METHOD FOR DETERMINING THE CAPABILITY OF A SENSOR CONTAINED IN A SATELLITE TO ACCESS A TARGET REGION, AND SATELLITE ACCESSING SYSTEM

Abstract

The invention relates to a method and a system for determining the capability of a sensor contained in a satellite to access a target region. The position of the satellite is ascertained, the viewing radius of the sensor in the direction of a target reference point in a target region is then determined, the extension of the target region in the direction of a satellite position point is ascertained, and the sensor is determined to be capable of accessing the target region if the distance between the satellite position point and the target reference point in the target region is less than or equal to the sum of the viewing radius of the sensor and the extension of the target region in the direction of the target reference point.

Claims

1-14. (canceled)

15. A method for determining the possibility of a sensor contained in a satellite to access a target region, wherein at least one position of the satellite is identified, and if there is a direct line of sight between the satellite and the target region, an angle γ is determined between a satellite reference direction and a target direction directed towards a target reference point in the target region about a satellite position point dependent on the position of the satellite, a view radius R.sub.sensor (φ) of the satellite in the direction of the angle γ is determined starting from the satellite position point, an angle γ is determined between a reference direction and a direction directed towards the satellite position point about the target reference point, an extension RoT (γ) of the target region in the direction of the angle γ is determined starting from the target reference point, and it is determined that there is access possibility if a distance between the satellite position point and the target reference point is less than or equal to the sum of the view radius R.sub.sensor (φ) of the satellite and the extension RoT (γ) of the target region in the direction of the angle γ.

16. The method according to claim 15, wherein the viewing radius R.sub.sensor (φ) of the satellite is determined by representing a region of regard, FoR, which is a region of the Earth's surface or of a reference ellipsoid which can be reached by the sensor from the position of the satellite, by an ellipse or a polygon and the distance between the satellite reference point and the ellipse or the polygon in the direction of the angle γ is determined as the view radius R.sub.sensor (φ).

17. The method according to claim 16, wherein the view radius R.sub.sensor (φ) is determined by identifying a reference view radius RoR (φ) from a table or function in which values of RoR are assigned to values of the angle φ for a reference altitude a.sub.ref of the satellite, and calculating the view radius R.sub.sensor (φ) from the reference view radius RoR (φ) for a current altitude a of the satellite as R.sub.sensor (φ)=RoR (φ) a/a.sub.ref.

18. The method according to claim 15, wherein the extension RoT (γ) of the target region in the direction of the angle γ is determined by representing the target region as an ellipse or polygon and determining the distance between the target reference point and this ellipse or this polygon in the direction of the angle γ as the extension RoT (γ).

19. The method according to claim 18, wherein the extension RoT (γ) of the target region is identified from a table or function in which values of the extension RoT of the target region are assigned to values of the angle γ.

20. The method according to claim 15, wherein the satellite reference direction is a propagation direction of the satellite and/or wherein the target reference point is the geometric centroid of the target region and/or wherein the satellite position point is the nadir of the satellite.

21. The method according to claim 15, wherein the angle γ is determined between the north direction as a reference direction and a direction pointing from the target reference point towards a nadir of the satellite.

22. The method according to claim 15, wherein the position of the satellite is identified in a time-dependent manner by determining coordinates of the satellite at a first point in time, which is the point in time at which said satellite goes above the horizon or a later point in time, and at a second point in time, which is a point in time at which said satellite disappears behind the horizon or an earlier point in time later than the first point in time, each viewed from the target reference point, and the positions of the satellite are determined for a plurality of points in time between the first point in time and the second point in time, and wherein it is determined for the plurality of points in time whether there is the possibility for the access.

23. The method according to claim 15, wherein an overlap of a region of regard FoR of the satellite with the target region is determined as an overlap area of a circle having the radius R.sub.sensor (φ) about the satellite position point and a circle having the radius RoT (γ) about the target reference point.

24. The method according to claim 15, wherein a current resolution of the sensor Res is approximated as
Res=(Res.sub.ref*√(D{circumflex over ( )}2+a{circumflex over ( )}2))/a.sub.ref, wherein Res.sub.ref is a resolution of the sensor at a reference altitude a.sub.ref of the satellite, a is a current altitude of the satellite, and D is a distance on the Earth's surface or the reference ellipsoid between the target reference point and the current satellite position point.

25. The method according to claim 15, wherein the access possibility at at least one target point in time is determined by the position of the satellite being identified at the at least one target point in time as its position and the angle φ, the view radius R.sub.sensor (φ) and the angle γ being determined at the at least one target point in time.

26. The method according to claim 15, wherein, after determining the position of the satellite, it is first determined whether there is the direct line of sight between the satellite and the target region and it is determined that there is no access possibility when there is no direct line of sight between the satellite and the target region or the target reference point.

27. A satellite access system for determining the possibility of a sensor contained in a satellite to access a target region, comprising a position-identification unit, which is configured to identify at least one position of the satellite, an overlap-determining unit, which is configured to determine an angle γ between a satellite reference direction and a target direction directed towards a target reference point in the target region about a satellite position point dependent on the position of the satellite, to determine a view radius R.sub.sensor (φ) of the satellite in the direction of the angle γ starting from the satellite position point, to determine an angle γ between a reference direction and a direction directed towards the satellite position point about the target reference point, and to determine an extension RoT (γ) of the target region in the direction of the angle γ starting from the target reference point, and wherein the overlap-determining unit is configured to determine that there is access possibility if a distance between the satellite position point and the target reference point is less than or equal to the sum of the view radius R.sub.sensor (φ) of the satellite and the extension RoT (γ) of the target region in the direction of the angle γ.

Description

[0048] The invention will be explained in the following by way of example with reference to a number of figures, in which:

[0049] FIG. 1 shows a field of regard of a satellite,

[0050] FIG. 2 shows a field of regard described by a polygon,

[0051] FIG. 3 shows a target region described by a polygon,

[0052] FIG. 4 shows a field of regard of a satellite over time, as well as a target region,

[0053] FIG. 5 is a schematic view of an example of the method according to the invention,

[0054] FIG. 6 is a schematic view of a calculation of an overlap, and

[0055] FIG. 7 is an exemplary view of access capabilities of a large number of satellites over the course of a day.

[0056] FIG. 1 shows a field of regard FoR 1 of a satellite 2. In this figure, sub-FIG. 1A is a plan view and sub-FIG. 1B is a perspective view. The field of regard 1 is the region which is accessible to a sensor 3 of the satellite 2 at a given position of the satellite which the sensor can thus access. In the example shown in FIG. 1, the region of regard 1 is approximated by an ellipse which extends on the surface of the Earth 4 about a nadir 5 of the satellite. The nadir 5 represents a satellite position point on the Earth's surface 4 here. A target direction 7 directed towards a target reference point 9 in a target region 8 encloses an angle ϕ with a satellite reference direction 6, which may for example be the direction of movement of the nadir 5 on the Earth's surface. The distance between the satellite reference point 5 and the outer boundary of the region of regard 1, i.e., the ellipse 1 here, is referred to as the reference view radius RoR (ϕ). In this case, the reference view radius RoR (ϕ) is the distance between the satellite position point 5 and the edge of the region of regard when the satellite 2 is at a reference altitude a.sub.ref.

[0057] The reference altitude a.sub.ref is marked as the orbit altitude in FIG. 1B. When the satellite 2 is at any altitude a, the distance between the satellite position point 5 and the resulting boundary of the region of regard 1 can be calculated as R.sub.sensor (ϕ)=RoR (ϕ) a/a.sub.ref from RoR (ϕ) in a good approximation.

[0058] In FIG. 1, the region of regard 1 of the satellite 2 is approximated by an ellipse. FIG. 2 shows an example which achieves greater accuracy. In this figure, the region of regard 1 is approximated by a polygon, i.e., a region enclosed by straight sections. In the example shown in FIG. 2, three directions of view 71, 72 and 73 are marked, which correspond to different angles ϕ.sub.1, ϕ.sub.2 and ϕ.sub.3. The corresponding view radius R.sub.sensor (ϕ) or RoR (ϕ) results in each case as the distance between the satellite reference point 5 and the corresponding portion of the polygon in the direction 71, 72 or 73, i.e., between the satellite reference point and the point of intersection of a straight line extending in the corresponding direction and the polygon. Since a polygon is technically usually defined by its vertices, these can also be used directly as anchor points for determining RoR.

[0059] FIG. 3 shows an example of a target region, which represented by a polygon here. In the example shown, the polygon is composed of six sections, which enclose the target region 8. A direction 10 directed towards the satellite position point 5 is indicated here as the angle γ in relation to a reference direction 11, the north direction here, about a target reference point 9. From the angle γ, an extension RoT(γ) of the target region in the direction of the angle can then be determined starting from the target reference point 9. In this case, the extension in the direction of the angle γ is the extension in the direction which is at the angle γ to the reference direction 11. This extension RoT(γ) is the distance between the target reference point 9 and the polygon 8 in said direction in the direction of the satellite position point 5.

[0060] FIG. 4 shows four regions of regard 1a, 1b, 1c, 1d at different points in time t.sub.0, t.sub.1, t.sub.2 and t.sub.3 during which the satellite is moving. During the points in time t.sub.1 and t.sub.2, the region of regard 1 of the satellite overlaps a target region 8. From the position of the nadir 5 of the satellite, the target reference point 9 appears in the direction of the angle ϕ relative to the propagation direction 6 of the satellite. From the point of view of the target reference point 9, the nadir 5 of the satellite appears at the angle γ relative to the north direction 11. The distance between the satellite reference point, i.e., the nadir 5, and the target reference point 9 is denoted D.sub.ij 7 in FIG. 4. At a given position of the satellite 2, the satellite is then capable of accessing the target region 8 when the region of regard 1 overlaps the target region 8. This may for example be determined by the distance D.sub.ij being determined. If this distance D.sub.ij≤RoT (γ)+R.sub.sensor(ϕ), the region of regard 1 and the target region 8 overlap and the sensor is capable of accessing the target region 8. Therefore, for example, the sensor can measure measured values from the target region 8 or capture the target region 8, for example in the form of an optical sensor. In the example shown in FIG. 4, this is the case at the points in time t.sub.1 and t.sub.2, whereas at the points in time t.sub.0 and t.sub.3 there is no overlap between the region of regard 1 and the target region 8. If, therefore, the method according to the invention is performed at the points in time t.sub.1 or t.sub.2, the result would be that there is access possibility. At the points in time t.sub.0 or t.sub.3, however, the result would be that there is no access possibility.

[0061] As shown in FIG. 4, the method can be carried out such that it is determined, in the manner according to the invention, at each of a plurality of points in time t.sub.0, t.sub.1, t.sub.2, t.sub.3, whether there is the access possibility. In this way, it can be determined when there is the access possibility; in this case, this is at the points in time t.sub.1 and t.sub.2. In the example shown, the points in time are each spaced apart from one another in time by an interval Δt. Since the method according to the invention allows for very rapid calculation, Δt can be selected to be very small. If the method is to be further accelerated, Δt can be increased. It is also possible to dynamically adapt the increment Δt by it being scaled with the difference between the distance D.sub.ij and the radius sum RoT (γ)+R.sub.sensor(ϕ)). For a large difference, large increments can be selected, and for small differences, narrower increments can be selected.

[0062] FIG. 5 schematically shows the method according to the invention. In this figure, the target region 8 as well as sensor parameters (resolution, field of view, etc.) are predetermined. This results in an angle γ for the target region 8, as described above, and an angle ϕ for the region of regard 1 of the sensor. By means of the angle γ, the extension RoT(γ) 10 can be identified using a look-up table 51a, for example. A view radius R.sub.sensor (ϕ) 52 can be determined from the angle ϕ by means of another look-up table 51b and the current orbit altitude 53 as well as the ROR (ϕ) 52. It is also predetermined, as a satellite access possibility 53, whether there is a line of sight between the satellite and the target region 8, for example the target reference point 9. In a step 54, the distance (at a given time) between the satellite reference point 5 and the target reference point 9 can be determined as D.sub.ji. A comparison 55 is then performed in which it is determined whether D.sub.ji≤RoT (γ)+R.sub.sensor (ϕ). If this is not the case, it can be determined as a result 56 that there is no possibility for accessing the target region. If, however, this condition is fulfilled, it can be determined as a result 57 that it is possible for the sensor to access the target region. Sensor access 58 can therefore take place. If the decision 57 shows that there is access possibility, in a step 59, an area of the overlap region A and/or a resolution 60 can thus optionally also be determined. Other possible variables 61 characterising the sensor access can thus optionally also be determined.

[0063] The dashed boxes in FIG. 5 indicate which steps are performed for each of the propagation steps, as shown in FIG. 4, for example. It is advantageous for RoT (γ) 10 and RoR (ϕ) 52 to be able to be obtained by using look-up tables 51a, 51b, for example, since they only require a few calculations that can be performed very rapidly in the propagation step 62. In this way, the method can be performed very rapidly.

[0064] FIG. 6 shows an example of how the area of an overlap region 63 between the target region 8 and the region of regard 1 can be estimated. Here, both the target region 8 and also the sensor region of regard 1 can advantageously be approximated by a circle. The overlap area between two circles can be calculated as described above, with it advantageously being possible to assume that the region of regard and the target region extend on a planar surface. For most applications, the accuracy of the overlap is not crucial, since it is only a rough estimation of whether the overlap is even large enough to be of use for the intended application.

[0065] In the following, an example of a procedure according to the invention will be described again in detail.

[0066] The following information can be predetermined for the calculation of the access characteristic of a sensor: [0067] The movement of the satellite, on board which the sensor is positioned, specifically its coordinates when the satellite goes above or falls below the horizon (for propagation with state of the art software). [0068] The period of time in which the access analysis is intended to take place. Normally, the period of time is in the range of a few days, since the accuracy of the TLEs decreases over time (approximately 1-2 seconds of accuracy lost per 48 hours). [0069] The region in which the sensor access is intended to be analysed. This is represented by a polygon, for example. [0070] The sensor characteristics: geometry of the sensor area on the ground at a reference altitude of the satellite. [0071] Depending on the application, optionally other physical models, for example for the elevation or atmosphere or the maximum sensor resolution in the nadir.

[0072] In a first step, the satellites to be observed are propagated and the visual contact between the satellite and target region is calculated. This calculation is geometrically less challenging and can be carried out using existing software solutions (e.g., Orekit or STK). Specifically, the temporal and spatial coordinates of the satellite are calculated for when it appears over the horizon and disappears behind the horizon again from the view of the target region.

[0073] Within a software implementation, the access to the geometric centroid of the target region can be used as a starting point therein, for example. If the extension of the target region is large enough that it would be expected that sensor access would be obtained upon access at the centroid of the region, a plurality of points, e.g., on the contour of the target region, can instead be incorporated into the calculation. The step of satellite propagation and determining the start and end coordinates of the satellite access (line of sight present between satellite and target region) are part of the prior art.

[0074] The instances of satellite access obtained (position and time of start and end of each access) are forwarded in a second step together with the sensor characteristics for sensor propagation and calculation of the coverage. This takes place e.g., incrementally between the starting point and end point of the satellite access (position of the satellite with longitude and latitude as well as orbit altitude). In this process, the position of the satellite is propagated in time increments between the start and end of the satellite access and, for each time increment, it is calculated by means of the algorithm set out below whether there is an overlap between the sensors on board the satellite and the target region. It is noted at this point that there are a range of options for reducing the number of propagation steps and thus further accelerating a software implementation. Therefore, for example by using a Runge-Kutta method, the increments can be dynamically adapted by an estimation being made for the first contact between the sensor field of view and the target area after the first pair of increments.

[0075] Before the algorithm is discussed, two terms that are important in this context will be briefly explained: the field of view (FoV) and the field of regard (FoR). The point located directly below the satellite is called the “nadir”. At a particular point in time, the sensor is aligned in a defined direction, and the projection of the sensor onto the Earth's surface, i.e., its current field of view, is called the FoV. Since the satellite and the sensor can usually change their alignment, the position of the FoVs can change accordingly. The integral of all the possible FoVs is called the FoR and has a different form depending on the sensor type.

[0076] In the case outlined, the FoR can be determined by two parameters, the short RoR.sub.along and long RoR.sub.across semi-axes of the ellipse shown. The reference direction is e.g., the propagation direction of the satellite here.

[0077] In FIG. 1, the FoR is indicated as an ellipse, and more generally it is any polygon (FIG. 2). By using polar coordinates, such a polygon can be geometrically approximated.

[0078] The following geometric simplifications, which drastically reduce the computing complexity for the sensor contact, are advantageous. [0079] 1. The sensor area is reduced to a direction-dependent and altitude-dependent parameter. If the angle ϕ and the current altitude a of the satellite between the target region and the propagation direction of the satellite are known, the corresponding sensor radius R.sub.sensor can thus be immediately calculated using RoR(φ).

R.sub.sensor(φ)=ROR(ϕ)α/α.sub.ref

[0080] where

R.sub.0R(ϕ)=√{square root over ((R.sub.0R.sub.across sin ϕ).sup.2+(R.sub.0R.sub.along cos ϕ).sup.2)} [0081] in the case of the ellipse as shown in FIG. 1. The radius is scaled with the reference altitude of the satellite a.sub.ref here. The transfer into polar coordinates has the advantage that a refinement of the resolution (by reducing the angular increments) has a linear effect on the computing complexity. In network-based methods, the dependency is quadratic. [0082] 2. Analogously thereto, the description of the target region R, is reduced to an angle-dependent parameter, which reduces the radius of target (RoT). The angle is e.g., measured between the north direction and the satellite position. [0083] With a software implementation, RoR(φ) and RoT(γ) only need to be determined once at the start of the calculation and can e.g., be retrieved by using a look-up table without being calculated again. Interpolation can then be carried out between individual table values at angles in order to obtain greater accuracy. [0084] 3. In order to identify an overlap between the sensor Sj and the target region Ri, the distance D.sub.ji between the projected satellite position on the Earth's surface and the reference point (e.g., geometric midpoint) of the radius RoT of the target region is determined. Here, the distance is e.g., calculated along the corresponding great circle of the globe, e.g., using Vincenty's algorithm [T. Vincenty, “DIRECT AND INVERSE SOLUTIONS OF GEODESICS ON THE ELLIPSOID WITH APPLICATION OF NESTED EQUATIONS,” Surv. Rev., vol. 23, no. 176, pp. 88-93, 1975.] [0085] If it is smaller than the sum of R.sub.sensor and RoT at the corresponding angle, both areas overlap. [0086] There is therefore access if RoT(γ)+R.sub.sensor (φ).

[0087] It should again be emphasised that the geometric approximation of the projected sensor area and the target region area only needs to be carried out once before the sensor propagation is performed. For each time increment, only the angles γ and φ spare then determined and, on the basis of this and the current altitude a, it is identified whether there is an overlap.

[0088] The approach is again schematically shown in FIG. 4. FIG. 4 illustrates the propagation here, and FIG. 5 shows a programmatic implementation.

[0089] With regard to FIG. 5: the input data are set out on the left-hand side. The compilation of a look-up table 51a, 51b (Lookup) is optional. For each propagation step (dashed box 62), it is determined whether there is access from the target radius 10, the sensor radius 52 and the distance 54 between the satellite and the region. Other parameters, such as overlap A or resolution Res, are optionally determined. The instances of access are then output for further processing.

[0090] For some applications, it may be advantageous to determine other characteristics of the sensor contact, e.g.: [0091] 1. The size of the overlap A can be estimated by the intersection between two circles having the radii R.sub.sensor (φ) and RoT (γ) (FIG. 6). The overlap comes about as the area of the intermediate lens-shaped portion as a function of the distance between the two centres of the circles D.sub.ji, which has already been calculated in the previous step 54.

[00003]$A_1={\mathrm{RoT}}_{\mathrm{Avg}}^2\mathrm{acos}\left(\frac{D_{\mathrm{ji}}^2+{\mathrm{RoT}\left(\gamma \right)}^2-{R_{\mathrm{Sensor}}\left(\varphi \right)}^2}{2D_{\mathrm{ji}}\mathrm{RoT}\left(\gamma \right)}\right)A_2={\mathrm{RoR}}^2\mathrm{acos}\left(\frac{D_{\mathrm{ji}}^2+{R_{\mathrm{Sensor}}\left(\varphi \right)}^2-{\mathrm{RoT}\left(\gamma \right)}^2}{2D_{\mathrm{ji}}{R}_{\mathrm{Sensor}}\left(\varphi \right)}\right)A_3=\left(-D_{\mathrm{ji}}+\mathrm{RoT}\left(\gamma \right)+R_{\mathrm{Sensor}}\left(\varphi \right)\right)\left(D_{\mathrm{ji}}+\mathrm{RoT}\left(\gamma \right)-R_{\mathrm{Sensor}}\left(\varphi \right)\right)\left(D_{\mathrm{ji}}-\mathrm{RoT}\left(\gamma \right)+R_{\mathrm{Sensor}}\left(\varphi \right)\right)\left(D_{\mathrm{ji}}+\mathrm{RoT}\left(\gamma \right)+R_{\mathrm{Sensor}}\left(\varphi \right)\right)A=A_1+A_2-\frac{1}{2}\sqrt{A_3}$ [0092] Depending on the complexity of the surface geometry, the overlap can be estimated more or less accurately as a result. Since the projected position of the satellite is subject to uncertainties anyway, the accuracy of the overlap is not usually crucial. It can, however, give an important indication of the overlap to be expected and especially of whether this only relates to a small part of the target region and is therefore possibly not of any interest to a user. [0093] 2. In optical sensors, the resolution scales linearly with the optical path length. This can be estimated from D.sub.ji and orbit altitude in relation to reference values Res.sub.Ref and a.sub.Ref.

[00004]$\mathrm{Res}=\frac{{\mathrm{Res}}_{\mathrm{Ref}}\sqrt{D_{\mathrm{ji}}^2+a^2}}{a_{\mathrm{Ref}}}$

[0094] The advantages of the invention over existing methods are the following, for example: [0095] 1. Implementation: the solution is simple to implement in software and has high parallelisability. [0096] 2. Quality: compared with previous analytical methods, complicated target-region and field-of-view geometries can also be processed. [0097] 3. Detail: compared with analytical methods, detailed time-dependent and location-dependent statements can be made. It is possible to calculate important physical parameters, such as the resolution or level of coverage that can be achieved, in a simple manner. [0098] 4. Scalability: By contrast with numerical methods, the computing time does not increase quadratically, but linearly with the size of the target region, while the accuracy is maintained. [0099] 5. Low complexity: Reducing the number of characterising variables to three distances allows the calculation speed to be drastically increased compared with network-based, numerical methods. [0100] 6. Universal applicability: Simplifying the sensor model allows many satellites to be implemented rapidly, without software having to be accordingly adapted. [0101] 7. Statements in real time: By simplifying the calculations, statements can be made in real time, even taking into account hundreds of satellites, which enables new and improved applications.

[0102] FIG. 7 shows the access capabilities of a range of satellites plotted on the vertical axis over the course of a day, which is plotted along the horizontal axis. A triangle in the view in FIG. 4 means that the corresponding satellite has the possibility of accessing the target region, which is a location on Hawaii here, at the corresponding time at which the triangle is shown. The grey background shows the night-time period, while the non-grey background shows the daytime period. The times are given in UTC. The uppermost line in FIG. 7 below the times states the summary of all the access capabilities. It can be immediately established whether one of the satellites or none of the satellites has access.

[0103] Owing to the high speed of the method, it can be used for incremental optimisation methods in order to simulate new constellations and adapt them optimally. Owing to the universal adaptability of the method to various sensor configurations, various models can be run rapidly and adapted accordingly.

[0104] Furthermore, there are many applications in which time criticality is of overriding importance. This may be the case when assisting military deployment or in crisis and catastrophe management. The method reliably gives decision-makers a rapid overview of potentially available satellite data as a well-founded information base.

[0105] An important subject in space technology, as in other technology sectors, is equipping satellites with artificial intelligence. In this context, a resource-efficient algorithm can also be used directly on board a satellite in order to optimise the Earth observation performance, for example using swarms of intelligent microsatellites, with regard to repetition rate and coverage. Therefore, it would be possible, inter alio, a) to establish redundancy and to maintain the coverage when parts of the swarm become inoperative, b) to automatically increase the repetition rate over time over a particular region in the event of a crisis or c) to automatically adapt the task distribution under changing boundary conditions.