JP6102597B2 - Information processing apparatus, program, and method - Google Patents

Description

  The present invention relates to an information processing apparatus, a program, and a method.

  Artificial satellites communicate with ground station antennas using radio waves in a limited frequency band. For this reason, when two satellites using close frequencies are present in close directions when viewed from the ground station, a phenomenon occurs in which both radio waves interfere with each other. FIG. 1 is a diagram exemplifying a case where two satellites exist in directions closer to each other as radio wave interference occurs when viewed from the ground station. As shown in the drawing, both the satellite A and the satellite B exist within the beam width from the antenna of the ground station 1. In such a situation, for example, the uplink from the ground station 1 may interfere with the satellite B. Alternatively, the downlink from the satellite B may interfere with the ground station 1.

  Therefore, by determining whether two satellites are close to each other when viewed from the ground station based on the predicted orbit of the satellite, the possibility of radio wave interference is determined, and when radio wave interference may occur In order to avoid interference of radio waves, such as stopping radio waves of low-priority satellites.

  In this regard, satellite communication systems are known for increasing capacity through spectrum reuse by multiple satellites. In addition, a technique is known that enables the orbit of a spacecraft to be obtained with high accuracy with simple equipment. (For example, see Patent Document 1 and Patent Document 2)

Special table 2009-517793 JP 2007-256004 A

  As described above, radio wave interference can occur when two satellites are in the close direction when viewed from the ground station. Therefore, it is determined based on the predicted orbit of the satellite whether the two satellites are in the close direction when viewed from the ground station. Here, the prediction of the orbit of the satellite 2 actually has an error, and in particular, a prediction error of a magnitude that cannot be ignored occurs in a medium altitude satellite where radio wave interference frequently occurs. For this reason, when determining whether two satellites are close to each other when viewed from the ground station, an orbit prediction error must also be taken into consideration. Orbital prediction errors mainly occur in the direction of satellite travel. However, there has been no method that can easily reflect the prediction error of the traveling direction of the satellite in determining whether the two satellites are in the close direction when viewed from the ground station. In one aspect, an object of the present invention is to provide a technique that can easily reflect a prediction error in the traveling direction of a satellite in determining whether two satellites are in the close direction when viewed from a ground station. To do.

  A program according to an aspect of the present invention includes a first predicted position at a predetermined time of a first satellite from a first satellite orbital calendar including a momentary predicted position and velocity of a first satellite in a computer, and a first A process for acquiring the speed is executed. Moreover, the process which converts the prediction error of the 1st prediction position of the advancing direction of a 1st satellite into a 1st time error using a 1st speed is performed. A process of acquiring the second predicted position and the second speed of the second satellite at a predetermined time from the second satellite orbital calendar including the predicted position and speed of the second satellite every moment is executed. A process of converting the prediction error of the second predicted position in the traveling direction of the second satellite into the second time error using the second speed is executed. A process of acquiring a predicted position before the first time error from the predetermined time and a predicted position after the first time error from the predetermined time from the first satellite orbital calendar is executed. A process of acquiring a predicted position before the second time error from the predetermined time and a predicted position after the second time error from the predetermined time from the second satellite orbital calendar is executed. The second satellite is located at a position where radio wave interference may occur in communication at a predetermined time between the ground station and the first satellite using the following first to sixth vector. A process of determining whether or not it exists is executed. Here, the first line-of-sight vector is a vector obtained by viewing the first predicted position from the ground station. The second line-of-sight vector is a vector obtained by viewing the predicted position before the first time error from the ground station. The third line-of-sight vector is a vector obtained by viewing the predicted position after the first time error from the ground station. The fourth line-of-sight vector is a vector obtained by viewing the second predicted position from the ground station. The fifth line-of-sight vector is a vector obtained by viewing the predicted position before the second time error from the ground station. The sixth line-of-sight vector is a vector that looks at the predicted position after the second time error.

  It is possible to provide a method that can easily reflect the prediction error of the traveling direction of the satellite in determining whether the two satellites are in the close direction when viewed from the ground station.

It is a figure which illustrates the case where two satellites exist in the direction which adjoined so that radio wave interference occurred. It is a figure which illustrates the gaze direction vector of the satellite on the basis of a ground station. It is a figure which illustrates the graph of AZ-EL coordinate. It is a figure which illustrates the orbit of two satellites seen from the ground station. It is a figure explaining a gaze direction vector. It is a figure which shows an example of the threshold value with respect to a scissors angle, and determination of radio wave interference. It is a figure which illustrates the satellite orbital calendar concerning one embodiment. It is a figure which illustrates the relationship between the prediction error (DELTA) L of the advancing direction, and time error (DELTA) T. It is a figure explaining the prediction error of a gaze direction unit vector and a traveling direction. It is a figure which illustrates determination of the radio wave interference which concerns on embodiment when all prediction errors are small. It is a figure which shows an example in case a prediction error is large. It is a figure which shows another example in case prediction error is large. It is a figure which illustrates the line segment showing the range of the prediction error of the position in the advancing direction of a satellite. It is a figure which illustrates the interference area | region of a satellite. It is a figure which shows the example of the determination of the radio wave interference which concerns on embodiment when a prediction error is large. It is a figure which shows another example of determination of the radio wave interference which concerns on embodiment when a prediction error is large. It is a figure explaining coordinate system XYZs defined using a gaze direction unit vector. It is a figure explaining the intersection determination of the line segment which two unit vector pairs comprise. It is a figure explaining the inclusion determination of the gaze direction vector in an interference area. It is a figure explaining the inclusion determination of the gaze direction vector in an interference area. It is a figure which illustrates the functional block structure of the information processing apparatus which concerns on embodiment. It is a figure which illustrates the electromagnetic wave interference determination process in the time T performed by the control part of information processing apparatus. It is a figure which illustrates the electromagnetic wave interference determination process in the time T performed by the control part of information processing apparatus. It is a figure which illustrates the hardware constitutions of the computer for implement | achieving the information processing apparatus which concerns on embodiment.

  Hereinafter, some embodiments of the present invention will be described in detail with reference to the drawings. In addition, the same code | symbol was attached | subjected to the corresponding element in several drawing.

  First, an example of a method for determining whether or not two satellites are in the close direction when viewed from the ground station in consideration of the prediction error of the satellites and thereby determining the possibility of radio wave interference will be described. In general, the satellite orbital calendar of a satellite in a specific period (for example, the position information and the velocity information of the satellite's orbit every moment) can be calculated in advance, and the predicted orbits of the two satellites are given in advance. It shall be. The position vector of the ground station 1 at a predetermined time is a value that can be calculated.

  In an example of this radio wave interference determination method, first, a line-of-sight direction vector that is a direction vector of a satellite viewed from the ground station 1 is calculated. FIG. 2 is a diagram illustrating a line-of-sight direction vector of the satellite 2 with the ground station 1 as a reference. Usually, the line-of-sight direction vector is expressed by an azimuth angle (AZ: Azimuth) and an elevation angle (EL: Elevation) with respect to the ground station 1 as shown in FIG. FIG. 3 is a diagram illustrating a graph of AZ-EL coordinates representing the trajectory of the orbit in the line-of-sight direction of the satellite 2 using the azimuth angle and the elevation angle with respect to the ground station 1. An example of a radio wave interference determination method in consideration of the prediction error of the orbit of the satellite 2 will be described using the two expressions illustrated in FIGS.

FIG. 4 is a diagram illustrating the orbits of two satellites 2 (for example, satellite A and satellite B) viewed from the ground station 1. In an example of a radio wave interference determination method considering the prediction error of the orbit of the satellite 2, first, the line-of-sight direction vectors of the two satellites 2 (for example, the satellite A and the satellite B) are calculated. FIG. 5 is a diagram for explaining the line-of-sight direction vector. For example, Ra is the position vector from the center of the satellite A at the time when it is desired to check for the presence of radio wave interference. Also, S is the position vector of the ground station 1 from the earth center at the time when it is desired to check for the presence or absence of radio wave interference. In this case, the line-of-sight direction vector ρa of the satellite A at the time when it is desired to check the presence or absence of radio wave interference can be calculated by, for example, the following Equation 1.
ρa = Ra−S Equation 1

  Here, the position vector Ra of the satellite A can be calculated in advance, and can be obtained from, for example, a satellite orbital calendar calculated in advance. The position vector S of the ground station 1 is also a value that can be calculated. Therefore, the line-of-sight direction vector ρa of the satellite A at the time when it is desired to check the presence or absence of radio wave interference can be calculated.

Similarly, for the line-of-sight direction vector of the satellite B, for example, the position vector of the satellite B at the time when the presence / absence of radio wave interference is desired to be examined is Rb. The position vector of the ground station 1 is S. In this case, the line-of-sight direction vector of the satellite B at the time when it is desired to examine the presence or absence of radio wave interference can be calculated by, for example, the following equation 2.
ρb = Rb−S Equation 2

  Here, the position vector Rb of the satellite B can be calculated in advance, and can be acquired from, for example, a satellite orbital calendar calculated in advance. The position vector S of the ground station 1 is also a value that can be calculated. Therefore, it is also possible to calculate the line-of-sight direction vector ρb of the satellite B at the time when it is desired to check the presence or absence of radio wave interference.

  Subsequently, an angle formed by two vectors of the sight line direction vector ρa of the satellite A and the sight line direction vector ρb of the satellite B is calculated. Note that the angle formed by the line-of-sight direction vectors of the two satellites 2 (for example, satellite A and satellite B) is referred to as “scissor angle”. In an example of the radio wave interference determination method considering the prediction error of the orbit of the satellite 2, it is determined that there is interference when the scissor angle is equal to or less than a predetermined threshold.

  Here, for example, when the orbit of the satellite 2 can be accurately predicted, the predetermined threshold value used for the determination may be determined by radio wave characteristics such as the beam width of the antenna of the ground station 1. That is, the predetermined threshold may be set to, for example, the beam width of the antenna of the ground station 1, and it may be determined that radio wave interference does not occur if the scissor angle is wider than the beam width. However, in reality, an error occurs in the prediction of the orbit of the satellite 2. In particular, a medium altitude satellite with an altitude of several hundred kilometers to 1,000 kilometers has a prediction error that cannot be ignored in the prediction of orbit due to the influence of atmospheric resistance and the like. For this reason, in determining whether or not radio wave interference has occurred, trajectory prediction errors must be taken into account. As an example of a technique for reflecting a prediction error in radio wave interference determination, it is conceivable to add a prediction error as a margin to a predetermined threshold for the scissor angle.

  FIG. 6 is a diagram exemplifying determination of radio wave interference when adding a prediction error as a margin to a predetermined threshold for the scissor angle. For example, the beam width of the antenna used by the ground station 1 in communication with the satellite A is θb. In this case, θb is expressed as a range of a circle 40 indicated by a solid line in the AZ-EL coordinates of FIG. Further, in FIG. 6, a range in which a margin corresponding to a prediction error is taken as θb by an angle of θm is indicated by a dashed circle 41. In addition, in the determination of the radio wave interference when the prediction error of the trajectory is taken into consideration by adding the prediction error as a margin to the predetermined threshold for the scissor angle, the angle (θb + θm) taking this margin is used as the predetermined threshold. . That is, the area within the circle 41 is used as an area where it is determined that there is radio wave interference, and it is determined that there is interference when the target satellite B to be examined whether radio wave interference occurs is within the circle 41 range. To do. With this configuration, even if there is a prediction error in the orbit prediction of two satellites 2 (for example, satellite A and satellite B) that are desired to be examined for the occurrence of radio wave interference, radio wave interference may occur. A case can be detected.

  However, when a margin for the prediction error is added to the scissor angle in this way, the influence of the trajectory error is added not only in the traveling direction but also in the vertical direction (cross-track direction). The cross track direction is, for example, a direction perpendicular to the traveling direction of the satellite in the satellite fixed coordinate system. However, in the mid-altitude satellite 2, orbit prediction errors are mainly added in the traveling direction of the satellite 2. Therefore, when a sufficient margin for the prediction error is taken in the traveling direction of the satellite 2, an excessive margin is considered in the vertical direction (cross-track direction) of the satellite 2. As a result, there arises a problem that the occurrence of interference is excessively determined. Therefore, there is a demand for a technique that can easily reflect a prediction error in the traveling direction of the satellite in the determination of the presence or absence of radio wave interference that may occur when two satellites are seen in the close direction from the ground station.

  In the method for determining the radio wave interference of the satellite 2 according to the embodiment, the traveling direction component of the orbit prediction error is reflected in the area where it is determined that there is radio wave interference, and other satellites 2 interfere with the radio wave using this area. Determine whether or not. Hereinafter, determination of radio wave interference of the satellite 2 according to the embodiment will be described with reference to FIGS. 7 to 22 (FIGS. 22A and 22B).

  In the determination of the radio wave interference of the satellite 2 according to the embodiment, the prediction of the occurrence of radio wave interference determines the presence / absence of interference at a specified time interval for a specified period. In the following, the determination of radio wave interference at an arbitrary time T will be described.

  First, the handling of orbit prediction errors in the radio wave interference determination method of the satellite 2 according to the embodiment will be described. As described above, in the middle altitude satellite 2, the orbit prediction error is mainly added to the traveling direction of the satellite 2. On the other hand, the prediction error in the cross track direction is smaller than the error in the traveling direction, and the prediction error in the cross track direction does not change depending on time. Therefore, the prediction error in the cross track direction may be added as a margin to the threshold value of the scissor angle if it is necessary to consider. That is, it is noted that the prediction error to be considered is a component in the traveling direction.

  Here, in general, the satellite orbital calendar (positional information of the orbit of the satellite at every moment) of the satellite 2 in a specific period can be calculated in advance. Accordingly, it is assumed that the predicted orbits of two satellites 2 (for example, satellite A and satellite B) that are desired to be examined for the presence of radio wave interference are given in advance as a satellite orbit calendar 700, for example. FIG. 7 is a diagram illustrating a satellite ephemeris 700 according to an embodiment. The satellite orbit calendar 700 stores, for example, time-series data of satellite position vectors and velocity vectors represented by equatorial plane coordinates (T.O.D .: True of date). Position and velocity information can be retrieved.

When attention is paid to the satellite 2 at a medium altitude, the prediction error of the position in the traveling direction at a certain time T is calculated by the following equation.
ΔL = δL + (3n / 2) δa · (T−Ta) + (3n / 4) δadot · (T−Tad) ² Formula 3

  Here, δL is a constant value of the traveling direction position error. δa is an orbital radius error. Ta is the prediction start time of the trajectory length radius error. δadot is the orbital length radius change rate error. Tad is the prediction start time of the trajectory radius change rate error. n is an average motion at time T and is a value calculated from the position vector of satellite 2 / the velocity vector of satellite 2. These parameters (δL, δa, Ta, δadot, Tad, and n) are values that can be calculated in advance. Therefore, the prediction error ΔL of the position in the traveling direction at a certain time T can be calculated by the above equation 3.

FIG. 8 is a diagram illustrating the relationship between the calculated prediction error ΔL of the position of the satellite 2 in the traveling direction and ΔT converted to a time error. As shown in the figure, the range of the prediction error of the position in the traveling direction is shown with a ΔL spread before and after the predicted position of the satellite at time T. Then, the prediction error ΔL of the position in the traveling direction can be converted into a time error: ΔT by the following expression 4 when the magnitude of the speed at time T is V. The velocity magnitude V at time T can be obtained from the velocity vector at time T in the satellite orbit calendar 700, for example.
ΔT = ΔL / V Equation 4

That is, as shown in FIG. 8, the range of the prediction error spread of the position of the satellite 2 at a certain time is a time that is advanced by ΔT time from the time T from the position of the satellite 2 at time T1 that is returned by ΔT time from the time T. It can be understood as a range up to the position of the satellite 2 at T2.
T1 = T−ΔT Expression 5 (Expression 5-1)
T2 = T + ΔT Formula 5 (Formula 5-2)

  The position information of the orbit of the satellite 2 from moment to moment is stored in the satellite orbit calendar 700 as described above. Therefore, from the satellite orbital calendar 700, the satellite position vector R0 at time T expressed in equatorial plane coordinates, the satellite position vector R1 at time T1 (T1 = T−ΔT), and the satellite position vector R2 at time T2 (T2 = T + ΔT). Can be obtained respectively.

Further, a position vector: S representing the position of the ground station 1 from the geocenter at the time T in the equatorial plane coordinates (T.O.D.) is a value that can be calculated. get. Then, the line-of-sight unit vector ρ0 when viewing the satellite 2 at the time T from the position of the ground station 1 at the time T, the line-of-sight unit vector ρ1 when viewing the satellite at the time T1, and the line-of-sight unit vector ρ2 when viewing the satellite at the time T2. Respectively. FIG. 9 is a diagram for explaining these line-of-sight direction unit vectors (ρ0, ρ1, and ρ2) when the satellite 2 is viewed from the ground station 1. These line-of-sight direction unit vectors can be calculated by, for example, the following Expression 6 (Expression 6-1 to Expression 6-3).
ρ0 = (R0−S) / | R0−S | Expression 6 (Expression 6-1)
ρ1 = (R1-S) / | R1-S | Equation 6 (Formula 6-2)
ρ2 = (R2-S) / | R2-S | Expression 6 (Expression 6-3)

Subsequently, an angle θ1 formed by ρ0 and ρ1 and an angle θ2 formed by ρ0 and ρ2 are respectively obtained. The angle formed by these line-of-sight direction unit vectors can be calculated by, for example, the following Expression 7 (Expression 7-1 to Expression 7-2).
θ1 = cos ⁻¹ (ρ0 · ρ1) Expression 7 (Expression 7-1)
θ2 = cos ⁻¹ (ρ0 · ρ2) Expression 7 (Expression 7-2)

  Therefore, the range of the prediction error of the position in the traveling direction at the time T of the satellite 2 has a spread of (θ1 + θ2) from the line-of-sight direction unit vector ρ0 at the time T of the satellite 2, as shown in FIG.

  Subsequently, the radio wave interference determination method according to the embodiment using the line-of-sight direction unit vectors ρ1 and ρ2 obtained by converting the above-described prediction error of the position of the satellite 2 into a time error and the angles θ1 and θ2 will be described below. Explained.

  Hereinafter, determination of whether or not the satellite A and the satellite B at a certain time T are in a positional relationship causing radio wave interference when viewed from the ground station 1 will be described. In the following description, the parameter for satellite A is indicated with a suffix “a”, and the parameter for satellite B is indicated with a suffix “b”. First, for each of the satellite A and the satellite B, the above-described ρ0, ρ1, and ρ2, and θ1 and θ2 at the time T at which the presence / absence of radio wave interference is to be examined are obtained by the above-described equations 3 to 7. The values of ρ0, ρ1, and ρ2, and θ1 and θ2 obtained for the satellite A are denoted by ρa0, ρa1, and ρa2, and θa1 and θa2, respectively, with the suffix “a”. Further, the values of ρ0, ρ1, and ρ2 obtained with respect to the satellite B, and θ1 and θ2 are denoted by ρb0, ρb1, and ρb2, and θb1 and θb2, respectively, with the suffix “b”.

  In the radio wave interference determination method according to the embodiment, the magnitude relationship between (θa1, θa2) of satellite A and (θb1, θb2) of satellite B obtained above and a predetermined threshold set for the scissor angle. The process is divided into two types. In the radio wave interference determination method according to the embodiment, for example, the beam width of the antenna used by the ground station 1 in communication with the satellite A may be used as the predetermined threshold θc. Alternatively, in another embodiment, a value obtained by adding a predetermined angle θm or the like as a margin corresponding to the prediction error in the cross track direction may be used for the beam width of the antenna. Below, the case where the beam width of an antenna is used for the predetermined threshold value θc will be described as an example.

<Case 1>
First, a case where (θa1, θa2) of satellite A and (θb1, θb2) of satellite B are smaller than a predetermined threshold θc of the scissor angle will be described. That is, a case where the following conditional expression 1 is satisfied will be described. Note that the predetermined threshold value θc may be, for example, the antenna beam width of the ground station 1 and a value obtained by adding a margin corresponding to a prediction error in the cross-track direction to the antenna beam width.
θa1, θa2, θb1, and θb2 are all ≦ θc (Condition 1)

  When this conditional expression 1 is satisfied, the position prediction errors of the two satellites (satellite A and satellite B) in the traveling direction are both small, indicating that the predetermined threshold θc of the scissor angle is larger. FIG. 10 is a diagram exemplifying a case where the position prediction errors in the traveling direction of the two satellites (satellite A and satellite B) are both small and the conditional expression 1 is satisfied. In FIG. 10, the angle θa1 formed by ρa0 and ρa1 of the satellite A at the time T at which it is desired to check for the presence of radio wave interference is inside the threshold θc, and the angle θa2 formed by ρa0 and ρa2 of the satellite A is also the threshold θc. Is on the inside. For satellite B, the angle θb1 formed by ρb0 and ρb1 of satellite B at time T at which it is desired to check for the presence of radio wave interference is inside threshold value θc, and the angle θa2 formed by ρb0 and ρb2 of satellite B is also the threshold value. It is inside θc. Therefore, all of θa1, θa2, θb1, and θb2 are angles equal to or smaller than θc and satisfy the above conditional expression 1.

In this case, the scissor angles for the nine combinations of the line-of-sight direction unit vectors ρa0, ρa1, and ρa2 obtained for the satellite A and the line-of-sight direction unit vectors ρb0, ρb1, and ρb2 obtained for the satellite B are as follows: It calculates with Formula 8 (Formula 8-1-Formula 8-9).
θ00 = cos ⁻¹ (ρa0 · ρb0) Expression 8 (Expression 8-1)
θ01 = cos ⁻¹ (ρa0 · ρb1) Expression 8 (Expression 8-2)
θ02 = cos ⁻¹ (ρa0 · ρb2) Expression 8 (Expression 8-3)
θ10 = cos ⁻¹ (ρa1 · ρb0) Expression 8 (Expression 8-4)
θ11 = cos ⁻¹ (ρa1 · ρb1) Expression 8 (Expression 8-5)
θ12 = cos ⁻¹ (ρa1 · ρb2) Expression 8 (Expression 8-6)
θ20 = cos ⁻¹ (ρa2 · ρb0) Expression 8 (Expression 8-7)
θ21 = cos ⁻¹ (ρa2 · ρb1) Expression 8 (Expression 8-8)
θ22 = cos ⁻¹ (ρa2 · ρb2) Expression 8 (Expression 8-9)

Then, if any one of the nine scissors angles θ00, θ01, θ02, θ10, θ11, θ12, θ20, θ21, and θ22 is less than the threshold θc, it is determined that there is interference.
Any of θ00, θ01, θ02, θ10, θ11, θ12, θ20, θ21, and θ22 is ≦ θc Equation 9

  As described above, the presence or absence of radio wave interference can be determined when (θa1, θa2) of satellite A and (θb1, θb2) of satellite B are smaller than the scissor angle threshold value θc. In this method of determining the presence or absence of radio wave interference, if there is a satellite orbital calendar 700 that predicts the orbit of satellite 2, it is possible to obtain a line-of-sight direction vector that represents the range of prediction error in the traveling direction at the time at which it is desired to check the presence or absence of radio wave interference. it can. That is, the prediction error in the traveling direction of the satellite 2 is converted into time, and the position vector shifted by the time error is read from the satellite orbital calendar 700, so that the line-of-sight direction vector ρ1 in consideration of the error indicating the spread of the prediction error in the traveling direction is taken into consideration. And ρ2 can be obtained. The presence / absence of radio wave interference can be determined from the obtained line-of-sight direction vector that does not consider the error and the line-of-sight direction vector that considers the error. In addition, the predetermined threshold value θc used for the determination of the presence or absence of radio wave interference includes, for example, the beam width of the antenna used by the ground station 1 in communication with the satellite A or the beam width, for example, a prediction error in the cross track direction. A value obtained by adding a corresponding margin or the like can be used. In other words, since the prediction error in the traveling direction is taken into consideration by the line-of-sight direction vectors: ρ1 and ρ2, the value of the predetermined threshold θc does not need to be added as a margin for the prediction error in the traveling direction. Therefore, for example, a much narrower value than the case described with reference to FIG. 6 (for example, the antenna beam width of the ground station 1 and the margin corresponding to the prediction error in the cross track direction are added to the antenna beam width). Value) can be set as the predetermined threshold value θc. Therefore, it is possible to determine the radio wave interference by appropriately considering the position error of the satellite in the traveling direction that cannot be ignored in the radio wave interference prediction of the intermediate altitude satellite, and without considering an excessive margin in the cross track direction. , It is possible to suppress excessive determination of the occurrence of interference.

<Case 2>
Next, a case will be described in which any of (θa1, θa2) of satellite A and (θb1, θb2) of satellite B is greater than a predetermined threshold θc of the scissor angle. That is, a case where the following conditional expression 2 is satisfied will be described. Note that the predetermined threshold θc may be, for example, a value obtained by adding the antenna beam width of the ground station 1 and a margin corresponding to the prediction error in the cross track direction to the antenna beam width.
Any of θa1, θa2, θb1, and θb2 is> θc Conditional expression 2

  FIG. 11 is a diagram illustrating a case where the position prediction error in the traveling direction of two satellites (satellite A and satellite B) is large and satisfies conditional expression 2. As shown in the figure, a line segment 50 (a) from ρa1 to ρa2 representing the range of the prediction error in the traveling direction of the satellite A, and a line segment from ρb1 to ρb2 representing the range of the prediction error in the traveling direction of the satellite B. 50 (b) intersects. That is, when the ground station 1 communicates with the satellite A, the satellite B may exist in a range where radio wave interference can occur. However, since none of ρb0, ρb1, and ρb2 is within the predetermined threshold θc from each of ρa0, ρa1, and ρa2, in the determination using Equation 9 in <Case 1> above, the radio wave It is not determined that there is interference.

  FIG. 12 is a diagram illustrating another case where the position prediction error in the traveling direction of the two satellites (satellite A and satellite B) is large and satisfies the conditional expression 2. In FIG. 12, the prediction error of the traveling direction of the satellite B is within a predetermined threshold θc from the line segment 50 (a) from the end point of ρa1 to the ending point of ρa2 representing the range of the prediction error of the traveling direction of the satellite A. There is a line segment 50 (b) representing the range from the end point of ρb1 to the end point of ρb2. That is, when the ground station 1 communicates with the satellite A, the satellite B may exist in a range where radio wave interference can occur. However, since none of ρb0, ρb1, and ρb2 is within the predetermined threshold θc from each of ρa0, ρa1, and ρa2, in the determination using Equation 9 in <Case 1> above, the radio wave It is not determined that there is interference.

  In <Case 2>, the presence / absence of radio wave interference is determined when Conditional Expression 2 including the situation shown in FIGS. 11 and 12 illustrated above is satisfied. First, “a line segment 50 from the end point of the line-of-sight unit vector ρ1 representing the range of the prediction error in the advancing direction in the AZ-EL coordinates to the end point of ρ2 is two vectors of ρ1 and ρ2 in the section of the line segment 50. It is assumed that it will not deviate significantly from the plane that is formed. Thereby, the range of the prediction error of the line-of-sight direction vector for determining the presence or absence of radio wave interference is approximated by the line segment 50 in FIG. This is a reasonable approximation for medium altitude satellite 2. In order to identify an invalid case, a warning (warning) may be output if the altitude of the satellite 2 is larger than a predetermined determination value (for example, a value close to the altitude of the geostationary satellite).

  When the range of the prediction error in the traveling direction of the satellite 2 is approximated as a line segment 50 in FIG. 13, the radio wave interference area 51 of the satellite A at time T according to the embodiment is as shown by a thick rectangular frame in FIG. I can express. In the embodiment, the radio wave interference area 51 is an area where it is determined that there is a possibility of radio wave interference when another satellite 2 is within the area. The interference area 51 takes an angle of a predetermined threshold value θc from the line segment 50 representing the range of prediction error in the traveling direction of the satellite 2 along the traveling direction of the satellite 2, and also in the cross track direction of the satellite 2. This is a range in which the angle of the threshold value θc is taken on both sides. Note that the cross-track direction is, for example, the right hand with respect to the Z axis and the X axis when the direction of the vector ρ1 is the X axis and the direction perpendicular to the plane formed by the vectors ρ1 and ρ2 is the Z axis. This is the direction of the Y axis defined by the system. The four corner direction vectors P1, P2, Q1, and Q2 of the interference region 51 can be calculated from the above-described ρa1, ρa2, and the predetermined threshold value θc by using vector calculation and matrix calculation. It will be described later.

  In the determination of the presence or absence of radio wave interference according to the embodiment, when <Case 2> is satisfied, the line-of-sight direction unit vector of the satellite B with respect to the interference area 51 of the satellite A is as follows (determination condition 1) If there is any positional relationship of condition 2), it is determined that there is “interference”.

(Determination condition 1) Of the vectors to the points constituting the four corners of the interference area 51, either the line segment 60 formed by the end point of the vector (P1, P2) or the line segment 61 formed by the end point of the vector (Q1, Q2) The line segment 50 formed by the end points of the line-of-sight direction unit vectors (ρb1, ρb2) intersects.
(Determination condition 2) One or more end points of the line-of-sight direction unit vectors (ρb0, ρb1, ρb2) of the satellite B are included in the interference area 51 of the satellite A.

  When the above determination (determination condition 1) is determined to be YES, for example, the situation shown in FIG. 15 is included. FIG. 15 is a diagram illustrating an example in which the above determination (determination condition 1) is executed for the situation illustrated in FIG. As shown in the figure, a line segment 50 representing the range of the prediction error in the traveling direction of the satellite B indicated by the line-of-sight direction unit vector (ρb0, ρb1, ρb2) of the satellite B is the end point of the vector (P1, P2). Crosses with line segment 60. A line segment 50 representing the range of the prediction error in the traveling direction of the line-of-sight direction vector of the satellite B intersects with the line segment 61 formed by the end points of the vectors (Q1, Q2). Therefore, the determination of (determination condition 1) is YES, and it can be determined that there is “interference”.

  Further, when the above determination (determination condition 2) is determined to be YES, for example, a situation as shown in FIG. 16 is included. FIG. 16 is a diagram illustrating an example in which the above determination (determination condition 2) is performed for the situation illustrated in FIG. As shown in the drawing, the line-of-sight unit vectors (ρb0, ρb1, ρb2) of the satellite B exist in the interference region 51 formed by the end points of the vectors (P1, P2, Q1, Q2). Therefore, the above determination (determination condition 2) is YES, and it can be determined that there is “interference”.

  As described above, even when either (θa1, θa2) of satellite A or (θb1, θb2) of satellite B is larger than the predetermined threshold θc of the scissor angle, the above (determination condition 1) and (determination) The presence or absence of radio wave interference can be determined by the determination of condition 2). Hereinafter, the determinations of (determination condition 1) and (determination condition 2) will be described in more detail.

<Calculation of direction vector of interference area 51>
The calculation of the direction vectors P1, P2, Q1, and Q2 at the four corners of the interference area 51 shown in FIGS. 14 to 16 will be described. First, a coordinate system XYZs is defined as shown in FIG. 17 using line-of-sight direction unit vectors ρ1 and ρ2. In the coordinate system XYZs, the three axes are determined as follows.
-Xs direction: ρ1 direction-Zs direction: perpendicular to the plane formed by ρ1 and ρ2-Ys direction: Defined in the right-handed system with respect to Zs and Xs

In this case, unit vectors XS, ZS, and YS in each axial direction are calculated as follows.
XS = ρ1
ZS = ρ1 × ρ2
YS = ZS × XS

  When the line-of-sight direction unit vector ρ1 is converted into XYZs coordinates, the corner vector P1 of the interference region 51 described above can be obtained by rotating ρ1 around the Y axis by −θc and then around the Z axis by −θc. it can. In addition, the positive and negative of the rotation direction, when the direction in which the right screw advances is matched to the direction of each axis, the rotation direction of the shaft that matches the rotation direction of the right screw is the positive rotation direction, and the opposite rotation direction is negative. The direction of rotation. The vector Q1 can be obtained by rotating around the Y axis by + θc, and then rotating around the Z axis by −θc. Similarly, the vectors P2 and Q2 can be obtained by defining the coordinate system with the line-of-sight vector ρ2 as the Xs direction. The relationship between the coordinate system defined by the line-of-sight direction unit vector and the rotation direction of the vector is summarized as follows.

The calculation of each of these direction vectors: P1, P2, Q1, and Q2 is shown below.
First, ZS is calculated in advance.
ZS = ρ1 × ρ2 Equation 10

Also, let Ry (θ), which is a vector rotation matrix around the Y axis, be as follows.

Let Rz (θ), which is a vector rotation matrix around the Z axis, be as follows.

Let Φ be the transformation matrix from equatorial plane coordinates to XYZs coordinates.

In this case, the direction vector: P1 can be obtained as follows.
(A) Vector P1
XS = ρ1 Formula 11 (Formula 11-1)
YS = ZS × XS Formula 11 (Formula 11-2)
P1 = Rz (−θc) · Ry (−θc) · Φ · ρ1 Formula 11 (Formula 11-3)
The direction vector: P2 can be obtained as follows.
(B) Vector P2
XS = ρ2 Formula 12 (Formula 12-1)
YS = ZS × XS Formula 12 (Formula 12-2)
P2 = Rz (+ θc) · Ry (−θc) · Φ · ρ2 Formula 12 (Formula 12-3)
The direction vector: Q1 can be obtained as follows.
(C) Vector Q1
XS = ρ1 Formula 13 (Formula 13-1)
YS = ZS × XS Formula 13 (Formula 13-2)
Q1 = Rz (−θc) · Ry (+ θc) · Φ · ρ1 Formula 13 (Formula 13-3)
The direction vector: Q2 can be obtained as follows.
(D) Vector Q2
XS = ρ2 Formula 14 (Formula 14-1)
YS = ZS × XS Formula 14 (Formula 14-2)
Q2 = Rz (+ θc) · Ry (+ θc) · Φ · ρ2 Formula 14 (Formula 14-3)

  As described above, the direction vectors P1, P2, Q1, and Q2 at the four corners of the interference region 51 can be obtained.

<Intersection determination of line segment formed by interference area and line-of-sight direction vector>
Subsequently, the determination of (determination condition 1) will be described. As an example, in the following description, the line segment 60 and the line segment 61 of the interference area 51 set for the line segment 50 representing the range of the prediction error of the traveling direction of the line-of-sight direction vector of the satellite A, The determination of the intersection of the line segments 50 representing the range of the prediction error will be described. FIG. 18 is a diagram for explaining the intersection determination of the line segment formed by the two unit vector pairs described below.

[Judgment of intersection of line segment 60 formed by vectors P1 and P2 of satellite A and line segment 50 of satellite B]
The intersection of the line segment 60 formed by the vectors P1 and P2 in the interference area 51 and the line segment 50 formed by the vector (ρb1, ρb2) representing the range of the prediction error in the traveling direction of the satellite B can be calculated as follows. First, for the convenience of explanation, the line-of-sight vectors (ρb1, ρb2) of the satellite B are set as (V1, V2), respectively. Also, the direction vectors (P1, P2) are set as (U1, U2), respectively. A normal vector H1 of the surface formed by the vectors (U1, U2) is obtained.
H1 = U1 × U2 Expression 15

A normal vector H2 of the surface formed by the vectors (V1, V2) is obtained.
H2 = V1 × V2 Expression 16

The intersecting direction vectors W1 and W2 of the two surfaces are obtained as follows.
W1 = H1 × H2 Expression 17
W2 = −W1 Expression 18

  Here, assuming that the angle formed by (U1, U2) is α and the angle formed by (V1, V2) is β, it is assumed that α <180 deg and β <180 deg. This is a reasonable premise as long as an area of EL ≧ 0 deg from the ground station 1 is targeted. In the region where EL <0 deg from the ground station 1, the ground station 1 may be excluded from the determination because it is difficult to communicate directly with the satellite 2 using radio waves.

Subsequently, the following Ca and Cb are defined.
Ca = U1 · U2 Formula 19 (Formula 19-1)
Cb = V1 · V2 Expression 19 (Expression 19-2)

In this case, when the following condition is satisfied, the line segments (thick lines in FIG. 18) of the two vector pairs (U1, U2) (V1, V2) intersect.

[Judgment of intersection of line segment 61 formed by satellite A vectors Q1 and Q2 and line segment 50 of satellite B]
Subsequently, as in the case of the vectors P1 and P2 of the satellite A, the line segment 61 formed by the vectors Q1 and Q2 of the interference region 51 and vectors (ρb1 and ρb2) representing the range of the prediction error in the traveling direction of the satellite B are obtained. The intersection with the line segment 50 is calculated. After setting the direction vectors (Q1, Q2) as (U1, U2), respectively, the above Expressions 15 to 19 are calculated, and Expression 20 is determined.

  Then, the intersection determination of the line segment 50 of the satellite B and the line segment 60 formed by the vectors P1 and P2 of the satellite A or the line segment 61 formed by the vectors Q1 and Q2 of the satellite A is performed by the expression 20 If any of the intersection determinations is YES and intersect, it is determined that there is “interference”.

  Based on the above determination, the line segment 60 formed by the direction vectors P1 and P2 or the line segment 61 formed by Q1 and Q2 among the direction vectors at the four corners of the interference area 51 of the satellite A and the line-of-sight vector (ρb1, ρb2 of the satellite B) It can be determined whether or not the line segment 50 formed by) intersects. Therefore, it is possible to detect a state in which radio wave interference may occur, including the case illustrated in FIG.

<Containment condition of gaze direction vector in interference area>
Described below is the determination of whether or not the interference direction 51 of the satellite A includes the line-of-sight direction vectors (ρb0, ρb1, ρb2) of the satellite B. FIGS. 19 and 20 are diagrams for explaining whether or not the interference region 51 of the satellite A includes the line-of-sight direction vectors (ρb0, ρb1, and ρb2) of the satellite B.

First, for convenience of explanation, the direction vectors (P1, Q1, Q2, P2) of the interference region 51 are respectively set as (U1, U2, U3, U4). Then, normal vectors of the plane formed by the two vectors (U1, U2) (U2, U3) (U3, U4) (U4, U1) are obtained.
H12 = U1 × U2 Expression 21 (Expression 21-1)
H23 = U2 × U3 Expression 21 (Expression 21-2)
H34 = U3 × U4 Formula 21 (Formula 21-3)
H41 = U4 × U1 Formula 21 (Formula 21-4)

[Determining whether or not the gaze direction vector: ρb0 is included in the interference area]
The line-of-sight vector of satellite B: ρb0 is set as U. In this case, as shown in FIGS. 19 and 20, when the following expression 22 is satisfied, it can be determined that the vector U (ie, ρb0) exists in the interference region 51.

[Determining whether or not the gaze direction vector: ρb1 is included in the interference area]
Similarly, the line-of-sight vector ρb1 of the satellite B is set as U. In this case, when Expression 22 is satisfied, it can be determined that the vector U (that is, ρb1) exists in the interference region 51.

[Determining whether or not the gaze direction vector: ρb2 is included in the interference area]
Similarly, the line-of-sight vector ρb2 of the satellite B is set as U. In this case, when Expression 22 is satisfied, it can be determined that the vector U (that is, ρb2) exists in the interference region 51.

  Then, in the determination of (Case 2) in <Case 2>, if any of the determinations of Expression 22 performed for ρb0, ρb1, and ρb2 described above is satisfied, it is determined that there is interference.

  Based on the determination described above, for example, it is possible to determine whether or not the line-of-sight vector (ρb0, ρb1, ρb2) of the satellite B exists in the interference region 51 of the satellite A. Therefore, for example, it is possible to detect a state in which radio wave interference including the case illustrated in FIG. 16 may occur.

  As a result of the determinations of <Case 1> and <Case 2> described above in (Determination condition 1) and (Determination condition 2), satellite A and satellite B cause radio wave interference when viewed from the ground station 1 at a certain time T. It is possible to determine whether or not the positional relationship is awake. In this method of determining the presence or absence of radio wave interference, if there is a satellite ephemeris 700 of the orbit of satellite 2 predicted without considering the error, it represents the range of prediction error in the traveling direction at the time at which it is desired to investigate the presence or absence of radio wave interference. A gaze direction vector can be obtained. In other words, the prediction error in the traveling direction of the satellite 2 is converted into a time error, and an error indicating the spread of the prediction error in the traveling direction of the satellite 2 is taken into account by reading the position vector shifted by the time error from the satellite orbital calendar 700. Gaze direction vectors: ρ1 and ρ2 can be obtained. The presence or absence of radio wave interference can be determined based on the line-of-sight direction vectors ρ1 and ρ2 in consideration of the obtained error.

  Furthermore, the predetermined threshold value θc has already been considered with respect to the prediction error in the traveling direction by the obtained line-of-sight direction vectors: ρ1 and ρ2, and therefore, the prediction error in the traveling direction illustrated with reference to FIG. It is not necessary to add θm including the minute as a margin. For example, the predetermined threshold θc used for determining the presence or absence of radio wave interference corresponds to the antenna beam width used by the ground station 1 in communication with the satellite A or the beam width of the antenna, for example, a prediction error in the cross track direction. A value obtained by adding a margin or the like to be added can be used. Therefore, for example, the predetermined threshold value θc can be set to a much narrower value than the method described with reference to FIG. Accordingly, it is possible to suppress the excessive determination of the occurrence of interference while performing the interference determination that appropriately considers the prediction error of the position in the traveling direction of the satellite 2 that cannot be ignored in the prediction of the radio wave interference of the intermediate altitude satellite 2. it can.

  Furthermore, as described above, in the method for determining the presence or absence of radio wave interference according to the embodiment, the position error is converted into a time error, and the position vector of the satellite 2 read out from the predicted satellite ephemeris 700 without considering the error. Is used to determine radio wave interference. Therefore, it is not necessary to perform trajectory prediction in consideration of errors using, for example, error covariance having a high calculation load.

  Next, the information processing apparatus 100 according to the embodiment that implements the radio wave interference determination method described above will be described. FIG. 21 is a diagram illustrating a functional block configuration of the information processing apparatus 100 according to the embodiment. The information processing apparatus 100 includes a control unit 2100 and a storage unit 2110, for example. The control unit 2100 includes functional units 2101 such as a conversion unit 2111, an acquisition unit 2112, and a determination unit 2113, for example. The storage unit 2110 of the information processing apparatus 100 may store a program 2120 and a satellite orbit calendar 700, for example. Furthermore, the storage unit 2110 of the information processing apparatus 100 may store other information such as the parameter of Expression 3 described above and the predetermined threshold value θc, for example. The control unit 2100 of the information processing apparatus 100 functions as a functional unit 2101 such as a conversion unit 2111, an acquisition unit 2112, and a determination unit 2113 by reading and executing the program 2120. Details of each of these functional units 2101 will be described later.

  22A and 22B are diagrams illustrating a radio wave interference determination process at time T executed by the control unit 2100 of the information processing apparatus 100. The operation flow of the radio wave interference determination process in FIGS. 22A and 22B is implemented, for example, when the control unit 2100 of the information processing apparatus 100 reads and executes the program 2120 stored in the storage unit 2110. In one embodiment, the radio wave interference determination process starts when an instruction to execute the radio wave interference determination process is input to the information processing apparatus 100.

  Note that the control unit 2100 of the information processing apparatus 100 can acquire a position vector and a velocity vector that represent the position and velocity of the orbit of the satellite A from the satellite orbit calendar 700 for the satellite A that has been created in advance. And Similarly, the control unit 2100 of the information processing apparatus 100 can acquire a position vector and a velocity vector representing the position and velocity of the orbit of the satellite B from the satellite orbit calendar 700 for the satellite B that has been created in advance. It shall be. The satellite orbit calendar 700 may be stored in the storage unit 2110 of the information processing apparatus 100 in one embodiment. In another embodiment, the control unit 2100 of the information processing apparatus 100 may acquire the position vector and velocity vector of the satellite A and satellite B from the satellite orbit calendar 700 held by another information processing apparatus.

  In step S2201, the control unit 2100 of the information processing apparatus 100 sets a prediction error ΔL in the traveling direction with respect to the predicted positions of the two satellites 2 that the user wants to check whether radio waves interfere with communication with the ground station 1 at a predetermined time T. calculate. Note that the two satellites 2 that are to be examined whether or not radio waves interfere with each other are assumed to be satellite A and satellite B, for example.

  The prediction error ΔL can be calculated by, for example, Equation 3 described above. Note that the parameters (δL, δa, Ta, δadot, Tad, and n) in Equation 3 are values that can be calculated in advance, and these values are calculated in advance for each of satellite A and satellite B, for example. And may be stored in the storage unit 2110. Alternatively, in another embodiment, a value obtained by causing the control unit 2100 of the information processing apparatus 100 to calculate when used for the calculation may be used. The control unit 2100 of the information processing apparatus 100 executes the calculation of Equation 3 for each of the satellite A and the satellite B, and acquires ΔL (ΔLa) for the satellite A and ΔL (ΔLb) for the satellite B.

  Subsequently, the control unit 2100 of the information processing apparatus 100 calculates the above equation 4 using the value of ΔLa of the satellite A and the velocity vector at the time T read from the satellite ephemeris 700 of the satellite A, and the satellite A The position prediction error: ΔLa is converted into a time error: ΔTa. Similarly, using the value of ΔLb of satellite B and the velocity vector at time T read from satellite B's satellite ephemeris 700, Equation 4 above is calculated, and the prediction error of the position of satellite B: ΔLa is calculated as time. Error: Converted to ΔTb.

  In step S2202, the control unit 2100 performs the calculation of Expression 5 using a predetermined time T at which the presence or absence of radio wave interference is to be investigated and the calculated ΔTa of the satellite A, and the time when the satellite A has returned ΔTa time from the time T. Ta1 and time Ta2 advanced by ΔTa time from time T are calculated. Similarly, with respect to the satellite B, the calculation of Expression 5 is performed using the predetermined time T at which the presence / absence of radio wave interference is to be investigated and the calculated ΔTb of the satellite B, and the satellite B has returned ΔTb time from the time T. Time Tb1 and time Tb2 advanced by ΔTb time from time T are calculated.

  When the time Ta1 calculated for the satellite A is smaller than Tas, the calculated value of Ta1 is replaced with Tas. When the calculated time Ta2 is larger than Tae, the calculated value of Ta2 is replaced with Tae. Similarly, when the time Tb1 calculated for the satellite B is smaller than Tbs, the calculated value of Tb1 is replaced with Tbs. If the calculated time Tb2 is greater than Tbe, the calculated value of Tb2 is replaced with Tbe. Here, Tas may be the earliest time at which the ground station 1 can establish communication with the satellite A in the orbit of the satellite A at the time T, for example. Tae may be the latest time at which the ground station 1 can establish communication with the satellite A in the orbit of the satellite A at the time T, for example. Similarly, Tbs may be the earliest time at which the ground station 1 can establish communication with the satellite B in the orbit of the satellite B at the time T, for example. Tbe may be the latest time at which the ground station 1 can establish communication with the satellite B in the orbit of the satellite B at the time T, for example.

  The above replacement is, for example, for the following reason. For example, the ground station 1 cannot communicate with the trajectory of the satellite A during the period from Ta1 to Ta2 calculated for the satellite A (that is, corresponding to the line segment 50 indicating the range of the prediction error in the traveling direction). The position of satellite A may be included. For example, when the satellite A is below the horizon when viewed from the ground station 1 (the EL from the ground station 1 is less than <0 deg), the ground station 1 cannot establish direct communication with the satellite A. . Therefore, it is not necessary to determine the presence or absence of radio wave interference at the position of satellite A. Therefore, when the satellite A is in a position where communication cannot be established when viewed from the ground station 1 at the time Ta1, the value of the time Ta1 is set, and the ground station 1 establishes communication with the satellite A at the orbit around the time T. The earliest possible time Tas is replaced. If the satellite A is in a position where communication cannot be established when viewed from the ground station 1 at the time Ta2, the value of the time Ta2 is set, and the ground station 1 establishes communication with the satellite A at the orbit around the time T. It is replaced with the latest time Tae that can be performed. The same applies to the replacement of Tb1 and Tbs and the replacement of Tb2 and Tbe of the satellite B. The time Tas and the time Tae are values that can be calculated in advance by the control unit 2100 based on the satellite orbit calendar 700 of the satellite A, for example. Similarly, the time Tbs and the time Tbe are values that can be calculated in advance by the control unit 2100 based on the satellite orbit calendar 700 of the satellite B. For example, the control unit 2100 may read values of time Tas, time Tae, time Tbs, and time Tbe that are calculated in advance and stored in the storage unit 2110, and may use them in step S2202.

  In step S2203, the control unit 2100 reads the position vector Ra0 of the satellite A at time T, the position vector Ra1 of the satellite A at time Ta1, and the position vector Ra2 of the satellite A at time Ta2 from the satellite ephemeris 700 of the satellite A. Further, the control unit 2100 reads the position vector Rb0 of the satellite B at the time T, the position vector Rb1 of the satellite B at the time Tb1, and the position vector Rb2 of the satellite B at the time Tb2 from the satellite ephemeris 700 of the satellite B.

    In the subsequent processes from step S2204 to step S2206, the control unit 2100 executes the radio wave interference determination process in the case of <Case 1> described above. In step S2204, control unit 2100 calculates position vector S of ground station 1 at time T. Subsequently, the control unit 2100 obtains the line-of-sight direction unit vectors (ρa0, ρa1, ρa2) of the satellite A from the position vector S of the ground station 1 and the position vector of the satellite A acquired in step S2203 according to the above-described equation 6. calculate. Further, the control unit 2100 calculates the line-of-sight direction unit vector (ρb0, ρb1, ρb2) of the satellite B from the position vector S of the ground station 1 and the position vector of the satellite B acquired in step S2203 by the above-described equation 6. To do. Further, the control unit 2100 calculates the scissors angles of the line-of-sight unit vectors (ρa0, ρa1, ρa2) of the satellite A and the line-of-sight unit vectors (ρb0, ρb1, ρb2) of the satellite B by the above equation 8.

  In step S <b> 2205, the control unit 2100 determines any one of the scissors angles (θ00, θ01, θ02, θ10, θ11, θ12, θ20, θ21, and θ22) calculated by Equation 8 based on the determination of Equation 9 above. It is determined whether or not there is a predetermined threshold value θc or less. Note that the value of the predetermined threshold θc may be stored in the storage unit 2110 in advance, for example. If there is a scissor angle that is equal to or smaller than the predetermined threshold value θc (YES in step S2205), the flow proceeds to step S2223, for example, a determination result that there is radio wave interference is output, and this operation flow ends. On the other hand, when all the scissors angles obtained by the above equation 8 are larger than the predetermined threshold value θc (NO in step S2205), the flow proceeds to step S2206.

  In step S2206, the control unit 2100 obtains the angle θa1 formed by ρa0 and ρa1 and the angle θa2 formed by ρa0 and ρa2 with respect to the satellite A by the above-described Expression 7. Also for the satellite B, the angle θb1 formed by ρb0 and ρb1 and the angle θb2 formed by ρb0 and ρb2 are obtained by the above equation 7, respectively. Then, it is determined whether any one of θa1, θa2, θb1, and θb2 is larger than a predetermined threshold value θc. If none of θa1, θa2, θb1, and θb2 is greater than the predetermined threshold value θc (NO in step S2206), the flow proceeds to step S2222, and for example, a determination result of no radio wave interference is output. This operation flow ends. On the other hand, if any one of θa1, θa2, θb1, and θb2 is larger than the predetermined threshold value θc (YES in step S2206), the flow proceeds to step S2207.

  In the subsequent processes from step S2207 to step S2221, the control unit 2100 executes the process of determining the possibility of radio wave interference described in <Case 2>. In step S2207, the control unit 2100 determines whether or not the magnitude of the position vector R0 of the satellite A at time T is larger than a predetermined threshold value Rchk. Further, the control unit 2100 determines whether or not the magnitude of the position vector R0 of the satellite B at time T is larger than a predetermined threshold value Rchk. As the predetermined threshold value Rchk, for example, an altitude close to the stationary altitude of the satellite can be used, and for example, 30,000 kilometers or 40,000 kilometers may be used. If either the magnitude of the position vector Ra0 of the satellite A or the magnitude of the position vector Rb0 of the satellite B is larger than the predetermined threshold Rchk in step S2207 (YES in step S2207), the flow proceeds to step S2208. In step S2208, the control unit 2100 outputs a warning (warning), and the flow proceeds to step S2209. On the other hand, if both the magnitude of the position vector Ra0 of the satellite A and the magnitude of the position vector Rb0 of the satellite B are equal to or smaller than the predetermined threshold Rchk in step S2207 (NO in step S2207), the flow proceeds to step S2209. move on.

  Note that the processing from step S2207 to step S2208 is processing for detecting a case where the satellite A and the satellite B are at an altitude close to a geostationary orbit. For example, when the satellite 2 is at an altitude close to a geosynchronous orbit, the speed of the satellite 2 viewed from the ground station 1 becomes slow, and as a result, the locus of the satellite 2 in the AZ-EL coordinates due to the influence of the rotation of the earth, for example, The trajectory deviates greatly from the straight line. As a result, the spread due to the error from ρ1 to ρ2 in the AZ-EL coordinates described in the above <Case 2> greatly deviates from the plane formed by these two vectors in the section of the line-of-sight unit vector (ρ1, ρ2). There is a possibility that the premise that there is nothing is not true. For this reason, when either of the position vectors Ra0 and Rb0 of the satellite A or the satellite B is larger than a predetermined threshold value Rchk, a warning is output, and for example, the user is alerted.

  In step S2209, the control unit 2100 calculates a direction vector (for example, direction vectors: P1, P2, Q1, and Q2) to the points constituting the four corners of the interference region 51 using the above formulas 10 to 14. . In the following description, it is assumed that the arrangement of the direction vectors P1, P2, Q1, and Q2 in the interference region 51 is the arrangement illustrated in FIGS. 14 to 16 with respect to the traveling direction of the satellite A. Further, in the following description, of the satellite A and the satellite B, the position where the line segment 50 indicating the range of the prediction error in the traveling direction of the satellite B causes the radio wave interference with respect to the interference area 51 calculated for the satellite A. The case where it is determined whether or not it exists is explained as an example. However, in another example, with respect to the interference region 51 calculated for the satellite B, it is determined whether or not the line segment 50 representing the range of the prediction error in the traveling direction of the satellite A exists at a position causing the radio wave interference. May be.

  In subsequent processing from step S2210 to step S2214, control unit 2100 executes processing for determining the possibility of radio wave interference described in (Criteria 1) of <Case 2> above. In step S2210, control unit 2100 places line-of-sight direction unit vector ρb1 of satellite B as vector V1. The line-of-sight direction unit vector ρb2 of the satellite B is set as a vector V2. In step S2211, the control unit 2100 determines the direction vector P1 among the direction vectors P1, P2, Q1, and Q2 from the ground station 1 to the points that form the four corners of the interference area 51 of the satellite A, and the vector U1. Put. Control unit 2100 places direction vector P2 as vector U2. Then, the control unit 2100 calculates Expression 19 from Expression 15 above.

  In step S2212, the control unit 2100 determines whether or not either of the above formulas 20-1 or 20-2 is satisfied. If it is determined that either of the above formulas 20-1 or 20-2 is satisfied (YES in step S2212), the flow proceeds to step S2223, and for example, a determination result indicating that there is radio wave interference is output. This operation flow ends. If YES is determined in step S2212, the prediction error of the traveling direction formed by the line segment 60 formed by the direction vectors P1 and P2 and the line-of-sight vector (ρb1, ρb2) of the satellite B is exemplified as illustrated in FIG. It shows that the line segment 50 representing the range intersects. In this case, since the satellite B exists at a position where radio wave interference may occur in the communication between the ground station 1 and the satellite A, the determination result that there is radio wave interference is output in step S2223. On the other hand, when it is determined that neither of the above formula 20-1 or formula 20-2 is satisfied (step S2212 is NO), the flow proceeds to step S2213.

  In the subsequent processes from step S2213 to step S2214, the determination performed for the line segment 60 formed by the direction vectors P1 and P2 in steps S2210 to S2212 is performed for the line segment 61 formed by the direction vectors Q1 and Q2. It is. In step S2213, the control unit 2100 determines the direction vector Q1 among the direction vectors P1, P2, Q1, and Q2 from the ground station 1 to the points that form the four corners of the interference area 51 of the satellite A, and the vector U1. Put. Control unit 2100 places direction vector Q2 as vector U2. Then, the control unit 2100 calculates Expression 19 from Expression 15 above.

  In step S2214, the control unit 2100 determines whether either of the above formula 20-1 or 20-2 is satisfied. If it is determined that either of the above formulas 20-1 or 20-2 is satisfied (step S2214 is YES), the flow proceeds to step S2223, and for example, a determination result with radio wave interference is output. This operation flow ends. If YES is determined in step S2214, as illustrated in FIG. 15, the prediction error in the traveling direction formed by the line segment 61 formed by the direction vectors Q1 and Q2 and the line-of-sight vector (ρb1, ρb2) of the satellite B is illustrated. It shows that the line segment 50 representing the range intersects. In this case, since the satellite B exists at a position where radio wave interference may occur in the communication between the ground station 1 and the satellite A, the determination result that there is radio wave interference is output in step S2223. On the other hand, when it is determined that none of the above formula 20-1 or 20-2 is satisfied (step S2214 is NO), the flow proceeds to step S2215.

  In subsequent processing from step S2215 to step S2221, control unit 2100 executes processing for determining the possibility of radio wave interference described in (Criteria 2) of <Case 2>. In step S2215, the control unit 2100 sets the direction vector P1 as U1 among the direction vectors P1, P2, Q1, and Q2 from the ground station 1 to the points constituting the four corners of the interference area 51 of the satellite A. Put. The direction vector Q1 is set as U2. The direction vector Q2 is set as U3. The direction vector P2 is set as U4. And the said Formula 21 is calculated.

  In step S2216, the control unit 2100 places the line-of-sight direction unit vector: ρb0 of the satellite B as the vector U. In step S2217, the control unit 2100 determines whether or not the expression 22 is satisfied. If the above expression 22 is satisfied (YES in step S2217), the flow proceeds to step S2223, for example, a determination result that there is radio wave interference is output, and this operation flow ends. If YES is determined in step S <b> 2217, for example, as illustrated in FIG. 16, it indicates that the line-of-sight vector ρb0 of the satellite B exists in the interference area 51 of the satellite A. In this case, since the satellite B exists at a position where radio wave interference may occur in the communication between the ground station 1 and the satellite A, the determination result that there is radio wave interference is output in step S2223. On the other hand, if it is determined that the above expression 22 is not satisfied (step S2217 is NO), the flow proceeds to step S2218.

  The subsequent processing from step S2218 to step S2219 is processing for executing the determination made on the line-of-sight direction unit vector: ρb0 of the satellite B in steps S2215 to S2217 on the line-of-sight direction unit vector: ρb1. In step S2218, the control unit 2100 places the line-of-sight direction unit vector: ρb1 of the satellite B as the vector U. In step S2219, the control unit 2100 determines whether or not the expression 22 is satisfied. If the above expression 22 is satisfied (YES in step S2219), the flow proceeds to step S2223, for example, a determination result that there is radio wave interference is output, and this operation flow ends. If YES is determined in step S2219, for example, the line-of-sight vector ρb1 of the satellite B exists in the interference region 51 of the satellite A as illustrated in FIG. In this case, since the satellite B exists at a position where radio wave interference may occur in the communication between the ground station 1 and the satellite A, the determination result that there is radio wave interference is output in step S2223. On the other hand, when it determines with not satisfy | filling the said Formula 22 (step S2219 is NO), a flow progresses to step S2220.

  The subsequent processing from step S2220 to step S2221 is processing for executing the determination performed on the line-of-sight direction unit vector: ρb0 of the satellite B in steps S2215 to S2217 on the line-of-sight direction unit vector: ρb2. In step S2220, control unit 2100 places line-of-sight unit vector ρb2 of satellite B as vector U. In step S2221, the control unit 2100 determines whether or not the expression 22 is satisfied. If the above equation 22 is satisfied (YES in step S2221), the flow proceeds to step S2223, for example, a determination result that there is radio wave interference is output, and this operation flow ends. If YES is determined in step S <b> 2221, for example, as illustrated in FIG. 16, the line-of-sight vector ρb <b> 2 of the satellite B is present in the interference area 51 of the satellite A. In this case, since the satellite B exists at a position where radio wave interference may occur in the communication between the ground station 1 and the satellite A, the determination result that there is radio wave interference is output in step S2223. On the other hand, when it determines with not satisfy | filling the said Formula 22 (step S2221 is NO), a flow progresses to step S2222.

  In step S2222, for example, the control unit 2100 outputs a determination result indicating that there is no radio wave interference, and the operation flow ends. In step S2222, in the processes from step S2205 to step S2221, it is not determined that there is radio wave interference in any of the determinations of <Case 1> and <Case 2> in (Determination condition 1) and (Determination condition 2). The judgment result of none is output.

  22A and 22B, the control unit 2100 of the information processing apparatus 100 determines whether the satellite A and the satellite B have a positional relationship that causes radio wave interference when viewed from the ground station 1 at a predetermined time T. Can be determined. In this method of determining the presence or absence of radio wave interference, if there is a satellite ephemeris 700 of the orbit of satellite 2 predicted without considering the error, it represents the range of prediction error in the traveling direction at the time at which it is desired to investigate the presence or absence of radio wave interference. A gaze direction vector can be obtained. In other words, the prediction error in the traveling direction of the satellite 2 is converted into a time error, and an error indicating the spread of the prediction error in the traveling direction of the satellite 2 is taken into account by reading the position vector shifted by the time error from the satellite orbital calendar 700. Gaze direction vectors: ρ1 and ρ2 can be obtained. The presence or absence of radio wave interference can be determined based on the line-of-sight direction vectors ρ1 and ρ2 in consideration of the obtained error.

  Furthermore, the predetermined threshold value θc has already been considered with respect to the prediction error in the traveling direction by the obtained line-of-sight direction vectors: ρ1 and ρ2, and therefore, the prediction error in the traveling direction illustrated with reference to FIG. It is not necessary to add θm including the minute as a margin. For example, the predetermined threshold θc used for determining the presence or absence of radio wave interference corresponds to the antenna beam width used by the ground station 1 in communication with the satellite A or the beam width of the antenna, for example, a prediction error in the cross track direction. A value obtained by adding a margin or the like to be added can be used. Therefore, for example, the predetermined threshold value θc can be set to a much narrower value than the method described with reference to FIG. Accordingly, it is possible to suppress the excessive determination of the occurrence of interference while performing the interference determination that appropriately considers the prediction error of the position in the traveling direction of the satellite 2 that cannot be ignored in the prediction of the radio wave interference of the intermediate altitude satellite 2. it can.

  Furthermore, as described above, in the method for determining the presence or absence of radio wave interference according to the embodiment, the position error is converted into a time error, and the position vector of the satellite 2 read out from the predicted satellite ephemeris 700 without considering the error. Is used to determine radio wave interference. Therefore, this determination can be performed by a simple vector operation, and the load on the calculation can be reduced as compared with the case where error covariance or the like is used for prediction of the orbit of the satellite 2, for example. Therefore, for example, the determination method according to the embodiment is suitable for determining the presence or absence of radio wave interference between satellites in which radio wave interference frequently occurs, such as a medium altitude satellite.

  In the above-described embodiment, a technique that can easily reflect the prediction error in the traveling direction of the satellite is applied to the determination of the presence or absence of radio wave interference that may occur when two satellites are seen in the close direction from the ground station. The explanation is given by taking the case of doing as an example. However, the embodiment is not limited to this. For example, the determination method according to the embodiment may be used in the tracking control field of artificial satellites, the observation field of unknown space objects, and the like.

  In the operation flow of FIG. 22 described above, the control unit 300 of the information processing apparatus 1 functions as, for example, the conversion unit 2111 in the processing from step S2201 to step S2202. In the process of step S2203, the control unit 300 of the information processing apparatus 1 functions as, for example, the acquisition unit 2112. In the processing from step S2204 to step S2223, the control unit 300 of the information processing apparatus 1 functions as the determination unit 2113, for example.

  FIG. 23 is a diagram illustrating a hardware configuration of a computer 2300 for realizing the information processing apparatus 100 according to the embodiment. The hardware configuration for realizing the information processing apparatus 100 in FIG. 23 includes, for example, a processor 2301, a memory 2302, a storage device 2303, a reading device 2304, a communication interface 2306, and an input / output interface 2307. Note that the processor 2301, the memory 2302, the storage device 2303, the reading device 2304, the communication interface 2306, and the input / output interface 2307 are connected to each other via a bus 2308, for example.

  The processor 2301 provides a part or all of the functions of each functional unit described above by executing a program 2120 including a program describing the procedure of the above-described operation flow using the memory 2302. For example, the control unit 2100 of the information processing apparatus 100 is, for example, a processor 2301, and the storage unit 2110 includes, for example, a memory 2302, a storage device 2303, and a removable storage medium 2305. For example, the processor 2301 of the information processing apparatus 100 functions as the conversion unit 2111, the acquisition unit 2112, and the determination unit 2113 by reading and executing the program 2120 stored in the storage device 2303. The storage device 2303 of the information processing apparatus 100 may store values such as the satellite orbital calendar 700, the parameter of the above-described Expression 3, and the predetermined threshold value θc, for example.

  The memory 2302 is a semiconductor memory, for example, and includes a RAM area and a ROM area. The storage device 2303 is, for example, a semiconductor memory such as a hard disk or a flash memory, or an external storage device.

  The reading device 2304 accesses the removable storage medium 2305 in accordance with instructions from the processor 2301. The detachable storage medium 2305 includes, for example, a semiconductor device (USB memory or the like), a medium to / from which information is input / output by magnetic action (magnetic disk or the like), a medium to / from which information is input / output by optical action (CD-ROM, For example, a DVD). The communication interface 2306 transmits and receives data via the network 2320 in accordance with instructions from the processor 2301. The input / output interface 2307 corresponds to, for example, an interface between the input device and the output device. The input device is, for example, a device such as a keyboard or a mouse that receives an instruction from the user. The output device is a display device such as a display and an audio device such as a speaker.

Each program according to the embodiment is provided to the information processing apparatus 100 in the following form, for example.
(1) Installed in advance in the storage device 2303.
(2) Provided by the removable storage medium 2305.
(3) Provided from a server 2330 such as a program server.

  In the above, several embodiments have been described. However, the embodiments are not limited to the above-described embodiments, and should be understood as including various modifications and alternatives of the above-described embodiments. For example, it will be understood that various embodiments can be embodied by modifying the components without departing from the spirit and scope thereof. It will be understood that various embodiments can be made by appropriately combining a plurality of components disclosed in the above-described embodiments. Further, various embodiments may be implemented by deleting or replacing some components from all the components shown in the embodiments, or adding some components to the components shown in the embodiments. Those skilled in the art will appreciate that this can be done.

DESCRIPTION OF SYMBOLS 1 Ground station 2 Satellite 100 Information processing apparatus 2100 Control part 2110 Storage part 2111 Conversion part 2112 Acquisition part 2113 Determination part 2300 Computer 2301 Processor 2302 Memory 2303 Storage apparatus 2304 Reading apparatus 2305 Removable storage medium 2306 Communication interface 2307 Input / output interface 2308 Bus 2320 network 2330 server

Claims (6)

A first predicted position and a first speed of the first satellite at a predetermined time are obtained from a first satellite orbital calendar including the predicted position and speed of the first satellite every moment, and the first speed is obtained. And converting the prediction error of the first predicted position in the traveling direction of the first satellite into a first time error,
A second predicted position and a second speed of the second satellite at the predetermined time are obtained from a second satellite orbital calendar including the predicted position and speed of the second satellite every moment, and the second speed is obtained. Is used to convert the prediction error of the second predicted position in the direction of travel of the second satellite into a second time error,
A predicted position before the first time error from the predetermined time and a predicted position after the first time error from the predetermined time are obtained from the first satellite orbital calendar, and the second position from the predetermined time. A predicted position before the time error and a predicted position after the second time error from the predetermined time are obtained from the second satellite orbital calendar,
A first line-of-sight vector looking at the first predicted position from a ground station, a second line-of-sight vector looking at the predicted position before the first time error, and a predicted position after the first time error The third line-of-sight vector that viewed the second predicted position, the fourth line-of-sight vector that viewed the second predicted position, the fifth line-of-sight vector viewed the predicted position before the second time error, and the second time Using the sixth line-of-sight vector that looks at the predicted position after the error, the second station is located at a position where radio wave interference may occur in the communication at the predetermined time between the ground station and the first satellite. Determine if a satellite is present,
A program that causes a computer to execute processing.   The determination includes a first angle formed by the first line-of-sight vector and the second line-of-sight vector, a second angle formed by the first line-of-sight vector and the third line-of-sight vector, When the third angle formed by the line-of-sight vector and the fifth line-of-sight vector and the fourth angle formed by the fourth line-of-sight vector and the sixth line-of-sight vector are both equal to or less than a predetermined threshold value, An angle formed by each of the first to third line-of-sight vectors and each of the fourth to sixth line-of-sight vectors is calculated, and even if one of the obtained angles is equal to or less than the predetermined threshold value The program according to claim 1, wherein the second satellite is determined to be present at a position where radio wave interference may occur.   The determination includes a first angle formed by the first line-of-sight vector and the second line-of-sight vector, a second angle formed by the first line-of-sight vector and the third line-of-sight vector, When any of the third angle formed by the line-of-sight vector and the fifth line-of-sight vector and the fourth angle formed by the fourth line-of-sight vector and the sixth line-of-sight vector is greater than a predetermined threshold. Taking the predetermined threshold range forward and backward with respect to the traveling direction of the first satellite from the line segment formed by the end point of the second line-of-sight vector and the end point of the third line-of-sight vector, and Lines of two sides along the traveling direction among the sides of the rectangular area formed by taking the predetermined threshold range in a direction perpendicular to the plane formed by the second line-of-sight vector and the third line-of-sight vector One of the minutes and the fifth line-of-sight vector It is determined whether or not a line segment formed by the end point of the sixth line-of-sight vector and the end point of the sixth line-of-sight vector intersect. If the line segment intersects, the second satellite exists at a position where radio wave interference may occur. The program according to claim 1, wherein the program is determined.   The determination includes a first angle formed by the first line-of-sight vector and the second line-of-sight vector, a second angle formed by the first line-of-sight vector and the third line-of-sight vector, When any of the third angle formed by the line-of-sight vector and the fifth line-of-sight vector and the fourth angle formed by the fourth line-of-sight vector and the sixth line-of-sight vector is greater than a predetermined threshold. Taking the predetermined threshold range forward and backward with respect to the traveling direction of the first satellite from the line segment formed by the end point of the second line-of-sight vector and the end point of the third line-of-sight vector, and The fourth line-of-sight vector and the fifth line-of-sight are formed in a rectangular area formed by taking the predetermined threshold range in a direction perpendicular to the plane formed by the second line-of-sight vector and the third line-of-sight vector. Vector and the sixth line-of-sight vector 4. The method according to claim 1, wherein if the second satellite is included, the second satellite is determined to exist at a position where radio wave interference may occur. A program according to any one of the above. A first predicted position and a first speed of the first satellite at a predetermined time are obtained from a first satellite orbital calendar including the predicted position and speed of the first satellite every moment, and the first speed is obtained. And converting the prediction error of the first predicted position in the traveling direction of the first satellite into a first time error,
A second predicted position and a second speed of the second satellite at the predetermined time are obtained from a second satellite orbital calendar including the predicted position and speed of the second satellite every moment, and the second speed is obtained. A prediction error of the second predicted position in the traveling direction of the second satellite is converted into a second time error using
A conversion unit;
A predicted position before the first time error from the predetermined time and a predicted position after the first time error from the predetermined time are obtained from the first satellite orbital calendar, and the second position from the predetermined time. An acquisition unit that acquires the predicted position before the time error and the predicted position after the second time error from the predetermined time from the second satellite orbital calendar;
A first line-of-sight vector looking at the first predicted position from a ground station, a second line-of-sight vector looking at the predicted position before the first time error, and a predicted position after the first time error The third line-of-sight vector that viewed the second predicted position, the fourth line-of-sight vector that viewed the second predicted position, the fifth line-of-sight vector viewed the predicted position before the second time error, and the second time Using the sixth line-of-sight vector that looks at the predicted position after the error, the second station is located at a position where radio wave interference may occur in the communication at the predetermined time between the ground station and the first satellite. A determination unit for determining whether or not a satellite exists;
Including an information processing apparatus. A first predicted position and a first speed of the first satellite at a predetermined time are obtained from a first satellite orbital calendar including the predicted position and speed of the first satellite every moment, and the first speed is obtained. Converting the prediction error of the first predicted position in the traveling direction of the first satellite into a first time error using:
A second predicted position and a second speed of the second satellite at the predetermined time are obtained from a second satellite orbital calendar including the predicted position and speed of the second satellite every moment, and the second speed is obtained. Converting the prediction error of the second predicted position in the traveling direction of the second satellite into a second time error using
A predicted position before the first time error from the predetermined time and a predicted position after the first time error from the predetermined time are obtained from the first satellite orbital calendar, and the second position from the predetermined time. Obtaining from the second satellite orbital calendar a predicted position before the time error and a predicted position after the second time error from the predetermined time;
A first line-of-sight vector looking at the first predicted position from a ground station, a second line-of-sight vector looking at the predicted position before the first time error, and a predicted position after the first time error The third line-of-sight vector that viewed the second predicted position, the fourth line-of-sight vector that viewed the second predicted position, the fifth line-of-sight vector viewed the predicted position before the second time error, and the second time Using the sixth line-of-sight vector that looks at the predicted position after the error, the second station is located at a position where radio wave interference may occur in the communication at the predetermined time between the ground station and the first satellite. Determining whether a satellite is present;
A method performed by a computer, including: