Parameter value determination system, parameter value determination method and program

Abstract

To enable a parameter value of a model (non-gravitational disturbance model) to be determined on the basis of observation information for a relative short period in order to consider non-gravitational disturbance in the case of estimating an orbit of a spacecraft.SOLUTION: A parameter value determination system includes evaluation means for calculating an evaluation value showing evaluation of first orbit information on the basis of comparison between first orbit information calculated by using a non-gravitational disturbance model about an orbit of a target spacecraft being a spacecraft of an orbit calculation object and second orbit information being orbit information showing a time section including a time section common to a time section shown by the first orbit information, and parameter value determination means for determining a non-gravitational disturbance model parameter value being a parameter value to be used by the non-gravitational disturbance model on the basis of the evaluation value.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a parameter value determination system, a parameter value determination method, and a program. [Background technology]

[0002] When estimating the orbit of a spacecraft such as an artificial satellite, non-gravitational disturbances such as solar radiation pressure may be taken into consideration (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Special Publication No. 2010-508524 Summary of the Invention [Problem to be solved by the invention]

[0004] When estimating the trajectory of a spacecraft, it is preferable to be able to determine the parameter values ​​of a model used to take non-gravitational disturbances into account (non-gravitational disturbance model) based on observational information over a relatively short period of time.

[0005] An example of an object of the present invention is to provide a parameter value determination system, a parameter value determination method, and a program that can solve the above-mentioned problems. [Means for solving the problem]

[0006] According to a first aspect of the present invention, a parameter value determination system includes an evaluation means for calculating an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for the orbit of a target spacecraft, which is a spacecraft whose orbit is to be calculated, and second orbit information, which is orbit information indicating the orbit of the target spacecraft for a time period including a time period common to the time period indicated by the first orbit information, and a parameter value determination means for determining a non-gravitational disturbance model parameter value, which is a parameter value to be used in the non-gravitational disturbance model, based on the evaluation value.

[0007] According to a second aspect of the present invention, a parameter value determination method includes a computer calculating an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for an orbit of a target spacecraft, which is a spacecraft whose orbit is to be calculated, and second orbit information, which is orbit information indicating the orbit of the target spacecraft for a time period including a time period common to a time period indicated by the first orbit information, and determining a non-gravitational disturbance model parameter value, which is a parameter value to be used in the non-gravitational disturbance model, based on the evaluation value.

[0008] According to a third aspect of the present invention, a program causes a computer to execute the following steps: calculate an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for the orbit of a target spacecraft, which is a spacecraft whose orbit is to be calculated, and second orbit information, which is orbit information indicating the orbit of the target spacecraft for a time period including a time period common to the time period indicated by the first orbit information; and determine a non-gravitational disturbance model parameter value, which is a parameter value used in the non-gravitational disturbance model, based on the evaluation value. Effect of the Invention

[0009] According to the present invention, the parameter values ​​of the non-gravitational disturbance model can be determined based on observation information over a relatively short period of time. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram illustrating an example of a configuration of a parameter value determination system according to an embodiment. [Diagram 2] FIG. 2 is a diagram illustrating an example of a coordinate system according to the embodiment. [Diagram 3] FIG. 11 is a diagram showing an example of a period of target orbit information and a period of external orbit information according to the embodiment. [Figure 4] FIG. 4 is a diagram showing an example of a period of two pieces of object trajectory information according to the embodiment. [Diagram 5] 6A to 6C are diagrams illustrating examples of evaluation values ​​calculated by an evaluation value calculation unit according to the embodiment. [Figure 6] 10 is a diagram showing an example of initial data used by the optimization pre-processing unit according to the embodiment to calculate an evaluation function; FIG. [Figure 7] 5A to 5C are diagrams illustrating an example of input and output of data in the parameter value determination system according to the embodiment. [Figure 8] 11 is a diagram showing an example of a procedure of a process in which the parameter value determination system according to the embodiment determines non-gravity disturbance model parameter values. FIG. [Figure 9] FIG. 13 is a diagram showing another example of the configuration of a parameter value determining system according to the embodiment. [Figure 10] 1 is a diagram showing an example of a processing procedure in a parameter value determination method according to an embodiment; [Figure 11] FIG. 1 is a schematic block diagram illustrating a configuration of a computer according to at least one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] The following describes embodiments of the present invention, but the following embodiments do not limit the scope of the invention. Furthermore, not all of the combinations of features described in the embodiments are necessarily essential to the solution of the invention.

[0012] Fig. 1 is a diagram showing an example of the configuration of a parameter value determination system according to an embodiment. In the configuration shown in Fig. 1, a parameter value determination system 100 includes a target orbit information acquisition unit 110, an external orbit information acquisition unit 120, a comparison information generation unit 130, an evaluation value calculation unit 140, an optimization pre-processing unit 150, an optimization calculation unit 160, and a parameter value reflection unit 170. The target orbit information acquisition unit 110 includes orbit estimation software 111 and a non-gravitational disturbance model 112. The parameter value determination system 100 also obtains data from an external trajectory information providing device 910 .

[0013] The parameter value determination system 100 determines parameter values ​​of the non-gravitational disturbance model 112 for estimating a spacecraft trajectory using the non-gravitational disturbance model 112. The parameter value determination system 100 may be configured using a computer such as a personal computer (PC) or a workstation (WS).

[0014] The orbit estimation software 111 is software for estimating an orbit using a non-gravitational disturbance model 112 . The parameters of the non-gravity disturbance model are also referred to as non-gravity disturbance model parameters, and the values ​​of the parameters are also referred to as non-gravity disturbance model parameter values.

[0015] The spacecraft that is the subject of orbit estimation is also referred to as a target spacecraft. Orbit information that indicates the orbit of the target spacecraft calculated by executing the orbit estimation software 111 is also referred to as target orbit information. The target orbit information corresponds to an example of the first orbit information. In this context, estimating a trajectory may include predicting a trajectory, and in particular, the trajectory estimation software 111 may be used to calculate a past trajectory, a present trajectory, or a future trajectory.

[0016] Here, in order to estimate the orbital position of a spacecraft (its position on the orbit at each time), it is possible to use observation information of the spacecraft. The observation information of the spacecraft here is information obtained by observing the spacecraft. The observation information may be obtained, for example, from a tracking control station or a monitoring station on the ground.

[0017] Spacecraft observation information reflects the effects of disturbances acting on the spacecraft. For more accurate orbit estimation, it is important to identify and model the disturbances shown in the observation information. The disturbance modeling here can be performed, for example, by adjusting parameter values ​​of a model (template).

[0018] There are two types of disturbances: gravitational disturbance and non-gravitational disturbance. Gravitational disturbance can be modeled regardless of the structure of the spacecraft. For this reason, it is expected that established models and parameter values ​​can be used as the gravitational disturbance model and its parameter values. On the other hand, non-gravitational disturbances depend on the structure of the spacecraft. There are general-purpose models for non-gravitational disturbances and models specialized for specific spacecraft. Examples of the non-gravity disturbance include solar radiation pressure, thermal radiation pressure, and radio wave radiation pressure. However, the non-gravity disturbance handled by the non-gravity disturbance model 112 for which the parameter value determination system 100 calculates the parameter values ​​is not limited to a specific one.

[0019] For modeling of non-gravitational disturbances, a method of modeling by adjusting parameter values ​​based on a specific approximation or equation, such as ECOM (Empirical CODE Orbit Model), can be used. For modeling of non-gravitational disturbances and for determining and estimating orbits, general-purpose orbit estimation software, such as Bernese from the University of Bern, can be used for a positioning satellite as an example. ECOM is one of the versatile models for non-gravitational disturbances, and is used especially for orbit calculations of positioning satellites.

[0020] In ECOM, disturbances of a spacecraft are expressed based on approximate expressions. To calculate ECOM parameter values, it is necessary to use mid- to long-term observation information and analysis information, for example, for several months or a year. As analysis information, for example, it is possible to use the difference between orbit information estimated using a model for which parameter values ​​are calculated and more accurate orbit information obtained by laser ranging or another model. The difference in orbit information here is a numerical representation of the degree of difference between orbits indicated by the orbit information. The difference in orbit information is also called an orbit difference.

[0021] The reason why mid- to long-term observational and analytical information is required is that non-gravitational disturbances change depending on the angle (β angle) between the spacecraft's orbital plane and the sun. For this reason, it has been difficult to provide an accurate disturbance model in the short term, such as in the early stages of a spacecraft launch. In addition, because spacecraft disturbances fluctuate from day to day even when located at the same β angle, it is desirable to update the model as quickly as possible, but the need for mid- to long-term observational and analytical information has made it difficult to update the disturbance model in the short term.

[0022] Models for non-gravitational disturbances specialized for specific spacecraft include the Box-Wing Model, etc. However, modeling non-gravitational disturbances specialized for a specific spacecraft requires sufficient and reliable information on the structure, shape, attitude, etc. of the spacecraft, and such information can only be used by the organization that manufactured the spacecraft and its related organizations.

[0023] The non-gravity disturbance model for which the parameter value determination system 100 calculates parameter values ​​is not limited to ECOM. Various non-gravity disturbance models configured using approximations or equations including parameters can be used as the target for parameter value calculation by the parameter value determination system 100.

[0024] The parameter value determination system 100 calculates the difference between the orbit information of the target spacecraft calculated by setting values ​​for the non-gravitational disturbance model parameters and executing the orbit estimation software 111, and the orbit information obtained by laser ranging or using another non-gravitational disturbance model. As described above, the difference between the two orbit information is also called the orbit difference.

[0025] As described later, the orbit estimation software 111 may be executed to calculate two pieces of orbit information having different target periods that partially overlap, and the difference between the two pieces of orbit information for the overlapping period may be calculated as an orbit difference. The target period of the orbit information here is the period of the orbit indicated in the orbit information. In other words, the orbit information indicates information on the orbit during the target period.

[0026] The parameter value determination system 100 receives the trajectory difference and the non-gravity disturbance model parameter values ​​as input, and adjusts the parameter values ​​using an optimization algorithm. Specifically, the parameter value determination system 100 searches for the non-gravity disturbance model parameter values ​​that minimize the trajectory difference. That is, the parameter value determination system 100 adjusts the non-gravity disturbance model parameter values ​​by executing the optimization algorithm using the trajectory difference as a cost function. The execution of an optimization algorithm is also referred to as an optimization calculation.

[0027] The non-gravity disturbance model parameter values ​​calculated by the parameter value determination system 100 are values ​​optimized for the spacecraft located at the β angle during the period for which the orbit difference was calculated. The non-gravity disturbance model parameter values ​​calculated by the parameter value determination system 100 can be used continuously as long as the β angle does not fluctuate significantly. The period during which the non-gravity disturbance model parameter values ​​calculated by the parameter value determination system 100 can be used depends on the accuracy required for orbit estimation.

[0028] The target period for orbit difference calculation can be freely determined within the constraints of the software used for orbit estimation (orbit estimation software 111). For example, the target period for orbit difference calculation may be set in units of one day, etc. For example, the parameter value determination system 100 may continue to calculate or update the non-gravitational disturbance model parameter values ​​daily based on the obtained orbit information, thereby allowing the model optimized for the β angle of the target spacecraft to be continuously used. In this way, the parameter value determination system 100 makes it possible to provide and update a non-gravity disturbance model in a shorter period of time than the existing methods described above.

[0029] The target orbit information acquisition unit 110 of the parameter value determination system 100 acquires orbit information from the orbit estimation software 111. For example, the target orbit information acquisition unit 110 sets the non-gravity disturbance model parameter values ​​in the non-gravity disturbance model 112 and executes the orbit estimation software 111 to calculate the orbit information.

[0030] Either or both of the trajectory estimation software 111 and the non-gravitational disturbance model 112 may be provided outside the parameter value determining system 100. For example, the target trajectory information acquiring unit 110 may acquire the target trajectory information from a server device that provides trajectory estimation using the trajectory estimation software 111.

[0031] The orbit estimation software 111 is software for estimating the orbit of the target spacecraft and outputting the orbit information. Existing software, such as the above-mentioned Bernese, may be used as the orbit estimation software 111. However, the orbit estimation software 111 is not limited to a specific software. As the orbit estimation software 111, various software that can calculate orbit information of the target spacecraft using a non-gravity disturbance model in which non-gravity disturbance model parameter values ​​are set can be used. Furthermore, although Bernese is used in positioning satellites, the parameter value determination system 100 is not limited to positioning satellites and can be applied to various spacecraft.

[0032] The format of the orbit information output by the orbit estimation software 111 is not limited to a specific one, and may be any of various formats capable of expressing the orbit of a satellite. For example, the format of the output of the orbit estimation software 111 may be an existing format such as the SP3c format (Extended Standard Product 3 Orbit Format), but is not limited to this.

[0033] As the non-gravity disturbance model 112, an existing non-gravity disturbance model such as the above-mentioned ECOM can be used. However, the non-gravity disturbance model 112 is not limited to a specific one. Depending on the software used as the orbit estimation software 111, various non-gravity disturbance models that receive parameter value settings and output information on non-gravity disturbances to the spacecraft can be used as the non-gravity disturbance model 112. In the following, an example will be described in which the non-gravity disturbance model 112 is expressed as in equation (1).

[0034]

number

[0035] μ represents the latitude argument of the target spacecraft, which is the angular distance from the ascending node (the point where the orbit of the spacecraft around a celestial body crosses the equatorial plane from south to north) to the spacecraft (the distance between two points on the celestial sphere expressed as the angle between two half lines extending from the observation point in each direction). D(μ), Y(μ), and B(μ) respectively represent coordinate values ​​in a coordinate system based on the relationship between the Earth, the Sun, and the target spacecraft.

[0036] FIG. 2 is a diagram showing an example of a coordinate system used in equation (1). In the example of Figure 2, point P11 represents the center of the Sun. Point P12 represents the center of the Earth. The D-axis is a coordinate axis whose positive direction is from the target spacecraft 920 to the center of the sun (point P11).

[0037] The Y-axis is a coordinate axis with the south direction of the solar panel of the target spacecraft 920 as the positive direction. The B-axis is a coordinate axis formed by the cross product (vector cross product) of the positive direction of the D-axis and the positive direction of the Y-axis. In formula (2), D(μ) represents the value of the D coordinate, Y(μ) represents the value of the Y coordinate, and B(μ) represents the value of the B coordinate.

[0038] D0, D c , C s Y0, Y c , Y s represent the coefficients used in the calculation of Y(μ). c , B s respectively represent coefficients used in the calculation of B(μ). D0, D c , C s , Y0, Y c , Y s , B0, B c , B s are examples of non-gravitational disturbance model parameters.

[0039] The external orbit information acquisition unit 120 acquires orbit information indicating the orbit of the target spacecraft, which is generated by a method other than the execution of the orbit estimation software 111. The orbit information indicating the orbit of the target spacecraft, which is generated by a method other than the execution of the orbit estimation software 111, is also referred to as external orbit information. The external orbit information corresponds to an example of the second orbit information.

[0040] The period in which the external trajectory information indicates a trajectory and the period in which the target trajectory information indicates a trajectory are at least partially overlapping (that is, including the same period). The period during which the orbit information indicates an orbit is also referred to as the period of the orbit information. For two orbit information, the period during which the two orbit information items overlap among the periods indicating the orbits is also referred to as an overlap period.

[0041] The external orbit information may be, for example, orbit information obtained by laser ranging of the target spacecraft. Alternatively, the external orbit information may be orbit information calculated using software or a system other than the orbit estimation software 111. Furthermore, for example, the external orbit information may be, but is not limited to, a precise orbital ephemeris published by the International GNSS Service (IGS) analysis center or a laser ranging result published by the International Laser Ranging Service (ILRS).

[0042] For example, the external trajectory information is converted into a format that can be compared with the target trajectory information, and is used to calculate an evaluation value for the optimization calculation performed by the parameter value determination system 100. As the external orbit information, it is preferable to use orbit information that represents an orbit close to the true orbit of the target spacecraft.

[0043] When external orbit information cannot be obtained, the parameter value determining system 100 may acquire two pieces of target orbit information (two types of target orbit information) in which the periods representing the orbits are different and partially overlap each other. That is, the parameter value determining system 100 may set two types of periods in which the periods are different and partially overlap each other, and execute the orbit estimation software 111 for each period to acquire orbit information.

[0044] For example, the parameter value determination system 100 uses observation information for the entire day (all day) of December 31st and observation information for the entire day of January 1st to obtain first target orbit information indicating an orbit from December 31st to January 1st. Furthermore, the parameter value determination system 100 uses observation information for the entire day of January 1st and observation information for the entire day of January 2nd to obtain second target orbit information indicating an orbit from January 1st to January 2nd. In this case, the period for the entire day of January 1st overlaps in the two obtained target orbit information. Again, the target trajectory information acquired by the parameter value determination system 100 may include a prediction of the trajectory.

[0045] Then, the parameter value determination system 100 may compare these two pieces of target trajectory information to calculate an evaluation value for optimization calculation. In this way, the parameter value determination system 100 executes orbit estimation using observation information including different ranges, so that the influence of disturbances estimated as a whole differs for each orbit information. This causes an error between the two orbit estimation results. That is, in the two orbit information obtained, differences occur in the orbits even during the overlapping period. This allows the parameter value determination system 100 to obtain the difference between the two orbit information obtained.

[0046] In this case, the parameter value determining system 100 may not include the external orbit information acquiring unit 120. In this case, the two pieces of target trajectory information correspond to examples of the first trajectory information and the second trajectory information.

[0047] The comparison information generating unit 130 converts the target orbit information acquired by the target orbit information acquiring unit 110 and the external orbit information acquired by the external orbit information acquiring unit 120 into a format that allows comparison between them, and outputs the converted information. The comparison information generating unit 130 corresponds to an example of a comparison information generating means. The two pieces of trajectory information converted into a comparable format are also referred to as comparison information. For example, the comparison information generating unit 130 converts the format of the trajectory information as necessary, and extracts information on the overlap period from each of the target trajectory information and the outer trajectory information.

[0048] Furthermore, when the sampling times (times at which the position of the target spacecraft is indicated) are different between the target orbit information and the external orbit information, the comparison information generating unit 130 performs interpolation on either the target orbit information or the external orbit information, or on both, so that the target orbit information and the external orbit information can be compared for the same time. When there are multiple target spacecraft, the comparison information generator 130 generates comparison information for each target spacecraft.

[0049] FIG. 3 is a diagram showing an example of a period of the target trajectory information and a period of the external trajectory information. In the example of FIG. 3, period T1 is the period from 0:00 on January 1st to 0:00 on January 2nd, and the period of the target orbit information and the period of the external orbit information overlap with each other for period T1. For example, the comparison information generating unit 130 may be configured to extract one day's worth of orbit information from the target orbit information and the external orbit information, and may extract orbit information for a period T1 from each of the target orbit information and the external orbit information.

[0050] Alternatively, when the parameter value determining system 100 does not use external trajectory information, the comparison information generating unit 130 may convert the two pieces of target trajectory information into a format that allows comparison, and output the converted information as comparison information. In this case, the comparison information generating unit 130 converts the format of the trajectory information as necessary, and also extracts information on the overlap period from each of the two target trajectory information.

[0051] Furthermore, if the sampling times (the times at which the position of the target spacecraft is indicated) are different between the two pieces of target orbit information, the comparison information generation unit 130 performs interpolation on one or both of the two pieces of target orbit information so that these two pieces of target orbit information can be compared for the same time.

[0052] FIG. 4 is a diagram showing an example of the periods of two pieces of object trajectory information. In the example of FIG. 4, period T1 is the period from 0:00 on January 1st to 0:00 on January 2nd, and the periods of the two pieces of target orbit information overlap with each other for period T1. For example, the comparison information generating unit 130 may be configured to extract one day's worth of orbit information from the target orbit information and the external orbit information, and may extract orbit information for a period T1 from each of the two pieces of target orbit information.

[0053] The evaluation value calculation unit 140 calculates an evaluation value to be used in optimization calculations using the comparison information output by the comparison information generation unit 130 as input. The evaluation value calculation unit 140 also associates the calculated evaluation value with the non-gravity disturbance model parameter value acquired by the target trajectory information acquisition unit 110, and obtains a pair of the evaluation value and the non-gravity disturbance model parameter value. The evaluation value calculation unit 140 corresponds to an example of an evaluation means. The evaluation value calculated by the evaluation value calculation unit 140 is also called a cost.

[0054] FIG. 5 is a diagram showing an example of the evaluation value calculated by evaluation value calculation section 140. As shown in FIG. FIG. 5 shows an example in which the position of the target spacecraft is expressed in X, Y, and Z coordinate values ​​in the Earth Centered Earth Fixed (ECEF) coordinate system in both the target orbit information and the external orbit information.

[0055] The evaluation value calculation unit 140 calculates the distance between the center of gravity of the Earth, which is the origin of the coordinate system, and the target spacecraft for each sampling time (the time when the position of the target spacecraft is shown) for each of the target orbit information and the external orbit information. Then, the evaluation value calculation unit 140 calculates an orbit difference by subtracting the distance between the center of gravity of the Earth and the target spacecraft in the external orbit information from the distance between the center of gravity of the Earth and the target spacecraft in the target orbit information for each sampling time.

[0056] The evaluation value calculation unit 140 calculates the magnitude (absolute value) of this trajectory difference as the evaluation value. For example, the evaluation value calculation unit 140 calculates the RMS (Root Mean Square) of the trajectory difference calculated for each sampling time as the evaluation value. Alternatively, the evaluation value calculation unit 140 may calculate the average of the absolute values ​​of the trajectory differences as the evaluation value. The smaller this evaluation value, the better the evaluation of the non-gravity disturbance model parameter value. The evaluation value calculation unit 140 outputs data that combines the calculated evaluation value with the non-gravity disturbance model parameter values ​​used in calculating the target trajectory information.

[0057] However, the evaluation value calculated by the evaluation value calculation unit 140 is not limited to a specific one. As the evaluation value calculated by the evaluation value calculation unit 140, various index values ​​capable of evaluating the degree of difference between the two trajectories can be used.

[0058] When the parameter value determining system 100 does not use the external trajectory information, the evaluation value calculation unit 140 calculates the evaluation value based on the two pieces of target trajectory information. For example, the evaluation value calculation unit 140 calculates the distance between the center of gravity of the Earth and the target spacecraft at each sampling time for each of the two target orbit information pieces. Then, the evaluation value calculation unit 140 calculates the absolute value of the difference between the two calculated distances as the evaluation value.

[0059] If the evaluation value calculated by the evaluation value calculation unit 140 indicates an evaluation better than a preset threshold value, the parameter value determination system 100 terminates the optimization calculation (solution search in the optimization calculation) and adopts the non-gravity disturbance model parameter value obtained at that time as the result of the optimization calculation.

[0060] However, the end condition of the optimization calculation of the parameter value determination system 100 is not limited to a specific condition. For example, the end condition of the optimization calculation may be that the solution search loop has been repeated a predetermined number of times or more. Alternatively, in the case where a smaller evaluation value indicates a better evaluation, the end condition of the optimization calculation may be that the decrease in the evaluation value is equal to or smaller than a predetermined value and continues for a predetermined number of times or more.

[0061] 5 shows an example in which the parameter value determination system 100 determines non-gravitational disturbance model parameter values ​​for orbit calculation of each of satellites A and B. The evaluation value calculation unit 140 calculates evaluation values ​​for each of satellites A and B.

[0062] The optimization pre-processing unit 150 generates an evaluation function based on the pair of the evaluation value and the non-gravitational disturbance model parameter value output by the evaluation value calculation unit 140. For example, as initial data, or by the parameter value determination system 100 repeating a processing loop in the optimization calculation, data combining the non-gravity disturbance model parameter value and time series data of the evaluation value for each non-gravity disturbance model parameter value is accumulated in the parameter value determination system 100. The optimization pre-processing unit 150 generates an approximation function for a plurality of pairs of non-gravitational disturbance model parameter values ​​and time-series data of evaluation values ​​using the least squares method, and sets the approximation function as an evaluation function.

[0063] FIG. 6 is a diagram showing an example of initial data used by the optimization pre-processing unit 150 to calculate an evaluation function. The initial data shown in FIG. 6 includes a plurality of pairs of non-gravitational disturbance model parameter values ​​and evaluation values.

[0064] In generating this initial data, for example, the object orbit information acquisition unit 110 calculates object orbit information for each of a plurality of non-gravity disturbance model parameter values. Then, the evaluation value calculation unit 140 compares each of the object orbit information with the external orbit information, and calculates an evaluation value for each object orbit information (hence, for each non-gravity disturbance model parameter value). The evaluation value calculation unit 140 combines the non-gravity disturbance model parameter values ​​and the evaluation values, and compiles the obtained plurality of pairs to generate the initial data exemplified in FIG. 6. Here, in comparing the object trajectory information and the external trajectory information for each non-gravitational disturbance model parameter value, the evaluation value calculation unit 140 uses one piece of external trajectory information common to the plurality of object trajectory information.

[0065] The optimization pre-processing unit 150 can generate an evaluation function having the non-gravity disturbance model parameters as arguments by using initial data in which evaluation values ​​are indicated for each of a plurality of non-gravity disturbance model parameter values ​​as in the example of Fig. 6. For example, the optimization pre-processing unit 150 generates an evaluation function that is differentiable with the non-gravity disturbance model parameters, and thus the optimization calculation unit 160 can use an algorithm that uses the differentiation of the evaluation function, such as the steepest descent method, as an optimization algorithm.

[0066] 6 shows an example in which the parameter value determination system 100 determines non-gravitational disturbance model parameter values ​​for orbit calculation of each of satellites A, B, .... The optimization pre-processing unit 150 generates an evaluation function for each of satellites A, B, ....

[0067] The calculation of the evaluation value performed by the evaluation value calculation unit 140 and the generation of the evaluation function performed by the optimization pre-processing unit 150 will be further described using an example. For example, as described with reference to Fig. 5, the evaluation value calculation unit 140 calculates the trajectory difference for each sampling time based on the comparison information generated by the comparison information generation unit 130. Here, it is assumed that the trajectory difference is calculated every 15 minutes for the period from 00:00 on Jan. 1, 2023 to H:m on M, D, 2023. The trajectory difference here may be the difference between the target orbit information and the external orbit information, or may be two pieces of target orbit information having different target periods that partially overlap. The period from 0:00 on Jan. 1, 2023 to H:m on D on M, 20203, which is the period for which the orbit difference calculation is performed, is not limited to a specific period. For example, the period for which the orbit difference calculation is performed here may be one day.

[0068] The trajectory differences calculated by the evaluation value calculation unit 140 are also denoted as Orb_diff_1, Orb_diff_2, . . . , Orb_diff_n, where n is an integer greater than or equal to 1 and represents the number of trajectory differences calculated by the evaluation value calculation unit. The evaluation value calculation unit 140 calculates the RMS of the trajectory difference as the evaluation value Cost for the target period for calculating the trajectory difference, as shown in equation (2).

[0069]

number

[0070] However, the evaluation value calculated by the evaluation value calculation unit 140 is not limited to a specific one, and may be various values ​​indicating the difference (degree of difference) between the two trajectories. For example, the evaluation value calculation unit 140 may calculate, as the evaluation value Cost, the average value of the magnitude (absolute value) of the trajectory difference for the target period for trajectory difference calculation, as in Equation (3).

[0071]

number

[0072] The evaluation value calculation unit 140 generates data combining the calculated evaluation value and the non-gravity disturbance model parameter value used in the calculation of the evaluation value. Here, the non-gravity disturbance model parameter value used in the calculation of the evaluation value is the non-gravity disturbance model parameter value used in the calculation of the first orbit information used in the calculation of the orbit difference used in the calculation of the evaluation value.

[0073] Here, the evaluation value calculation unit 140 calculates the trajectory differences Orb_diff_1, Orb_diff_2, ..., Orb_diff_n using the same first trajectory information. Therefore, the evaluation value calculation unit 140 generates data in which one set of non-gravity disturbance model parameter values ​​and the evaluation value for the non-gravity disturbance model parameter values ​​are in one-to-one correspondence, as in the example of Fig. 6.

[0074] As described above, when the evaluation value calculation unit 140 calculates the trajectory difference using the object trajectory information and the external trajectory information, the object trajectory information corresponds to an example of the first trajectory information. When the evaluation value calculation unit 140 calculates the trajectory difference using two pieces of object trajectory information, one of the two pieces of object trajectory information corresponds to an example of the first trajectory information.

[0075] The optimization pre-processing unit 150 generates an evaluation function by applying an approximation method to a data set of data pairs of non-gravity disturbance model parameter values ​​and evaluation values ​​generated by the evaluation value calculation unit 140. Here, as shown in the above formula (1), the non-gravity disturbance model parameters D0, D c , C s , Y0, Y c , Y s , B0, B c , B s An example will be described in which the optimization pre-processing unit 150 calculates the evaluation function using a linear multiple regression analysis based on the least squares method. In this case, the function expressed as in equation (4) is used as the evaluation function f.

[0076]

number

[0077] β0, β1, . . . , β9 are coefficients in the regression equation. The non-gravitational disturbance model parameters D0, D c , C s , Y0, Y c , Y s , B0, B c , B s corresponds to the explanatory variables. When Cost is the objective variable representing the evaluation value, the regression equation is expressed as shown in Equation (5).

[0078]

number

[0079] The optimization pre-processing unit 150 determines the values ​​of the coefficients β0, β1, ..., β9 by linear multiple regression analysis using a data set of data pairs of evaluation values ​​and non-gravity disturbance model parameter values. Here, in order for the optimization pre-processing unit 150 to determine the values ​​of the 10 coefficients β0, β1, ..., β9, the evaluation value calculation unit 140 prepares a data set including 10 or more sets of data pairs of non-gravity disturbance model parameter values ​​and evaluation values ​​as initial data for generating the evaluation function.

[0080] Note that the optimization calculation unit 160 or the optimization pre-processing unit 150 may fix the explanatory variables (non-gravity disturbance model parameters) that are determined to have a small contribution to the evaluation value and the coefficient values ​​of the explanatory variables in the regression equation to constants, etc., and exclude them from the update targets. This can reduce the time required for the optimization calculation.

[0081] The method of generating the approximation function used by the optimization pre-processing unit 150 is not limited to the least squares method, and various methods can be used. In addition, the evaluation function generated by the optimization pre-processing unit 150 is not limited to a specific one. The evaluation function generated by the optimization pre-processing unit 150 can be various functions that indicate a better evaluation as the evaluation function value is smaller, or various functions that indicate a better evaluation as the evaluation function value is larger. The evaluation function generated by the optimization pre-processing unit 150 is also called a cost function.

[0082] For example, when the optimization calculation unit 160 uses an optimization algorithm that uses the differentiation of an evaluation function, such as the steepest descent method, and when the optimization pre-processing unit 150 generates the evaluation function using multiple regression analysis, various models can be used as the regression formula under the condition that the regression formula is differentiable, and according to the number of pairs of non-gravity disturbance model parameter values ​​and evaluation values ​​prepared as initial data. Also, various solvers capable of calculating approximate functions, not limited to the least squares method, can be used as a solver for determining the values ​​of the coefficients of the regression analysis.

[0083] Furthermore, when the optimization calculation unit 160 uses an optimization algorithm that does not use differentiation of an evaluation function, such as a genetic algorithm, the optimization pre-processing unit 150 may generate an evaluation function that is not differentiable. Depending on the characteristics of the optimization algorithm used by the parameter value determining system 100, the processing by the optimization pre-processing unit 150 may be omitted.

[0084] The optimization calculation unit 160 receives the evaluation function obtained from the optimization pre-processing unit 150 as an input, and updates and outputs the non-gravitational disturbance model parameter values. The optimization calculation unit 160 corresponds to an example of a parameter value determining means. In addition, when the processing by the optimization pre-processing unit 150 is omitted, the optimization calculation unit 160 may receive as input a pair of the evaluation value output by the evaluation value calculation unit 140 and the non-gravity disturbance model parameter value, and update the non-gravity disturbance model parameter value based on an evaluation function, etc., generated according to the optimization algorithm used.

[0085] The optimization algorithm used by the optimization calculation unit 160 to calculate the non-gravity model parameter value is not limited to a specific one. For example, the optimization calculation unit 160 may use a known optimization algorithm such as a steepest descent method or a genetic algorithm. Alternatively, the optimization calculation unit 160 may use a machine learning method or deep learning.

[0086] As described above with respect to the optimization pre-processing unit 150, multiple pairs of non-gravitational disturbance model parameter values ​​and evaluation values ​​may be prepared as initial data depending on the characteristics of the optimization algorithm used by the optimization calculation unit 160. For example, when the optimization calculation unit 160 uses the steepest descent method as the optimization algorithm, the parameter value determination system 100 can calculate and update the non-gravitational disturbance model parameter values ​​in the following procedure.

[0087] (1) The evaluation value calculation unit 140 generates initial data including multiple pairs of non-gravity disturbance model parameter values ​​and evaluation values, as in the example of FIG. 6, as initial data for the optimization pre-processing unit 150 to generate an evaluation function. (2) The optimization pre-processing unit 150 generates an approximation function as an evaluation function by applying a method such as the least squares method to the data generated by the evaluation value calculation unit 140. In particular, the optimization pre-processing unit 150 generates an evaluation function that is differentiable with respect to the non-gravity disturbance model parameter values, using data indicating evaluation values ​​for each of a plurality of non-gravity disturbance model parameter values.

[0088] (3) In the first execution of the process of (3), the optimization calculation unit 160 determines an appropriate non-gravity disturbance model parameter value as the initial point of the solution search. On the other hand, in the second and subsequent executions of the process of (3), the optimization calculation unit 160 sets the non-gravity disturbance model parameter value having the smallest evaluation value as the starting point of the solution search. Alternatively, as a measure for when a local solution occurs, the optimization calculation unit 160 may randomly select one of the non-gravity disturbance model parameter values ​​obtained and set it as the starting point of the solution search. (4) The optimization calculation unit 160 determines the steepest descent direction using the evaluation function calculated by the optimization pre-processing unit 150. The optimization calculation unit 160 can determine the steepest descent direction based on the derivative of the evaluation function.

[0089] (5) The optimization calculation unit 160 updates the non-gravity disturbance model parameter values ​​by moving in the determined steepest descent direction by an appropriate step size in the space of the evaluation function. The step size in this case is set in advance as a meta parameter of the optimization calculation, for example. (6) The target orbit information acquisition unit 110 executes the orbit estimation software 111 using the non-gravitational disturbance model parameter values ​​updated by the optimization calculation unit 160 to calculate target orbit information.

[0090] (7) The evaluation value calculation unit 140 calculates an evaluation value using the target trajectory information calculated by the target trajectory information acquisition unit 110 and the external trajectory information used to generate the initial data in (1) above. (8) The evaluation value calculation unit 140 performs a convergence determination of the search solution. For example, the evaluation value calculation unit 140 compares the calculated evaluation value with a threshold, and determines that the search solution has converged when the evaluation value is smaller than the threshold.

[0091] (9) If the evaluation value calculation unit 140 determines in (8) above that the search solution has converged, the parameter value determination system 100 ends the optimization calculation. In this case, the parameter value determination system 100 adopts the latest non-gravity disturbance model parameter values ​​updated by the optimization calculation unit 160 as the results of the optimization calculation.

[0092] (10) If it is determined in (8) above that the search solution has not converged, the evaluation value calculation unit 140 generates data combining the evaluation value calculated in (7) above with the latest non-gravity disturbance model parameter value updated by the optimization calculation unit 160 in (5) above, which is the non-gravity disturbance model parameter value on which the evaluation value is based. Then, the evaluation value calculation unit 140 adds the generated data of the pair of the non-gravity disturbance model parameter value and the evaluation value to the data for the optimization pre-processing unit 150 to generate an evaluation function.

[0093] In the first execution of the process (10), the evaluation value calculation unit 140 adds a newly generated pair of a non-gravity disturbance model parameter value and an evaluation value to the initial data generated in the above (1). On the other hand, in the second and subsequent executions of the process (10), the evaluation value calculation unit 140 further adds a pair of a non-gravity disturbance model parameter value and an evaluation value to the data to which the pair of a non-gravity disturbance model parameter value and an evaluation value was added in the previous execution of (10). After the above (10), the parameter value determination system 100 repeats the above processes from (2).

[0094] The parameter value reflecting unit 170 reflects the non-gravitational disturbance model parameter values ​​acquired by the optimization calculation unit 160 in the input to the orbit estimation software 111 and the like. For example, when the target orbit information acquisition unit 110 has the trajectory estimation software 111 and the non-gravity disturbance model 112, each time the optimization calculation unit 160 calculates a non-gravity disturbance model parameter value during the optimization calculation process (each time the non-gravity disturbance model parameter value is searched for), the parameter value reflection unit 170 inputs the non-gravity disturbance model parameter value to the target orbit information acquisition unit 110. The orbit information calculated by the target orbit information acquisition unit 110 by executing the trajectory estimation software 111 based on the input non-gravity disturbance model parameter value is used as new target orbit information by the parameter value determination system 100 for further searching for a non-gravity disturbance model parameter value in the optimization calculation.

[0095] A precondition or preparation for the parameter value determination system 100 to perform processing for determining non-gravitational disturbance model parameter values ​​will be described. Regarding the orbit estimation software 111, input data corresponding to the orbit estimation software 111 and initial values ​​of the non-gravitational disturbance model parameter values ​​are stored in the parameter value determination system 100, and the orbit estimation software 111 is executed to enable orbit estimation.

[0096] The input data corresponding to the orbit estimation software 111 here is the original data used to calculate orbit information, such as observation information of the target spacecraft, or a latitude argument calculated from the observation information of the target spacecraft. Furthermore, the initial values ​​of the non-gravity disturbance model parameter values ​​can be any value within a range compatible with the trajectory estimation software 111 and the non-gravity disturbance model 112. For example, the parameter value determination system 100 may randomly determine the initial values ​​of the non-gravity disturbance model parameter values.

[0097] Regarding the external orbit information, information on a method of accessing the external orbit information, such as information on an external organization that provides the external orbit information, and information on the data format of the external orbit information, are registered in the external orbit information acquisition unit 120 so that the external orbit information acquisition unit 120 can acquire the external orbit information.

[0098] It should be noted that, when the parameter value determination system 100 does not use the external orbit information, preparation regarding the external orbit information can be omitted. In this case, for example, the periods of the two pieces of target orbit information are determined in advance so that the target orbit information acquisition unit 110 can calculate two pieces of target orbit information that have partially overlapping periods.

[0099] Regarding the evaluation value, the evaluation value calculated by the evaluation value calculation unit 140 is defined in advance. That is, a method for the evaluation value calculation unit 140 to calculate the evaluation value is determined in advance. Also, a threshold value for the evaluation value is determined, which is used by the optimization calculation unit 160. As described above, this threshold value is used as a termination condition for the optimization calculation. In addition, a method for generating the approximation function used by the optimization pre-processing unit 150 is determined in advance. In addition, the optimization algorithm to be used by the optimization calculation unit 160 is determined in advance.

[0100] FIG. 7 is a diagram showing an example of data input and output in the parameter value determining system 100. As shown in FIG. 7, the target orbit information acquisition unit 110 receives the non-gravity disturbance model parameter values ​​and input information required for the orbit information. Then, the target orbit information acquisition unit 110 sets the non-gravity disturbance model parameter values ​​in the non-gravity disturbance model 112, executes the orbit estimation software 111, and calculates the target orbit information based on the input information required for the orbit information. The target orbit information acquisition unit 110 outputs the calculated target orbit information to the comparison information generation unit 130.

[0101] Moreover, the external trajectory information acquisition unit 120 acquires external trajectory information, and outputs the acquired external trajectory to the comparison information generation unit 130 . The comparison information generation unit 130 generates comparison information by converting the target orbit information input from the target orbit information acquisition unit 110 and the external orbit information input from the external orbit information acquisition unit 120 into a format that allows comparison, and outputs the generated comparison information to the evaluation value calculation unit 140.

[0102] The evaluation value calculation unit 140 calculates an evaluation value based on the comparison information input from the comparison information generation unit 130. Then, the evaluation value calculation unit 140 generates data that combines the non-gravitational disturbance model parameter values ​​used in generating the target trajectory information with the calculated evaluation value, and outputs the generated data to the optimization pre-processing unit 150.

[0103] The optimization pre-processing unit 150 generates an evaluation function based on the data pairs of the non-gravity disturbance model parameter values ​​and the evaluation values ​​input from the evaluation value calculation unit 140 , and outputs the generated evaluation function to the optimization calculation unit 160 . The optimization calculation unit 160 performs optimization calculations using the evaluation function input from the optimization pre-processing unit 150. The optimization calculation unit 160 outputs to the parameter value reflection unit 170 the non-gravity disturbance model parameter values ​​updated in the solution search in the optimization calculations.

[0104] The parameter value reflection unit 170 reflects the non-gravity disturbance model parameter values ​​input from the optimization calculation unit 160 in the non-gravity disturbance model 112. For example, the parameter value reflection unit 170 outputs the non-gravity disturbance model parameter values ​​input from the optimization calculation unit 160 to the target trajectory information acquisition unit 110. Then, the target trajectory information acquisition unit 110 sets the non-gravity disturbance model parameter values ​​input from the parameter value reflection unit 170 in the non-gravity disturbance model 112. The parameter value reflection unit 170 also outputs the non-gravity disturbance model parameter values ​​input from the optimization calculation unit 160 to the evaluation value calculation unit 140. For example, the non-gravity disturbance model parameter values ​​output by the parameter value reflection unit 170 to the target trajectory information acquisition unit 110 may be input to the evaluation value calculation unit 140 via the comparison information generation unit 130.

[0105] FIG. 8 is a diagram showing an example of a processing procedure in which the parameter value determining system 100 determines the non-gravitational disturbance model parameter values. 8, the parameter value determination system 100 determines whether or not to use the external orbit information (step S11). For example, whether or not to use the external orbit information may be set in advance by a user, and the parameter value determination system 100 may determine whether or not to use the external orbit information in accordance with the setting.

[0106] When the parameter value determination system 100 determines that the external orbit information is to be used (step S11: YES), the external orbit information acquisition unit 120 acquires the external orbit information (step S21). Next, the target orbit information acquisition unit 110 acquires the target orbit information (step S31). For example, the target orbit information acquisition unit 110 sets the non-gravity disturbance model parameter values ​​in the non-gravity disturbance model 112 and executes the orbit estimation software 111 to calculate the target orbit information. Alternatively, the target orbit information acquisition unit 110 may access a server device that provides a function for executing the orbit estimation software 111 to acquire the target orbit information.

[0107] Next, the comparison information generating unit 130 generates comparison information by converting the target orbit information acquired by the target orbit information acquiring unit 110 and the external orbit information acquired by the external orbit information acquiring unit 120 into a format that allows comparison (step S32). For example, the comparison information generating unit 130 extracts only the orbit information of the target spacecraft from each of the target orbit information and the external orbit information. Then, the comparison information generating unit 130 performs various processes such as extraction of data for the same period, format conversion, and coordinate conversion on the orbit information extracted from each of the orbit information and the external orbit information, and converts and adjusts the orbit information so that it is for the same period and in the same format (coordinate system, time system, etc.) before outputting it.

[0108] Next, the evaluation value calculation unit 140 calculates an evaluation value based on the comparison information generated by the comparison information generation unit 130 (step S33). This evaluation value can be considered as a value indicating an evaluation of the target trajectory information, or a value indicating an evaluation of the non-gravitational disturbance model parameter values ​​used in generating the target trajectory information.

[0109] Furthermore, the evaluation value calculation unit 140 associates the non-gravity disturbance model parameter values ​​used in generating the target trajectory information with the calculated cost function. Specifically, the evaluation value calculation unit 140 generates and outputs data in which the non-gravity disturbance model parameter values ​​and the evaluation value are combined. The data output by the evaluation value calculation unit 140 is used, for example, by the optimization pre-processing unit 150 to generate an evaluation function.

[0110] Furthermore, the evaluation value calculation unit 140 judges whether the calculated evaluation value indicates a better evaluation than a threshold value (step S34). For example, when the evaluation value calculation unit 140 calculates an evaluation value in which a smaller value indicates a better evaluation, it judges whether the evaluation value is equal to or less than the threshold value. When the evaluation value calculation unit 140 determines that the evaluation value does not indicate an evaluation better than the threshold value (step S34: NO), the parameter value determination system 100 determines whether or not preprocessing is necessary for the optimization calculation (step S41). For example, whether or not preprocessing is performed may be set in advance by the user according to the optimization algorithm, and the parameter value determination system 100 may determine whether or not preprocessing is necessary according to the setting.

[0111] When the parameter value determination system 100 determines that preprocessing is necessary (step S41: YES), the optimization preprocessing unit 150 executes preprocessing for the optimization calculation (step S51). For example, the optimization preprocessing unit 150 generates an evaluation function to be used in the optimization calculation based on data in which the non-gravity disturbance model parameter values ​​and the evaluation values ​​are combined.

[0112] Next, the optimization calculation unit 160 performs one step of solution search in the optimization calculation to update the non-gravitational disturbance model parameter values ​​(step S52). The parameter value reflection unit 170 reflects the non-gravity disturbance model parameter values ​​updated by the optimization calculation unit 160 in the non-gravity disturbance model 112 (step S53). After step S53, the process returns to step S31.

[0113] On the other hand, if the parameter value determination system 100 determines in step S11 that the external orbit information is not to be used (step S11: NO), the process proceeds to step S31. In this case, in the process of step S31, the target orbit information acquisition unit 110 acquires two pieces of target orbit information that partially overlap in time period as described above. The target orbit information acquisition unit 110 acquires these two pieces of target orbit information for the same non-gravitational disturbance model parameter value.

[0114] On the other hand, if the parameter value determination system 100 determines in step S41 that preprocessing is not required (step S41: NO), the process proceeds to step S52. In this case, in step S52, the optimization calculation unit 160 may receive a pair of the non-gravity disturbance model parameter value and the evaluation value as input, and may update and output the non-gravity disturbance model parameter value based on an evaluation function or the like generated according to the characteristics of the optimization algorithm used. On the other hand, in step S34, if the evaluation value calculation section 140 determines that the evaluation value indicates an evaluation better than the threshold value (step S34: YES), the parameter value determining system 100 ends the processing of FIG.

[0115] 8, each time parameter value determination system 100 repeats the loops of steps S31 to S34 and S41 to S53, pairs of non-gravity disturbance model parameter values ​​and evaluation values ​​are accumulated. Therefore, data for optimization pre-processing unit 150 to generate an evaluation function increases with each loop repetition. As a result, it is expected that parameter value determination system 100 will be able to generate a more accurate evaluation function as the number of times the loop is executed increases.

[0116] In order to reduce the number of times the loop is executed, initial data including a plurality of pairs of non-gravity disturbance model parameter values ​​and evaluation values ​​may be prepared as in the example of Fig. 6. For example, the target trajectory information acquisition unit 110 may generate target trajectory information for each non-gravity disturbance model parameter value appropriately determined in advance. Then, the evaluation value calculation unit 140 may calculate an evaluation value for each target trajectory information (hence, for each non-gravity disturbance model parameter value) and combine the non-gravity disturbance model parameter value and the evaluation value. Then, the evaluation value calculation unit 140 may generate data that combines the pairs of the non-gravity disturbance model parameter values ​​and the evaluation values ​​as initial data for optimization calculation (initial data for the optimization pre-processing unit 150 to generate an evaluation function).

[0117] As described above, the evaluation value calculation unit 140 calculates an evaluation value indicating an evaluation of the first orbit information based on a comparison between the first orbit information calculated using a non-gravity disturbance model for the orbit of the target spacecraft, which is a spacecraft subject to orbit calculation, and the second orbit information, which is orbit information indicating the orbit of the target spacecraft for a time interval including a time interval common to the time interval indicated by the first orbit information. The optimization calculation unit 160 determines non-gravity disturbance model parameter values, which are parameter values ​​used in the non-gravity disturbance model, based on the evaluation value calculated by the evaluation value calculation unit 140.

[0118] In the parameter value determination system 100, by determining the non-gravitational disturbance model parameter values ​​based on a comparison between the first orbit information and the second orbit information, the non-gravitational disturbance model parameter values ​​can be determined based on observation information for a relatively short period of time, such as data for one day. For example, the parameter value determination system 100 can determine the non-gravitational disturbance model parameter values ​​even in a state where there is a sufficient lack of data, such as in the early stages of launch of the target spacecraft.

[0119] Moreover, the parameter value determination system 100 can use existing software as the orbit estimation software 111, and does not require special software for calculating the target orbit information. Moreover, the parameter value determination system 100 can determine the non-gravitational disturbance model parameter values ​​without requiring information that is generally difficult to obtain, such as information on the structure, shape, and attitude of the target spacecraft.

[0120] In addition, the second orbit information is information indicating an orbit calculated using a non-gravitational disturbance model for a time period in which the time period in which the first orbit information indicates an orbit and the time period in which the second orbit information indicates an orbit overlap in part. As a result, the parameter value determining system 100 can determine the non-gravitational disturbance model parameter values ​​even when external orbit information cannot be acquired.

[0121] Furthermore, the comparison information generating unit 130 performs an interpolation so that the first orbital information and the second orbital information, which indicate the positions of the target spacecraft at different times, indicate the position of the target spacecraft at the same time. The evaluation value calculating unit 140 calculates an evaluation value that indicates a better evaluation as the distance between the position of the target spacecraft indicated by the first orbital information and the position of the target spacecraft indicated by the second orbital information at the same time is smaller. According to the parameter value determination system 100, it is expected that the non-gravitational disturbance model parameter values ​​can be calculated with relatively high accuracy in that the difference in the position of the target spacecraft at the same time between the first orbit information and the second orbit information is evaluated.

[0122] As described above, the orbit estimation software 111 is not limited to a specific software, and the non-gravitational disturbance model 112 is not limited to a specific model. In addition, the method used by the optimization pre-processing unit 150 to generate the approximation function (the method used to generate the evaluation function) is not limited to the least squares method. For example, the optimization pre-processing unit 150 may generate the approximation function using a regression analysis method other than the least squares method.

[0123] In addition, the optimization algorithm used by the optimization calculation unit 160 to calculate the non-gravity disturbance model parameter value is not limited to the steepest descent method, and various algorithms can be used. Furthermore, the method used by the optimization calculation unit 160 to calculate the non-gravity disturbance model parameter value is not limited to the optimization technique. For example, the optimization calculation unit 160 may calculate the non-gravity disturbance model parameter value using a machine learning technique such as deep learning.

[0124] Furthermore, for the non-gravity disturbance model parameter values ​​calculated by the optimization calculation section 160, an upper limit value, a lower limit value, or both may be set for each parameter. For example, it is expected that the non-gravity disturbance model parameter values ​​calculated by the parameter value determination system 100 will be similar for conditions with different periods but similar β angles. Therefore, a fluctuation range may be set in advance for the non-gravity disturbance model parameter values ​​calculated by the parameter value determination system 100 within a range close to the non-gravity disturbance model parameter values ​​determined in similar cases. This is expected to reduce the possibility of falling into a local optimum solution in the optimization algorithm in the optimization calculation performed by the optimization calculation unit 160, and to reduce the number of repetitions of processing in the optimization calculation.

[0125] Furthermore, if the non-gravitational disturbance model parameter values ​​do not become close to each other (for example, if the values ​​do not become within a set fluctuation range) despite the β angle being close to each other, it is possible to detect that an unexpected situation has occurred in the attitude of the spacecraft or in operations such as paddle rotation. In addition, the parameter value determination system 100 may calculate non-gravitational disturbance model parameter values ​​common to multiple satellites with similar shapes and orbits, thereby calculating general-purpose non-gravitational disturbance model parameter values ​​that can be used for other satellites with similar shapes and orbits.

[0126] As described above, the parameter value determination system 100 can determine the non-gravity disturbance model parameter values ​​based on short-term data and can update the non-gravity disturbance model parameter values ​​in the short term. Also, the parameter value determination system 100 can determine the non-gravity disturbance model parameter values ​​using general public information, etc., and does not require information on the structure and shape of the spacecraft.

[0127] When the non-gravity disturbance model parameter values ​​are updated in the short term using the parameter value determination system 100, the β angle of the spacecraft changes little by little, so the change in the non-gravity disturbance model parameter values ​​is also expected to be small. Therefore, by appropriately setting the selection range of the non-gravity disturbance model parameter values ​​in the optimization algorithm, the rate at which the optimization algorithm leads to a local optimum solution can be reduced. For example, when the optimization calculation unit 160 searches for the non-gravity disturbance model parameter value by the steepest descent method, the step size in one search and the number of times the search is repeated may be limited. This makes it possible to obtain a search result in which the variation range of the non-gravity disturbance model parameter value is limited, and it is expected that local solutions can be avoided and the search time can be shortened. Depending on the optimization method used, the variation range of the non-gravity disturbance model parameter value may be directly limited.

[0128] 9 is a diagram showing another example of the configuration of the parameter value determination system according to the embodiment. In the configuration shown in FIG. In this configuration, the evaluation unit 611 calculates an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for the orbit of a target spacecraft, which is a spacecraft subject to orbit calculation, and second orbit information, which is orbit information indicating the orbit of the target spacecraft for a time interval including a time interval common to the time interval indicated by the first orbit information. The parameter value determination unit 612 determines non-gravitational disturbance model parameter values, which are parameter values ​​used in the non-gravitational disturbance model, based on the evaluation value. The evaluation unit 611 corresponds to an example of an evaluation means, and the parameter value determination unit 612 corresponds to an example of a parameter value determination means.

[0129] In the parameter value determination system 610, by determining the non-gravity disturbance model parameter values ​​based on a comparison between the first orbit information and the second orbit information, the non-gravity disturbance model parameter values ​​can be determined based on observation information for a relatively short period of time, such as data for one day. For example, the parameter value determination system 610 can determine the non-gravity disturbance model parameter values ​​even in a state where data is insufficient, such as in the early stages of launch of the target spacecraft.

[0130] Fig. 10 is a diagram showing an example of a processing procedure in a parameter value determination method according to the embodiment. The parameter value determination method shown in Fig. 10 includes performing an evaluation (step S611) and determining a parameter value (step S612). In performing the evaluation (step S611), the computer calculates an evaluation value indicating an evaluation of the first orbital information based on a comparison between first orbital information calculated using a non-gravitational disturbance model for the orbit of a target spacecraft, which is a spacecraft whose orbit is to be calculated, and second orbital information, which is orbital information indicating the orbit of the target spacecraft for a time period that includes a time period common to the time period indicated by the first orbital information. In determining parameter values ​​(step S612), the computer determines non-gravity disturbance model parameter values, which are parameter values ​​used in the non-gravity disturbance model, based on the evaluation values.

[0131] In the parameter value determination method shown in Fig. 10, the non-gravity disturbance model parameter values ​​are determined based on a comparison between the first orbit information and the second orbit information, so that the non-gravity disturbance model parameter values ​​can be determined based on observation information for a relatively short period of time, such as data for one day. For example, according to the parameter value determination method shown in Fig. 10, the non-gravity disturbance model parameter values ​​can be determined even in a state where there is insufficient data, such as at the beginning of the launch of the target spacecraft.

[0132] FIG. 11 is a schematic block diagram illustrating a computer configuration according to at least one embodiment. In the configuration shown in FIG. 11, a computer 700 includes a CPU 710, a main memory device 720, an auxiliary memory device 730, an interface 740, and a non-volatile recording medium 750.

[0133] Any one or more of the parameter value determination system 100 and the parameter value determination system 610 or a part thereof may be implemented in the computer 700. In this case, the operation of each of the above-mentioned processing units is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, develops it in the main storage device 720, and executes the above-mentioned processing according to the program. The CPU 710 also secures a storage area corresponding to each of the above-mentioned storage units in the main storage device 720 according to the program. Communication between each device and other devices is executed by the interface 740 having a communication function and performing communication according to the control of the CPU 710. The interface 740 also has a port for the nonvolatile recording medium 750, and reads information from the nonvolatile recording medium 750 and writes information to the nonvolatile recording medium 750.

[0134] When the parameter value determination system 100 is implemented in a computer 700, the operations of the target trajectory information acquisition unit 110, the trajectory estimation software 111, the non-gravitational disturbance model 112, the external trajectory information acquisition unit 120, the comparison information generation unit 130, the evaluation value calculation unit 140, the optimization pre-processing unit 150, the optimization calculation unit 160, and the parameter value reflection unit 170 are stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-mentioned processing according to the program.

[0135] Furthermore, the CPU 710, in accordance with the program, secures a storage area in the main storage device 720 for the parameter value determination system 100 to perform processing. Communication between the parameter value determination system 100 and other devices is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Interaction between the parameter value determination system 100 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0136] When the parameter value determination system 610 is implemented in a computer 700, the operations of the evaluation unit 611 and the parameter value determination unit 612 are stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-mentioned processing in accordance with the program.

[0137] Furthermore, the CPU 710, in accordance with the program, secures a storage area in the main storage device 720 for the parameter value determination system 610 to perform processing. Communication between the parameter value determination system 610 and other devices is performed by an interface 740 having a communication function and operating under the control of the CPU 710. Interaction between the parameter value determination system 610 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0138] Any one or more of the above-mentioned programs may be recorded in non-volatile recording medium 750. In this case, interface 740 may read the program from non-volatile recording medium 750. Then, CPU 710 may directly execute the program read by interface 740, or may temporarily store the program in main storage device 720 or auxiliary storage device 730 and execute it.

[0139] Note that the processing of each part may be performed by recording a program for executing all or part of the processing performed by the parameter value determination system 100 and the parameter value determination system 610 in a computer-readable recording medium, and having a computer system read and execute the program recorded in the recording medium. Note that the "computer system" referred to here includes the OS (Operating System) and hardware such as peripheral devices. Furthermore, the term "computer-readable recording medium" refers to portable media such as flexible disks, optical magnetic disks, ROMs (Read Only Memory), and CD-ROMs (Compact Disc Read Only Memory), as well as storage devices such as hard disks built into computer systems. The above-mentioned program may be for realizing part of the above-mentioned functions, or may be capable of realizing the above-mentioned functions in combination with a program already recorded in the computer system.

[0140] Although an embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and designs that do not deviate from the gist of the present invention are also included. [Explanation of symbols]

[0141] 100, 610 Parameter value determination system 110 Target trajectory information acquisition unit 111 Trajectory Estimation Software 112 Non-gravitational Disturbance Model 120 External orbit information acquisition unit 130 Comparison information generation section 140 Evaluation value calculation unit 150 Optimization preprocessing section 160 Optimization Calculation Section 170 Parameter value reflection section 611 Evaluation Department 612 Parameter value determination unit

Claims

1. an evaluation means for calculating an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for the orbit of a target spacecraft, which is a spacecraft whose orbit is to be calculated, and second orbit information which is orbit information indicating the orbit of the target spacecraft for a time period including a time period common to the time period indicated by the first orbit information; a parameter value determining means for determining a non-gravity disturbance model parameter value, which is a parameter value used in the non-gravity disturbance model, based on the evaluation value; A parameter value determination system comprising:

2. The second trajectory information is information indicating a trajectory calculated using the non-gravitational disturbance model for a time interval in which a time interval in which the first trajectory information indicates a trajectory and a time interval in which the second trajectory information indicates a trajectory partially overlap. The parameter value determination system according to claim 1 .

3. a comparison information generating means for performing an interpolation so that the first orbit information and the second orbit information, which indicate the positions of the target spacecraft at different times, indicate the position of the target spacecraft at the same time; the evaluation means calculates an evaluation value indicating a better evaluation as the distance between the position of the target spacecraft indicated by the first orbit information and the position of the target spacecraft indicated by the second orbit information for the same time is smaller. The parameter value determining system according to claim 1 or 2.

4. The computer calculating an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for an orbit of a target spacecraft, which is a spacecraft subject to orbit calculation, and second orbit information which is orbit information indicating the orbit of the target spacecraft for a time period including a time period common to the time period indicated by the first orbit information; determining non-gravity disturbance model parameter values, which are parameter values ​​used in the non-gravity disturbance model, based on the evaluation value; The method of claim 1, further comprising:

5. On the computer, calculating an evaluation value indicating an evaluation of the first orbit information based on a comparison between first orbit information calculated using a non-gravitational disturbance model for the orbit of a target spacecraft, which is a spacecraft subject to orbit calculation, and second orbit information which is orbit information indicating the orbit of the target spacecraft for a time interval including a time interval common to the time interval indicated by the first orbit information; determining non-gravity disturbance model parameter values, which are parameter values ​​used in the non-gravity disturbance model, based on the evaluation value; A program for executing.

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