; therefore, the minimum number of satellites required is 4, and the satellite coordinates can be obtained using a general least squares estimation method.

[0112] The parameters to be estimated in the single system equation are the satellite coordinate increment and the receiver clock error If there are multiple systems, it is necessary to add the deviation between the systems as the parameter to be estimated.

[0113] Next, the rough orbit data is preprocessed to remove outliers to obtain orbit data after outliers are removed. The outlier removal preprocessing includes using the geometric precision dilution PDOP and the number of satellite observations used for dynamic pseudorange orbit determination as indicators. The larger the PDOP value, the worse the geometric structure. When the PDOP value on the high-orbit satellite is poor, it can reach dozens. The PDOP value here is an empirical value obtained through a large number of engineering practice experiments, and there is no need to consider the difference in orbit types. The present invention is aimed at high-orbit GEO (geostationary orbit, geostationary orbit) satellites, and the present invention has been applied to the actual application of high-orbit satellite measurement, control and orbit determination and is running steadily.

[0114] Specifically, the outlier removal preprocessing includes:

[0115] When the geometric dilution of precision of the coarse orbit data is greater than 20, the corresponding orbit point is eliminated; or when the number of satellite observations used in the dynamic pseudorange orbit determination is less than or equal to 5, the corresponding orbit point is eliminated.

[0116] Next, the track data after outliers are removed is smoothed and sampled at equal intervals to obtain smoothed track data.

[0117] After removing the outliers, the orbit data with unequal intervals are fitted with the least squares quadratic term using a smoothing window. Noise points are removed and the points are fitted into equal intervals to facilitate the integration of the integrator for batch orbit determination. The smoothing window is selected as 5 minutes. For a group of unequally spaced data points (t i ,y i )(where t i Indicates time, y i represents the orbital points), the following quadratic polynomial can be used for fitting:

[0118] y(t)=a0+a1t+a2t 2

[0119] Among them, a0, a1, and a2 represent the parameters to be fitted.

[0120] The three parameters can be fitted by the least squares method. The goal of fitting is to minimize the error function J(a0, a1, a2).

[0121]

[0122] Among them, t i represents time, y i represents the orbital point, and n represents the number of points used for fitting parameters.

[0123] After data fitting, the triple mean error and the fitting residual threshold are used to剔除异常值 (remove outliers). The fitting residual threshold is set to 50m. The following formula is used to remove outliers:

[0124] |v[[ID=1s]] i | > 3σ or v i > 50

[0125] Among them, v i represents the fitting residual, and σ represents the standard deviation of the fitting residual, which is expressed by the following formula:

[0126]

[0127] Among them, represents the average value of v[[ID=az]] i .

[0128] By the above operations, the noise points, that is, the outliers are removed, and the polynomial parameters a0, a1, a2 are obtained. The equally spaced sampling points of the orbit can be regenerated. The sampling time is set to 30s, that is, t k = k * 30 (k is an integer). These sampling points are used as the input data for subsequent batch orbit determination, that is, the smoothed orbit data.

[0129] Next, the orbit determination arc segment is determined according to the scheduling time and the orbit maneuver time.

[0130] According to the current scheduling time, the required orbit determination arc segment (generally set to 3h), and the orbit maneuver time, the final orbit determination arc segment and the initial orbit at that time are determined. Assume that the current scheduling time is set as the end time t2 of the orbit determination arc segment. Then theoretically, the start time of the orbit determination arc segment is t1 = t2 - 3h. Assume that the orbit maneuver time is from tm1 to tm2, and the orbit integration point is the start time of orbit integration. Then, according to the following conditions, the orbit determination arc segment for this scheduling is determined:

[0131] When t1 > tm2, the batch orbit determination arc segment is from t1 to t2 and forecast for 1 day;

[0132] When tm1 < t1 < tm2 and t2 > tm2, the batch orbit determination arc segment is from tm2 to t2 and forecast for 1 day;

[0133] When tm1 < t1 < tm2 and t2 < tm2, the orbit integration point is t1 = t2 and forecast for 1 day; <00S0357>When t1 < tm1 and tm1 < t2 < tm2, the orbit determination integration point is that t1 = t2 forecasts one day.

[0135] Based on the starting time of the orbit determination arc segment and the above fitting formula, the initial orbit can be obtained. Each scheduling of orbit determination is separated by a certain time, such as 10 minutes or 30 minutes, then real-time orbit determination and prediction can be carried out to meet the orbit demand accuracy during high-orbit maneuvers.

[0136] Finally, based on the orbit determination arc segment and the smoothed orbit data, the motion equation and state transition matrix of the high-orbit satellite are used for batch least squares iteration to obtain the optimal orbit data and perform orbit prediction.

[0137] During the non-maneuvering period of the satellite, the motion equation of the high-orbit satellite in the inertial system is

[0138]

[0139] where r, respectively represent the position, velocity, and acceleration vectors of the satellite's center of mass; P represents the dynamic parameters to be estimated; GM e represents the Earth's gravitational constant; the first term f0 on the right end represents the central gravitational force of the two-body motion, and the second term f1 represents the sum of the orbital perturbation forces acting on the satellite other than the central gravitational force.

[0140] Transform the above motion equation into the following differential equation

[0141]

[0142] Set the state vector of the high-orbit satellite as Set the right function vector

[0143] Then the differential equation is transformed into

[0144]

[0145] By integrating the initial state vector at time t0, the state vector X t at time t is obtained, that is, the general solution of the above equation is obtained

[0146]

[0147] This equation is a nonlinear equation. After linearizing it, we get

[0148] X(t) = φ(t, t0)X(t0)

[0149] Among them, φ(t,t0) represents the state transfer matrix. The state transfer matrix can be obtained by integrating the motion equation of the high-orbit satellite and the variational equation derived from it.

[0150] The state transfer matrix of the high-orbit satellite is:

[0151]

[0152] Among them, X GNSSi Indicates the GNSS satellite at time t i The state vector of Represents the state vector of the GNSS satellite at the initial time.

[0153] According to the above state transfer matrix, the orbit state of each sampling point in the orbit arc can be obtained: And get the satellite status X at time i i , the error equation at time i is,

[0154]

[0155] Among them, ΔX0 represents the initial state correction amount, and Δp0 represents the initial parameter correction amount.

[0156] The data in the entire arc segment is used to perform batch least squares iteration to obtain the optimal orbit solution, i.e., orbit data.

[0157] The orbit prediction is obtained by performing the above-mentioned state transition using the smoothed orbit data and the solved parameters.

[0158] During satellite maneuvers, the orbit prediction must take into account the acceleration caused by the maneuvering force. During satellite maneuvers, the motion equation of a high-orbit satellite in the inertial system is:

[0159]

[0160] The magnitude of the acceleration generated by the satellite thrust f2 is,

[0161]

[0162] Where m1 and m2 represent the satellite masses at the time of satellite ignition and shutdown, respectively; w represents the total ignition pulse width; and T represents the pulse period.

[0163] According to the above motion equations and transfer matrices, orbit prediction during satellite maneuvers is achieved to meet the prediction accuracy during maneuvers.

[0164] The present invention addresses the data quality, maneuvering orbit determination and prediction problems existing in the measurement, control and orbit determination technology of high-orbit satellite autonomous orbit determination. First, dynamic pseudo-range real-time orbit determination is performed based on single-frequency onboard GNSS data to obtain a series of rough orbit positions. The rough orbit positions are then preprocessed in two steps to obtain equally spaced smooth orbit points without wild values ​​and noise. In the first step, the number of satellite observations and the geometric precision dilution PDOP value of the equation are used to eliminate the larger wild values ​​of the rough position. In the second step, a 5-minute sliding window is used for short-term quadratic fitting, and three times the mean square error and the fitting residual are used to further eliminate wild values ​​and noise, and equally spaced smooth orbit points are obtained by fitting. After preprocessing, the orbit arc segment of the real-time scheduling orbit determination task is determined according to the orbit maneuver time, and the orbit is determined and predicted using the orbit dynamics least squares batch processing method. During the maneuver, the orbit control force needs to be considered. The proposed autonomous measurement, control, and orbit determination method for high-orbit satellites is independent of ground-based or other sensors, offering simple, independent operation, simple data calculation, and low cost. Furthermore, the combination of pure dynamic orbit determination and dynamic orbit determination and prediction that considers maneuvering forces ensures orbit determination and prediction accuracy sufficient for frequent high-orbit control. Furthermore, through multi-precision control and real-time scheduling, the present invention meets real-time and reliable requirements. This present invention provides a comprehensive solution for autonomous orbit determination for high-orbit satellites undergoing frequent maneuvers.

[0165] The autonomous measurement and control orbit determination method for high-orbit satellites proposed in the present invention uses only on-board single-frequency GNSS data, broadcast ephemeris, orbit maneuver-related information, and relevant model files for dynamic orbit determination. It does not rely on information transmission from ground measurement and control resources, realizes autonomous orbit determination on the satellite, does not increase the load on other on-board sensors, reduces the complexity of data fusion calculations, has a small amount of calculation, and takes less time. To address the problems of frequent maneuvers of high-orbit satellites, the need for autonomous orbit determination, and signal quality loss, a dynamic orbit determination and prediction scheme based on single-frequency GNSS orbit determination data preprocessing and considering maneuvering forces is proposed. A relatively complete data preprocessing method is proposed, which uses the number of satellites and the geometric precision factor to eliminate outliers, then uses a sliding window-based quadratic term fitting, and uses triple the mean square error and fitting residual threshold to eliminate outliers, thereby obtaining equally spaced orbit data without outliers. It is proposed to use the maneuvering time and the real-time scheduling orbit determination arc time to determine the final orbit determination arc and orbit prediction time, solving the problem of decreased orbit determination and orbit prediction accuracy caused by frequent maneuvers in high-orbit, and has the characteristics of real-time high precision.

[0166] In one embodiment of the present invention, the present invention further provides a system for the above-mentioned high-orbit satellite autonomous measurement, control and orbit determination method, such as Figure 2 As shown, the system includes:

[0167] The ephemeris and observation data acquisition module is configured to obtain the onboard GNSS broadcast ephemeris data and single-frequency pseudo-range observation data of the high-orbit satellite;

[0168] a coarse orbit data generation module configured to generate coarse orbit data of a high-orbit satellite using a dynamic pseudorange orbit determination algorithm based on the GNSS broadcast ephemeris data and the single-frequency pseudorange observation data;

[0169] a preprocessing module configured to perform outlier removal preprocessing on the coarse track data to obtain track data after outlier removal;

[0170] A fitting module is configured to perform smooth fitting and equally spaced sampling on the orbital data after outliers are removed to obtain smoothed orbital data;

[0171] An orbit determination arc segment determination module is configured to determine the orbit determination arc segment according to the scheduling time and the orbit maneuvering time; and

[0172] The optimal orbit data and orbit prediction module is configured to obtain the optimal orbit data and perform orbit prediction based on the orbit determination arc and the smoothed orbit data using the motion equation of the high-orbit satellite and the state transfer matrix batch least squares iteration.

[0173] In one embodiment of the present invention, the present invention further provides an electronic device comprising: a processor, a graphics card having an artificial intelligence chip, and a memory, wherein the memory is configured to store machine-readable instructions, the graphics card is configured to train the high-orbit satellite autonomous measurement, control, and orbit determination method, and the processor is configured to execute the machine-readable instructions. When the processor and / or the graphics card execute the machine-readable instructions, the following processing steps are implemented: obtaining onboard GNSS broadcast ephemeris data and single-frequency pseudorange observation data of the high-orbit satellite; generating coarse orbit data of the high-orbit satellite using a dynamic pseudorange orbit determination algorithm based on the GNSS broadcast ephemeris data and single-frequency pseudorange observation data; performing outlier removal preprocessing on the coarse orbit data to obtain orbit data after outlier removal; performing smooth fitting and equal-interval sampling on the orbit data after outlier removal to obtain smoothed orbit data; determining an orbit determination arc segment based on the scheduling time and orbit maneuvering time; and, based on the orbit determination arc segment and the smoothed orbit data, using the motion equation of the high-orbit satellite and the state transition matrix batch least squares iteration to obtain optimal orbit data and perform orbit prediction.

[0174] The graphics card can preferably have a GPU computing power higher than 5.0. Since the amount of data required for training is large, providing a graphics card configuration can significantly improve the training speed.

[0175] The memory includes various media that can store machine-readable instructions, such as a USB flash drive, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk.

[0176] It can be understood that in addition to the memory and processor mentioned above, the above-mentioned computer system also includes other software and hardware components not listed in this specification. The specific components can be determined according to the model of the specific data processing equipment in different application scenarios. This specification will not list them one by one in detail.

[0177] In one embodiment of the present invention, the present invention also provides a computer-readable storage medium having machine-readable instructions stored thereon, which implement the following processing steps when executed by a processor: obtaining onboard GNSS broadcast ephemeris data and single-frequency pseudorange observation data of a high-orbit satellite; generating coarse orbit data of the high-orbit satellite through a dynamic pseudorange orbit determination algorithm based on the GNSS broadcast ephemeris data and single-frequency pseudorange observation data; performing outlier removal preprocessing on the coarse orbit data to obtain orbit data after outlier removal; performing smooth fitting and equal-interval sampling on the orbit data after outlier removal to obtain smoothed orbit data; determining an orbit determination arc segment based on the scheduling time and orbit maneuvering time; and using the motion equation of the high-orbit satellite and the state transfer matrix batch least squares iteration based on the orbit determination arc segment and the smoothed orbit data to obtain optimal orbit data and perform orbit prediction.

[0178] Although various embodiments of the present invention have been described above, it should be understood that they are presented as examples only and not as limitations. It will be apparent to those skilled in the relevant art that various combinations, modifications, and variations may be made thereto without departing from the spirit and scope of the present invention. Therefore, the breadth and scope of the present invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined based on the technical solutions of the present invention and their equivalents.

[0179] The references cited in this invention are listed as follows:

[0180] [1] Yang Chengyun. Simulation analysis of orbit determination of Tianqin probe based on leaked navigation signal of satellite-borne GNSS[D]. Sun Yat-sen University, 2022.

Claims

1. A method for autonomous measurement, control and orbit determination of a high-orbit satellite, characterized in that: It includes the following steps: Obtain the on-board GNSS broadcast ephemeris data and single-frequency pseudorange observation data of the high-orbit satellite; Based on the GNSS broadcast ephemeris data and the single-frequency pseudorange observation data, generate the coarse orbit data of the high-orbit satellite through the dynamic pseudorange orbit determination algorithm; Perform preprocessing for wild value rejection on the coarse orbit data to obtain the orbit data after wild value rejection; Perform smoothing fitting and equally spaced sampling on the orbit data after wild value rejection to obtain the smoothed orbit data; Determine the orbit determination arc segment according to the scheduling time and the orbit maneuver time; And Based on the orbit determination arc segment and the smoothed orbit data, use the motion equation and state transition matrix of the high-orbit satellite for batch least squares iteration to obtain the optimal orbit data and perform orbit prediction.

2. The high-orbit satellite autonomous measurement, control and orbit determination method according to claim 1, characterized in that: The dynamic pseudorange orbit determination algorithm uses the least squares method to calculate the minimum norm of the difference between the pseudorange observation value and the error model value; The pseudorange observation equation of the on-board receiver is as follows, Where s and T represent satellite and satellite system respectively, c represents the speed of light, and subscripts r and j represent reception and frequency respectively. is the pseudorange observation value obtained from the receiver, is the geometric distance between the high-orbit satellite and the satellite transmitting the leaked signal; dt r and dt s,T represent the satellite clock error and receiver clock error respectively. The satellite clock error is corrected using the broadcast ephemeris clock error parameters, and the receiver clock error is used as the parameter to be estimated. represents the frequency-dependent ionospheric delay amplification factor; represents the slant ionospheric delay corresponding to frequency f1, which is corrected using the ionospheric model published in the broadcast ephemeris; and They represent the receiver-side pseudorange hardware delay and the satellite-side pseudorange hardware delay, respectively. The receiver-side pseudorange hardware delay is estimated together with the receiver clock error, and the satellite-side pseudorange hardware delay is corrected using the TGD parameter in the broadcast ephemeris. represents the sum of pseudo-observation noise, multipath effects, and other unmodeled errors; The estimated equation after model correction and linearization is: in, Pseudorange observation value The difference from the error model value, u represents the direction cosine, and x represents the three-dimensional increment relative to the initial coordinate The parameters to be estimated are recorded as The parameters to be estimated include four estimation parameters: three-dimensional coordinate increment and parameterized receiver clock error; therefore, the minimum number of satellites required is 4, and the satellite coordinates are obtained using the least squares estimation method.

3. The high-orbit satellite autonomous measurement, control and orbit determination method according to claim 1, characterized in that: The preprocessing for wild value rejection includes: When the geometric dilution of precision of the coarse orbit data is greater than 20, reject the corresponding orbit points; or When the number of satellite observations used for dynamic pseudorange orbit determination is less than or equal to 5, reject the corresponding orbit points.

4. The high-orbit satellite autonomous measurement, control and orbit determination method according to claim 1, characterized in that: Performing smoothing fitting and equally spaced sampling on the orbit data after wild value rejection to obtain the smoothed orbit data includes: Perform quadratic polynomial fitting on the orbit data after wild value rejection using a sliding window. The quadratic polynomial fitting formula is, y(t)=a0+a1t+a2t 2 where a0, a1, and a2 represent the parameters to be fitted; The goal of fitting is to minimize the error function J(a0, a1, a2), Among them, t i Indicates time, y i represents the orbital point, and n represents the number of points used for fitting parameters; After data fitting, use the following formula to reject outliers, |v i |>3σ or v i >50 Among them, v i Represents the fitting residual, σ represents the standard deviation of the fitting residual, which is expressed as follows: in, Indicates v i The average value of Remove outliers and calculate the polynomial parameters a0, a1, a2 to generate equally spaced sampling points of the orbit, set the sampling time, and use the equally spaced sampling points as the smoothed orbit data.

5. The high-orbit satellite autonomous measurement, control and orbit determination method according to claim 1, characterized in that: Determining the orbit determination arc segment according to the scheduling time and the orbit maneuver time includes: Determine the orbit determination arc segment according to the following conditions: When t1 > tm2, the orbit determination arc segment for batch processing is from t1 to t2; When tm1 < t1 < tm2 and t2 > tm2, the orbit determination arc segment for batch processing is from tm2 to t2; When tm1 < t1 < tm2 and t2 < tm2, the orbit integration point is t1 = t2; When t1 < tm1 and tm1 < t2 < tm2, the orbit integration point is t1 = t2; where t1 is the start time of the orbit determination arc segment, t2 is the end time of the orbit determination arc segment, tm1 is the start time of the orbit maneuver, tm2 is the end time of the orbit maneuver, and the orbit integration point is the start time of orbit integration; Obtain the initial orbit according to the start time of the orbit determination arc segment and the fitting formula, and each scheduling of orbit determination is separated by a set time.

6. The high-orbit satellite autonomous measurement and control orbit determination method according to claim 4 or 5, wherein The sampling time is 30 seconds; and / or Each scheduling of orbit determination is separated by a set time of 10 minutes or 30 minutes.

7. The method for autonomous measurement, control and orbit determination of a high-orbit satellite according to claim 1, wherein: Based on the orbit determination arc segment and the smoothed orbit data, using the motion equation and state transition matrix of the high-orbit satellite for batch least squares iteration to obtain the optimal orbit data and perform orbit prediction includes: During the non-maneuvering period of the satellite, the motion equation of the high-orbit satellite in the inertial system is: Among them, r, Represent the position, velocity, and acceleration vectors of the satellite's center of mass respectively; P represents the dynamic parameters to be estimated; GM e represents the earth's gravitational constant; the first term f0 on the right side represents the central gravity of the two-body motion, and the second term f1 represents the sum of the orbital perturbations acting on the satellite except the central gravity; The equation of motion is transformed into the following differential equation, Assume the state vector of the high-orbit satellite is Let the right function vector Then the differential equation is transformed into, By the initial state vector at time t0 Integrate to get the state vector X at time t t , we get the general solution of the above formula, X(t)=φ(t,t0)X(t0) Among them, φ(t,t0) represents the state transfer matrix; The state transfer matrix of the high-orbit satellite is: Among them, X GNSSi Indicates the GNSS satellite at time t i The state vector of Represents the state vector of the GNSS satellite at the initial moment; According to the above state transfer matrix, the orbit state of each sampling point of the orbit arc segment is obtained And get the satellite status X at time i i , the error equation at time i is, Among them, ΔX0 represents the initial state correction amount, and Δp0 represents the initial parameter correction amount; The data in the entire arc segment is used to perform batch least squares iteration to obtain the optimal orbit data; The orbit prediction is obtained by performing the above-mentioned state transition using the smoothed orbit data and the solved parameters; During the satellite maneuver, the motion equation of the high-orbit satellite in the inertial system is: The magnitude of the acceleration generated by the satellite thrust f2 is, Where m1 and m2 represent the satellite mass at the time of satellite ignition and shutdown, respectively; w represents the total ignition pulse width; and T represents the pulse period. Based on the above motion equations and transfer matrices, orbit prediction during satellite maneuvers is achieved.

8. A system for the autonomous measurement, control and orbit determination method for a high-orbit satellite according to any one of claims 1 to 7, characterized in that: include: The ephemeris and observation data acquisition module is configured to obtain the onboard GNSS broadcast ephemeris data and single-frequency pseudo-range observation data of the high-orbit satellite; a coarse orbit data generation module configured to generate coarse orbit data of a high-orbit satellite using a dynamic pseudorange orbit determination algorithm based on the GNSS broadcast ephemeris data and the single-frequency pseudorange observation data; a preprocessing module configured to perform outlier removal preprocessing on the coarse track data to obtain track data after outlier removal; A fitting module is configured to perform smooth fitting and equally spaced sampling on the orbital data after outliers are removed to obtain smoothed orbital data; An orbit determination arc segment determination module is configured to determine the orbit determination arc segment according to the scheduling time and the orbit maneuvering time; as well as The optimal orbit data and orbit prediction module is configured to obtain the optimal orbit data and perform orbit prediction based on the orbit determination arc and the smoothed orbit data using the motion equation of the high-orbit satellite and the state transfer matrix batch least squares iteration.

9. An electronic device, characterized in that: include: a processor configured to execute machine-readable instructions; A graphics card with an artificial intelligence chip, configured to train the high-orbit satellite autonomous measurement, control and orbit determination method; as well as A memory configured to store machine-readable instructions, wherein the machine-readable instructions, when executed by a processor and / or a graphics card, perform the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that Machine-readable instructions are stored thereon, which, when executed by a processor, perform the steps of the method according to any one of claims 1 to 7.

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