A Multi-Station Local Sensing and Joint Orbit Determination Method for Low-Earth-Orbit Large Constellations

Abstract

The present invention belongs to the field of aerospace measurement and control technology, including main data streams and algorithm design. A multi-station local perception joint orbit determination method for low-Earth orbit large satellite constellations proposed by the present invention uses local perception data of a single measurement station for least squares filtering processing, generates a normal equation system and integrates it into the data center for joint orbit determination. This method distributes various types of data processing processes among each measurement station, and the data center can obtain a globally optimal orbit state estimate only by combining the normal equation systems of the measurement stations. Compared with the traditional orbit determination scheme, through the joint processing at the measurement and control stations and the data center, a large amount of measurement data transmission is avoided, and the overhead of data transmission and central calculation is also significantly reduced, enhancing the flexibility and robustness of the data center processing and meeting the measurement and control management requirements of large satellite constellations. Therefore, this solution is applicable to the orbit determination problem of large satellite constellations supported by multiple measurement stations and inter-satellite links.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace measurement and control, and relates to a joint orbit determination method based on multi-station local perception information processing for large low-Earth orbit satellite constellations. Background Technique

[0002] A satellite constellation refers to a satellite system composed of multiple satellites, which forms a large "virtual spacecraft" in a collaborative working mode to complete a series of space tasks with a wide coverage range and high continuity requirements, such as Earth observation, Internet communication, and battlefield situation awareness. In recent years, with the development of small satellite technology, the operation mode of multiple satellites jointly networking to form formations, constellations or satellite constellations in the low Earth orbit (LEO) has been highly favored, and various large satellite constellations have developed rapidly. Large Internet constellations such as "Starlink" and "OneWeb" have been rapidly deployed. Just Starlink has planned 42,000 satellites. Compared with the traditional single-satellite working mode, satellite constellations have great advantages in terms of cost, performance, flexibility and reliability; but it also brings huge challenges to the current ground-based dominant measurement, operation and control mode.

[0003] Currently, traditional aerospace measurement and control systems still rely on ground-based S-band measurement and control networks, mainly using the single-satellite tracking orbit determination method, that is, multiple or single measurement and control stations simultaneously or alternately track satellites, and the collected observation data is directly sent to the data center. The data center uses the single-satellite orbit determination method to calculate the satellite orbit and predict future tracking plans, and sends them to the measurement and control station guidance equipment for tracking. The traditional single-satellite orbit determination method is still applicable to single satellites or small-scale satellite constellations with a very small number; but for large satellite constellations with hundreds or thousands of satellites, the centralized processing mode of the data center for single-satellite orbit determination has huge overheads in terms of data transmission and computing resources, and cannot meet the task requirements of future multi-target measurement and control of satellite constellations. Therefore, it is necessary to research a new joint orbit determination scheme for large satellite constellations. Summary of the Invention

[0004] In order to overcome the problems existing in the prior art, the present invention proposes a multi-station local perception joint orbit determination method for large low-Earth orbit satellite constellations, which uses the local perception data of a single measurement station for least squares filtering processing, generates a normal equation system and sends it to the data center for joint orbit determination. This solution is applicable to the orbit determination problems of large satellite constellations supported by multiple measurement stations and inter-satellite links. The present invention adopts a generalized concept of satellite constellations, that is, satellite formations and constellations are special structures of satellite constellations.

[0005] The technical solution of the present invention is as follows:

[0006] A multi-station local perception joint orbit determination method for large low-Earth orbit satellite constellations, comprising the following steps:

[0007] Step 1, in the fixed orbit arc segment, the measuring station processes all the original observation data of local perception and constructs a linearized observation equation system for multi-source data fusion;

[0008] Step 2, each measuring station applies a local least squares filter to construct a normal equation system for orbit state estimation, and the normal equation system includes a normal matrix and the corresponding covariance; among them, for a satellite with only ground observations, an independent normal equation system is constructed; for a satellite related to inter-satellite link measurement, a unified multi-satellite normal equation system is constructed;

[0009] Step 3, send the normal equation systems of each measuring station to the data center, and the data center uses the recursive least squares method to combine the normal equations;

[0010] Step 4, solve the combined linear equation system to obtain the optimal estimate of the orbit state.

[0011] Furthermore, the multi-source data includes measurement data of ranging, instantaneous velocity measurement, azimuth angle, elevation angle, and inter-satellite ranging.

[0012] The observation matrices of the above-mentioned ranging, instantaneous velocity measurement, azimuth angle, elevation angle, and inter-satellite ranging are as follows:

[0013] Ranging ρ:

[0014] Instantaneous velocity measurement

[0015]

[0016] Azimuth angle A:

[0017] Elevation angle E:

[0018] Inter-satellite ranging R:

[0019] In the formula, h r (*) represents various observation matrices, that is, the partial derivative matrix of the observed value with respect to the position r(x, y, z); M represents the conversion matrix from the geocentric coordinate system to the measuring station coordinate system, and HG represents the conversion matrix from the inertial coordinate system to the geocentric coordinate system; ρ(ρ x , ρ y , ρ z ) represents the vector from the station center to the satellite in the measuring station coordinate system; the inter-satellite ranging between satellites a and b is expressed as

[0020] Furthermore, for satellite a with only measuring station observations, in measuring station i, an independent normal equation system is constructed according to the measurement relationship as follows:

[0021] For satellite a, its state to be estimated Construct the normal equation system

[0022] Or

[0023] Wherein, H is an m×n dimensional observation matrix, m and n are respectively the number of observation values of satellite a by station i and the number of unknown orbital parameters; the full rank rank(H) = n, which is the design matrix, a matrix containing various types of observation data; P is an m×m dimensional observation weight matrix, determined by the corresponding type of observation data, and the weights of each type of observation data are the same; the normal matrix of the independent normal equation system

[0024] The covariance of the normal matrix of the independent normal equation system

[0025] Wherein, the subscript of the normal matrix N represents the station, and the superscript represents the satellite. For example Represents the normal equation of satellite a generated from the single-station data of station i Is the posterior unit weight variance

[0026] Furthermore, for the satellite jointly observed by the inter-satellite link and the station, in station i, measure the satellite related to the inter-satellite link and construct a multi-satellite normal equation system Including

[0027] The normal matrix of the multi-satellite normal equation system

[0028] The covariance of the multi-satellite normal equation system

[0029] Wherein, the observation matrix H contains matrices of various types of observation data, and the weights of each type of observation data in the weight matrix P are the same; Represents the set of the measurement data set generated by station i tracking and measuring the corresponding satellite and the received end data of the inter-satellite link of the corresponding satellite received by station i

[0030] Furthermore, step 3 is specifically as follows:

[0031] (1) For the satellite observed only by the station, use recursive least squares to estimate the single-satellite orbit state, and merge the normal equations of multiple stations. For satellite a, merge the normal equations

[0032]

[0033] where \(l\) is the number of relevant stations involved;

[0034] (2) For satellites jointly observed by inter-satellite links and stations, the recursive least squares method is used to estimate the multi-satellite orbit state, and the normal equations of multiple stations are combined. For satellites \(b\),...,\(d\), the normal equations are combined

[0035]

[0036] where \(h\) is the number of relevant stations involved.

[0037] The beneficial effects of the present invention are as follows:

[0038] (1) Processing local perception observation data at the TT&C stations disperses the computational load of the data center and avoids a large amount of data transmission;

[0039] (2) The data center can obtain the globally optimal orbit state estimate without loss of accuracy, and only needs to jointly process the normal equation system of the TT&C stations, significantly reducing the computational load;

[0040] (3) The data center can flexibly process the normal equation systems of each station and can reject stations according to data quality. Therefore, through the joint processing at the TT&C stations and the data center, the present method will significantly reduce the data transmission and central computing overhead on the premise of ensuring the orbit determination accuracy, meet the TT&C management requirements of large satellite constellations, and is applicable to the orbit determination problem of large satellite constellations supported by multiple stations and inter-satellite links. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a schematic diagram of traditional single-satellite orbit determination and satellite constellation orbit determination.

[0042] Figure 2 is a traditional satellite constellation orbit determination scheme.

[0043] Figure 3 Local perception joint orbit determination scheme for large satellite constellations.

[0044] Figure 4 Orbit determination accuracy of the traditional orbit determination scheme (compared with the simulation "true" orbit).

[0045] Figure 5 Orbit determination result of the present invention scheme (compared with the simulation "true" orbit). DETAILED DESCRIPTION OF THE INVENTION

[0046] To better illustrate the advantages of the present invention, the following further details the specific embodiments of the present invention with reference to the accompanying drawings.

[0047] Example 1:

[0048] As Figure 3As shown in the figure, the process of multi-station and inter-satellite link jointly supporting the orbit determination of satellite constellations is as follows (for simplicity, taking three ground stations i, j, k and five satellites a, b, c, d, e as examples):

[0049] Ground stations: During the orbit determination arc segment, station i tracks and measures satellites a, b, c, generating a measurement data set Station j tracks and measures all five satellites, generating a measurement data set Station k tracks and measures satellites c, d, e, generating a measurement data set The ground-based measurement elements include range ρ, velocity azimuth angle A and elevation angle E.

[0050] Inter-satellite link: Some satellites in the satellite constellation (satellites b, c, d) use the inter-satellite link for two-way ranging, and the measurement data is downlinked at the receiving end. Then, station i receives the receiving-end data of the inter-satellite link of satellite b Station j receives the receiving-end data of the inter-satellite link of satellite c Station k receives the receiving-end data of the inter-satellite link of satellite d

[0051] In the traditional orbit determination scheme, all the above types of data will be sent to the data center as Figure 2 shown. In this embodiment, satellites a and e will adopt the single-satellite orbit determination method to process their respective observation data; due to the inter-satellite link, satellites b, c, d will adopt the multi-satellite joint orbit determination method to simultaneously process the inter-satellite and space-ground observation data and calculate the orbits of the three satellites.

[0052] The specific implementation steps are as follows:

[0053] Step 1: During the orbit determination arc segment, the stations process all the original observation data of local perception, and construct a linearized observation equation system for multi-source data fusion, including the residual calculation of measurement data such as range, velocity, azimuth angle, and elevation angle. The calculation of the observation matrix is carried out according to Equations (1) to (6).

[0054] Step 2: Each station applies a local least squares filter to construct a normal equation system for orbit state estimation, including the normal matrix and the corresponding covariance. For satellites with only ground-based observations, an independent normal equation system is constructed; for satellites related to inter-satellite link measurements, a unified multi-satellite normal equation system is constructed;

[0055] For example, in station i, according to the measurement relationship, two independent normal equation systems are constructed as follows:

[0056] For satellite a, its state to be estimated Construct the normal equation system As shown in Formulas (7) and (8).

[0057] Similarly, for satellites b, c, and d, a normal equation system is constructed. including

[0058] the normal matrix the covariance

[0059] The observation matrix and the weight matrix correspond to the corresponding observation data types.

[0060] For stations j and k, their respective normal equation systems are constructed in the same way.

[0061] Step 3: The normal equation systems of each station are sent to the data center, and the data center uses the recursive least squares method to combine the normal equations. It is divided into two cases:

[0062] (1) For the satellites observed only by the stations, the single-satellite orbit state estimation method is used to combine the normal equations of multiple stations. For satellite a, the combined normal equation is: and The normal equation: For satellite e, the combined normal equation is:

[0063] (2) For the satellites jointly observed by the inter-satellite links and the stations, the multi-satellite orbit state estimation method is used to combine the normal equations of multiple stations. For satellites b, c, and d, the combined normal equations are:

[0064]

[0065] Step 4: Solve the combined normal equations in the data center to obtain the global optimal orbit state estimation.

[0066] Example 2:

[0067] A simulation calculation is carried out for the orbit determination problem of 24 satellites under the tracking conditions of 8 stations. The tracking arc is 3 days. The ground-based measurements include ranging, velocity measurement, and angle measurement; the space-based measurements include inter-satellite link ranging. The orbit determination results of the traditional scheme are as Figure 4 , and the orbit determination results of the present invention are as Figure 5 . In the figure, P, R, A, and C represent position, radial, tangential, and normal respectively. The present invention does not show an obvious decrease in orbit determination accuracy, but can save data transmission and central calculation overhead.

[0068] Compared with the traditional scheme, the advantages are: ① no loss of accuracy, and the global optimal state estimation can be obtained; ② the observation data are processed at the stations and do not need to be sent to the data center, avoiding a large amount of data transmission; ③ the data center only needs to complete the superposition of the normal equations and the state fusion estimation, and the calculation amount is significantly reduced.

Claims

1. A multi-station local perception joint orbit determination method for low-earth-orbit large satellite constellations, characterized in that It includes the following steps: Step 1: At the fixed-orbit arc segment, the measuring station processes all the original observation data of local perception and constructs a linearized observation equation set for multi-source data fusion; Step 2: Each measuring station applies a local least-squares filter to construct a normal equation system for orbit state estimation. The normal equation system includes a normal matrix and the corresponding covariance. Among them, for satellites with only ground observations, an independent normal equation system is constructed; for satellites related to inter-satellite link measurements, a unified multi-satellite normal equation system is constructed; For a satellite with only ground-based observations, an independent normal equation system is constructed as follows: For satellite a, at station i, its state to be estimated Construct the normal equation system including Where, H is an m×n dimensional observation matrix, where m and n are the number of observations of satellite a by station i and the number of unknown orbital parameters, respectively; the full rank rank(H)=n, which is the design matrix and contains matrices of various types of observation data; P is an m×m dimensional observation weight matrix, which is determined by the corresponding type of observation data, and the weights of each type of observation data are the same; the normal matrix of the independent normal equation system The covariance of the normal matrix of the independent normal equation system In the formula, the subscript of the normal matrix N represents the survey station, and the superscript represents the satellite, is the posterior variance of unit weight; For the satellites related to inter-satellite link measurement, a unified multi-satellite normal equation system is constructed as follows: In station i, measure the satellites related to the inter-satellite link and construct a unified multi-satellite normal equation system including the normal matrix of the multi-satellite normal equation system The covariance of the multi-satellite normal equation system Wherein, the observation matrix H includes matrices of various types of observation data, and the weights of each type of observation data in the weight matrix P are the same; represents the set of the measurement data set generated by the tracking and measurement of the corresponding satellite by the station i and the set of the receiving-end data of the inter-satellite link received by the station i from the corresponding satellite; Step 3: Send the normal equation systems of each measuring station to the data center, and the data center uses the recursive least-squares method to merge the normal equations; Step 4: Solve the merged linear equation set to obtain the optimal estimation of the orbit state.

2. The multi-station local sensing joint orbit determination method for low-Earth orbit large satellite constellations according to claim 1, wherein The multi-source data includes measurement data of ranging, instantaneous velocity measurement, azimuth angle, elevation angle, and inter-satellite ranging.

3. The multi-station local perception joint orbit determination method for low-Earth orbit large satellite constellations according to claim 2, characterized in that The observation matrices of the ranging, instantaneous velocity measurement, azimuth angle, elevation angle, and inter-satellite ranging are as follows: Range measurement ρ: Instantaneous speed measurement Azimuth angle A: Elevation angle E: Inter-satellite ranging R: where h r (*) represents various observation matrices, i.e., the partial derivative matrix of the observed values with respect to the position r(x, y, z); M represents the transformation matrix from the geocentric coordinate system to the station coordinate system, and HG is the transformation matrix from the inertial coordinate system to the geocentric coordinate system; ρ(ρ x , ρ y , ρ z ) represents the vector of the distance from the station center to the satellite in the station coordinate system; the inter-satellite ranging between satellites a and b is expressed as 4. The multi-station local sensing and joint orbit determination method for low-Earth orbit large satellite constellations according to claim 1, wherein The specific content of Step 3 is: (1) For satellites with only ground observations, use the recursive least-squares method to estimate the single-satellite orbit state and merge the normal equations of multiple measuring stations. For satellite a, merge the normal equations In the formula, l is the number of relevant measuring stations involved; (2) For satellites related to inter-satellite link measurements, use the recursive least-squares method to estimate the multi-satellite orbit state and merge the normal equations of multiple measuring stations. For satellites b,..., d, merge the normal equations In the formula, h is the number of relevant measuring stations involved.

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