Method and device for determining a pointing rule for a satellite by determining a space-time distribution

Description

Domaine technique

[0001] The present invention belongs to the field of monitoring space objects, and more particularly relates to a method for automatically determining the pointing law of an observation instrument of at least one satellite for searching for such space objects. Etat de la technique

[0002] The constant increase in the number of uncontrolled space objects in Earth orbit represents a growing risk to the operations of space systems and to populations on the ground.

[0003] As a result, we are witnessing the development of systems for monitoring space objects in Earth orbit aimed at cataloguing space objects and their orbital parameters, in order to limit these risks.

[0004] It is estimated that approximately 750,000 space objects larger than 1 cm orbit the Earth, each with the capacity to damage or even destroy an operational satellite. These small, difficult-to-detect space objects represent a major threat to space operations, while knowledge of their trajectories remains incomplete. It should be noted that this number is likely to increase even without new launches, simply due to collisions between uncontrolled space objects.

[0005] Furthermore, for low earth orbits (LEO, altitude less than 2000 km), given the relative speeds of space objects evolving in these orbits, space objects larger than 5 mm represent a risk with catastrophic consequences in the event of collision with satellites operating in these orbits.

[0006] The main objective of space surveillance is to detect, and preferably determine and maintain as accurately as possible the trajectory knowledge (i.e. orbital parameters) of space objects present in orbit around the Earth. This allows on the one hand to minimize the risks of collision with satellites operated in orbit and, on the other hand, to minimize the number of false collision alarms. Indeed, in case of risk of collision, a collision avoidance maneuver is carried out by the satellite in danger. Such an avoidance maneuver generally results in service interruptions, additional operating costs and a reduction in the satellite's lifetime due to overconsumption of propellants. Therefore, it is important to reduce the number of false collision alarms in order to reduce the number of unnecessary avoidance maneuvers.

[0007] Space surveillance has until now been carried out by means positioned on the Earth's surface, in particular active means such as radars or lidars or passive means such as optical telescopes exploiting the solar illumination of the space objects to be monitored. However, these terrestrial surveillance systems have numerous physical and technological limitations in terms of range for systems based on active means, limiting the use of these active means to LEO orbits, and availability and detection capacity for systems based on passive means due to atmospheric disturbances. The most significant limitation is the minimum size of space objects that can be detected, of the order of 5 to 10 cm for LEO orbits.

[0008] New concepts for space surveillance systems are therefore being studied and developed to address the shortcomings of surveillance systems using means positioned on the Earth's surface. These systems consist of monitoring space using means positioned in space ("space-based surveillance system" or SBSS). Most of the SBSS systems currently being studied and / or developed are based on satellites operated in orbit, generally low, and comprising optical and passive observation instruments, most of which exploit the solar illumination diffused by the space objects to be monitored. Due to technological constraints and the laws of optics, the instantaneous field of view covered by these observation instruments is generally small, of the order of 5° 2< to 10° 2< , thus limiting the portion of space that can be monitored at a given time.Furthermore, even if the estimated number of space objects is large, the area to be monitored is extremely vast and the average density of space objects orbiting the Earth remains very low. Therefore, and also taking into account the limited field of view of the observation instruments, the choice of areas to be observed to favor the number of new detections of unreferenced (i.e. unknown) space objects. a priori) is non-trivial and crucial to the performance of SBSS systems. Document US9916507 B1 discloses a pointing law according to the prior art. Document US2015088475 A1 discloses a visualization of the observability probabilities of space objects. Exposé de l'invention

[0009] The present invention aims to overcome all or part of the drawbacks of the prior art, in particular those set out above, by proposing a solution which makes it possible to automatically develop pointing laws for the observation instrument(s) of an SBSS system. To this end, a method according to claim 1 is proposed.

[0010] According to a feature of the invention, said pointing law comprises successive pointing directions of said observation instrument extending over at least one orbital period of said satellite and said observation time window extends over a duration equal to or greater than one orbital period.

[0011] Thus, the method for determining the pointing law is based on a first list of spatial objects associated with their orbital parameters including their positions, speeds, size and covariance (for example, spatial objects referenced and / or deduced from spatial objects referenced by simulation using a fragmentation model of said referenced spatial objects). In general, here, “orbital parameters” means any information making it possible to describe the trajectory of a spatial object (for example, the Keplerian parameters, the state vector of the center of mass of the spatial object, etc.), but also in particular its size making it possible to deduce its visual magnitude. On the basis of this first list of spatial objects, a second list of spatial objects is determined which meet an observability criterion and are thus potentially observable during an observation window.Typically, for each instant of interest within this observation window, and therefore for different positions of the satellite during the observation window, it is determined which space objects are potentially observable. This notion of observability assumes for example that the observation instrument is potentially pointed towards each space object considered, and encompasses considerations such as: . verification by calculation that the space object, in relation to the satellite, is not masked by the Earth, verification by calculation that the direction of the space object in relation to the satellite is not dazzled by the Sun, verification by calculation that the space object is illuminated by the Sun, in particular in relation to the positions of the Earth and the Moon, verification by calculation that the apparent visual magnitude of the space object allows the satellite's observation instrument to detect it.

[0012] Then, it is proposed to determine for each satellite a spatio-temporal distribution of the potentially observable space objects over time over the observation time window. Such a spatio-temporal distribution describes, for example, for each pointing direction relative to the satellite (“spatial” distribution) and each instant (“temporal” distribution) of the observation time window, a quantity representative of a density of the potentially observable space objects in this pointing direction from said satellite at this instant of the observation time window. For example, a set of directions with associated probabilities of encountering potentially observable space objects during an observation window is determined.Advantageously, the spatio-temporal distribution is for example determined in an observation frame which depends at any time on the direction of the Sun and the direction of the Earth relative to the satellite. Indeed, the Sun and the Earth are determining factors for the observability of space objects and correspond to directions towards which it is generally not possible to observe space objects (masking by the Earth, glare by the Sun) and which are to be avoided. By positioning the observation frame relative to the directions of the Sun and the Earth and centered on the satellite (deduced from the orbital parameters of said satellite), that is to say by choosing an observation frame in which the directions of the Sun and the Earth vary little over time in said observation frame, then it is ensured that the directions of observable space objects are concentrated in limited ranges of solid angles.In such an observation frame, it is therefore easier to determine pointing laws for the detection of spatial objects.

[0013] The pointing law of the satellite observation instrument is then determined, for example, over the observation time window and in the observation frame, based on the spatio-temporal distribution of the spatial objects observable from said satellite. The pointing law extends over a limited time window, equal to or extended, relative to the observation time window used for calculating the spatio-temporal distribution. The pointing law that uses the observable spatial objects is based, for example, on observation probabilities. Some spatial objects in the second list may in particular be probable objects added to referenced objects.

[0014] The method for determining the pointing law according to the invention may further include, optionally, one or more of the following characteristics.

[0015] According to another feature of the invention, the first list of space objects associated with their orbital parameters is obtained from an extraction in a catalog of known space objects, this extraction then being increased by at least one statistical prediction of new space objects from known space objects or by at least one simulation of physical collision between two known space objects.

[0016] According to another feature of the invention, the determination of said pointing law is carried out using a cost function relating to the potentially observed spatial objects by excluding the revisited known spatial objects and under the constraint of a bounded and parameterizable mathematical scanning law. The cost function will for example aim to maximize the discovery of unknown objects.

[0017] According to another feature of the invention, the pointing law is selected from a plurality of candidate pointing laws, by an evaluation of each candidate pointing law comprising an estimation, as a function of the spatio-temporal distribution, of the unknown spatial objects potentially detected over said observation time window by applying said candidate pointing law, the selected candidate pointing law being that for which a criterion for detecting new spatial objects is verified.

[0018] According to another feature of the invention, the criterion is verified when the number of new different space objects detected at least once is maximized.

[0019] According to another feature of the invention, the criterion is verified when the number of new different spatial objects revisited a determined number of times is maximized.

[0020] The objective is in particular to increase the probability of detecting new space objects. Such arrangements make it possible to optimize scanning from the satellite, since dense areas of the spatio-temporal distribution are also areas in which the probability of detecting new space objects is higher. This arises in particular from the fact that many new space objects arise from the fragmentation of referenced space objects. The detection criterion may also, in some cases, include a revisit constraint, for example by maximizing the number of different new space objects detected a given number of times.

[0021] For example, a space object is considered to be detected when a specific detectability criterion is met.

[0022] According to another feature of the invention, a plurality of spatio-temporal distributions and a plurality of pointing laws are determined for a plurality of satellites respectively, the criterion for detecting space objects being a criterion for global detection by said plurality of satellites.

[0023] According to another feature of the invention, the candidate pointing laws are defined by at least one parameterizable pointing law and correspond to respective different candidate values ​​of parameters of the at least one parameterizable pointing law.

[0024] According to another feature of the invention, the at least one configurable pointing law comprises one of: a sinusoidal law, a harmonic law, a piecewise continuous law, a polynomial law, a law based on spline functions.

[0025] According to another feature of the invention, the spatio-temporal distribution is carried out in a determined satellite reference frame, called the observation reference frame, the observation reference frame varying over time as a function of a direction of the Sun and a direction of the Earth relative to said satellite, said pointing law also being determined in the observation reference frame.

[0026] According to another feature of the invention, the observation reference frame comprises three orthogonal axes, two of said three axes being at any time arranged in a plane defined by a satellite-Earth direction and a Sun-satellite direction.

[0027] According to another feature of the invention, the observation marker comprises: a first axis oriented along the satellite-Earth direction, a second axis oriented along the orthogonal projection of the Sun-satellite direction in a plane orthogonal to the first axis, a third axis orthogonal to the first axis and to the second axis.

[0028] According to another feature of the invention, another observation marker comprises: a first axis oriented along the orthogonal projection of the satellite-Earth direction in a plane orthogonal to a second axis oriented along the Sun-satellite direction, a third axis orthogonal to the first axis and to the second axis.

[0029] According to another feature of the invention, the pointing law also comprises an orientation of the observation instrument in yaw around each pointing direction of said observation instrument. Indeed, a pointing law mainly corresponds to a two-axis control of the orientation of the observation instrument, but it is also possible, in certain cases, to carry out a three-axis control by also controlling the orientation of the observation instrument around the pointing direction.

[0030] According to an example which is not covered by the scope of the claims, there is also provided a method for determining at least one pointing law of an observation instrument of at least one satellite in Earth orbit for searching for new space objects in Earth orbit, said pointing law comprising successive pointing directions of said observation instrument over a time window of at least one orbital period of said satellite, the pointing law being determined in a reference frame centered on said satellite, called observation reference frame, comprising three orthogonal axes, two of said three axes are at any time arranged in a plane defined by a satellite-Earth direction and a Sun-satellite direction, said observation reference frame defining angles in azimuth and in elevation, and said determination method comprising a determination, over the time window and as a function of orbital parameters of the at least one satellite: of a first excluded band in azimuth and a second excluded band in azimuth determining between them an authorized band in azimuth which corresponds to an angular range depending on time comprising only pointing directions in azimuth which, during the time window, are observable with respect to the Earth and the Sun, of a first excluded band in elevation and a second excluded band in elevation determining between them an authorized band in elevation which corresponds to an angular range depending on time comprising only pointing directions in elevation which, during the time window, are observable with respect to the Earth and the Sun, wherein the determined pointing law comprises an azimuth pointing law comprising only azimuth pointing directions within the authorized azimuth band and an elevation pointing law comprising only elevation pointing directions within the authorized elevation band.

[0031] The method for determining the pointing law may also optionally include one or more of the following characteristics, taken individually or in all technically possible combinations.

[0032] According to another feature of the example which is not covered by the scope of the claims, a pointing direction is considered to be observable with respect to the Earth and the Sun when an area pointed by said pointing direction is illuminated by the Sun and is not masked by the Earth, and when the observation instrument directed according to said pointing direction is not dazzled by the Sun.

[0033] According to another feature of the example which is not covered by the scope of the claims, the authorized band in azimuth is chosen to have a constant angular width during the time window and / or the authorized band in elevation is chosen to have a constant angular width during the time window.

[0034] According to another feature of the example which is not covered by the scope of the claims, the method for determining the pointing law further comprises: determining the authorized azimuth band and the authorized elevation band; determining, from a first list of space objects associated with their orbital parameters, a second list of space objects which are observable, in the authorized azimuth band and the authorized elevation band, from said at least one satellite in Earth orbit during the observation time window of duration equal to or greater than one orbital period, an observability criterion being verified as a function of at least orbital parameters of the space objects of the first list and the orbital parameters of the at least one satellite; determining a spatio-temporal distribution of the space objects observable during the observation time window from said at least one satellite.

[0035] Another object of the invention relates to a method for searching for new space objects by at least one satellite in Earth orbit, said at least one satellite comprising an observation instrument, comprising: a determination of a pointing law of the observation instrument of said at least one satellite, according to a method for determining a pointing law according to the invention, a control, as a function of the pointing law, of the pointing of the observation instrument, and acquisition of images by said observation instrument, over at least one orbital period, a search for new space objects in the images acquired by the observation instrument.

[0036] According to another feature of the invention, the pointing law is updated at the end of the first observation time window, for a new first observation time window.

[0037] According to another feature of the invention, the first list of spatial objects is supplemented by objects corresponding to new spatial objects detected.

[0038] Another subject of the invention relates to a computer program product comprising instructions which, when executed by at least one processor, configure said at least one processor to implement the method for determining the pointing law according to the invention.

[0039] Another object of the invention relates to a device for calculating a pointing law comprising at least one processor and at least one memory, said at least one processor being configured to implement the method for determining the pointing law according to the invention.

[0040] Another object of the invention relates to a space surveillance system from space, comprising: at least one satellite in Earth orbit, said at least one satellite comprising an observation instrument, a device for calculating a pointing law according to the invention. Présentation des figures

[0041] The invention will be better understood by reading the following description, given as a non-limiting example, and made with reference to the figures which represent: Figure 1 : a schematic representation of a satellite orbiting the Earth, for monitoring space objects, Figure 2 : a diagram illustrating the main steps of an example of the implementation of a method for determining the pointing law of a satellite observation instrument, Figure 3 : a schematic representation illustrating variables taken into account to evaluate an apparent visual magnitude constraint, Figure 4 : a schematic representation illustrating variables taken into account to evaluate an Earth masking constraint, Figure 5 : a schematic representation illustrating variables taken into account to evaluate a constraint of illumination by the Sun, Figure 6 : a schematic representation illustrating variables taken into account to evaluate a glare-free constraint, Figure 7 : a schematic representation of an example of an observation reference associated with a satellite, Figure 8 : a schematic representation of an example of spatio-temporal distribution in a space discretized in [azimuth, elevation], Figure 9 : a schematic representation of an example of spatio-temporal distribution and a pointing law, Figure 10 : a diagram illustrating the main steps of another example of embodiment of a method for determining the pointing law of a satellite observation instrument, this example not being covered by the scope of the claims, Figure 11 : an example of a method according to the invention.

[0042] In these figures, like references from one figure to another designate identical or similar elements. For reasons of clarity, the elements shown are not to scale, unless otherwise stated.

[0043] Furthermore, the order of steps shown in these figures is given only as a non-limiting example of the present disclosure which can be applied with the same steps performed in a different order. Description des modes de réalisation

[0044] There figure 1 schematically represents a satellite 20 in orbit around the Earth 30. Preferably, the satellite 20 is placed in a moving orbit, i.e. non-geostationary orbit (GEO), for example a low earth orbit (LEO) or a medium earth orbit (MEO). However, nothing precludes, in certain cases, considering a geosynchronous orbit (GSO) such as a GEO orbit. The orbit of the satellite 20 is preferably a circular orbit. However, nothing precludes, according to other examples, considering other types of orbits, in particular elliptical orbits.

[0045] As indicated above, the satellite 20 is implemented to monitor space, and in particular space objects 50 in Earth orbit. The space objects 50 to be searched for here correspond mainly to uncontrolled artificial space objects, such as space debris. For the sake of clarity, the figure 1 shows only a few 50 space objects, but several hundred thousand space objects orbit Earth 30.

[0046] The satellite 20 is implemented to monitor space objects 50 in Earth orbit. It should be noted that the Earth orbit of the satellite 20 and the Earth orbits of the space objects may have different characteristics. For example, the satellite 20 may be implemented to monitor space objects 50 in Earth orbits with altitudes higher than the altitude of the Earth orbit of said satellite 20. In addition, the figure 1 represents only one satellite 20, but the present disclosure is also applicable to a plurality of space surveillance satellites 20.

[0047] Satellite 20 can here be implemented to monitor unreferenced space objects (i.e., search for new, unknown space objects a priori). For this purpose, the satellite 20 comprises an observation instrument 21 adapted to acquire images. The observation instrument 21 comprises, in a manner known per se, passive optical acquisition means configured to capture the optical flow received in a field of view of said observation instrument 21, around a line of sight of said observation instrument 21. The passive optical acquisition means comprise, for example, at least one linear or matrix detector, sensitive in one or more wavelength bands preferably included in the visible and / or near infrared wavelength range (from 0.4 µm to 0.8 µm).

[0048] The observation instrument 21 is, for example, dedicated to space monitoring. In certain cases, the observation instrument 21 may also be implemented as part of an Earth observation mission 30.

[0049] There figure 2 schematically represents the main steps of a method 70 for determining at least one pointing law of the observation instrument 21 of the satellite 20, for space surveillance.

[0050] The determination method 70 is for example implemented by a calculation device (not shown in the figures). The calculation device comprises for example one or more processors (CPU, DSP, FPGA, ASIC, etc.). In the case of several processors, these can be integrated into the same equipment and / or integrated into hardware separate equipment. The calculation device also comprises one or more memories (magnetic hard disk, electronic memory, optical disk, etc.) in which is for example stored a computer program product, in the form of a set of program code instructions to be executed by the processor(s) to implement the different steps of the method 70 for determining the pointing law.

[0051] A pointing law corresponds to successive pointing directions of said observation instrument 21 (i.e., with which said observation instrument 21 must successively align its line of sight) over one or more orbital periods. In the remainder of the description, the case where the satellite 20 is in a moving orbit is considered, in a non-limiting manner, such that the satellite 20 moves relative to the Earth 30 during the time window. It should be noted that, once the pointing law has been determined, it can be repeated periodically to control the line of sight of the observation instrument 21. The law is calculated from a distribution calculated over an observation time window which extends, for example, over one or more orbits. The law can thus be determined over a reduced, identical or extended period relative to the observation time window.For example, the observation time window may correspond to an orbital period of the satellite 20 and the determined pointing law may provide for a repetition of a pointing sequence extending over several orbital periods. Generally, the time window is of a duration adapted to allow the acquisition, by the observation instrument 21, of several images during at least one orbit. For example, the pointing law extends over a duration equal to or greater than the orbital period of the satellite 20.

[0052] The determination method 70 uses for example a first list of space objects 50 associated with their orbital parameters. A space object corresponds for example to a referenced space object (known a priori). A space object 50 may also correspond to a space object generated by simulation, by applying fragmentation models to referenced space objects (including other satellites in this case). Referenced space objects are, for example, space objects from the MASTER (meteroid and space debris terrestrial environment reference) catalogue, which is divided into four types of orbits: LEO, MEO, GEO and others (high eccentricity orbits).

[0053] The first list of space objects is for example established according to the needs of the space surveillance mission. For example, the space objects 50 of the first list may correspond to space objects 50 placed in specific Earth orbits. According to another example, the space objects 50 of the first list may correspond to space objects 50 which are difficult to observe from Earth 30, etc.

[0054] As illustrated by the figure 2 , the determination method 70 comprises for example a step 71 of determining, among the space objects 50 of the first list, space objects 50 which are potentially observable from a satellite 20 during an observation window of duration equal to or greater than an orbital period of the satellite. In practice, the observation window extends for example over one or more orbits and the observation law also extends over one or more orbits.

[0055] The spatial objects 50 observable during the observation window are for example determined as a function of at least orbital parameters of the spatial objects 50 of the first list and orbital parameters of the at least one satellite 20. The orbital parameters of the spatial objects 50 and of the at least one satellite 20 make it possible for example to determine, in the same frame of reference (for example centered on the Earth 30), the positions of said spatial objects 50 and of the at least one satellite 20 for any instant within the observation window considered, as well as the positions of the Earth 30 and of the Sun (and optionally the Moon) relative to the spatial objects 50 and to the at least one satellite 20.

[0056] Consequently, the orbital parameters make it possible to determine in particular whether a space object 50 satisfies geometric observability constraints at a given instant with respect to the satellite 20 in question. For example, a space object 50 is observable from the satellite 20 if it is not masked by the Earth 30, if it is illuminated by the Sun and if the pointing direction from the satellite 20 is not dazzled by the Sun.

[0057] The observable space objects 50 are for example further determined based on additional information making it possible to calculate, for each space object 50, an apparent visual magnitude of said space object 50. This may for example be an albedo and a surface area for each space object 50. It should be noted that the apparent visual magnitude also depends on a distance between the space object 50 and the satellite 20, and on a phase angle relative to the Sun which can be determined from the orbital parameters.

[0058] Alternatively or in addition, it is also possible to take into account, for example, a relative angular velocity between the space object 50 and the satellite 20, which can be determined from the orbital parameters, and which also influences the ability of the observation instrument 21 to detect the space object 50. However, it is the apparent relative angular velocity, i.e. the relative angular velocity between the space object 50 and the line of sight of the observation instrument 21 (which further depends on a rotation speed of the satellite 20 on itself and therefore, in fine, of the pointing law that one seeks to determine), which is the most relevant for evaluating the capacity of the observation instrument 21 to detect the space object 50. Nothing, however, excludes taking into account the relative angular velocity during the step 71 of determining the second list, even if this potentially leads to considering as unobservable a space object 50 with too high a relative angular velocity while this space object could be made detectable by a rotation speed of the satellite 20 on itself which would lead to obtaining a less significant apparent relative angular velocity.

[0059] Generally speaking, the step 71 of determining the second list therefore aims to identify the space objects 50 which could potentially be observed during the observation window. A space object 50 being observable at a given instant of the observation window if, assuming the line of sight of the observation instrument 21 pointed towards said space object 50 relative to the satellite 20 at this instant, observability constraints are verified. The observability constraints are for example geometric, and may also include constraints linked to the apparent visual magnitude of the space object 50 and / or to the relative angular velocity of said space object 50.

[0060] If we consider a number N sat of satellites 20 ( N sat can be equal to 1), then it is possible to describe the satellite 20 of index k (1 ≤ k ≤ N sat ) by its state vector x k composed of the six usual Keplerian parameters (orbital parameters) ( a k , e k , i k , ω k , Ω k , M k ) set to a date t k . For every moment t i considered in the observation window, the positions r k ( t i ) and speeds v k ( t i ) of satellite 20 of index k can be propagated by modeling the laws of space mechanics (function propagate below) : r k t i , v k t i = propagate x k , t i − t k

[0061] The positions r k ( t i ) and speeds v k ( t i ) are for example expressed in a frame centered on the Earth 30, the position r k ( t i ) being a vector going from the center of the Earth 30 to the satellite 20 of index k. It goes without saying that the choice of a particular reference frame to evaluate the observability of the space objects 50 is absolutely not limiting of the present disclosure.

[0062] In the same way, if we consider N obj spatial objects 50, then it is possible to describe the spatial object 50 of index l (1 ≤ l ≤ N obj ) by its state vector x l composed of the six usual Keplerian parameters (orbital parameters) x l = ( a l , e l , i l , ω l , Ω l , M l ) set to a date t l . For every moment t i considered in a time window of observation, the positions r l ( t i ) (vector) and speeds v l ( t i ) of the spatial object 50 of index l , in the frame considered centered on the Earth 30, can be propagated by modeling the laws of space mechanics: r l t i , v l t i = propagate x l , t i − t l

[0063] We also associate with the spatial object 50 of index l an albedo ρ l and a surface A l .

[0064] We designate by r sun the vector giving the position of the Sun 40 in the frame considered centered on the Earth 30.

[0065] As stated above, at each moment t i in the observation window, a spatial object of index 50 l is considered observable by a satellite 20 of index k if it respects for example a set Λ of observability constraints c j , Λ = { c j } .

[0066] Finally, it is possible to associate for each satellite 20 of index k at each instant t i , a set O k ( t i ) of 50 observable space objects such as: O k t i = l / ∏ cj ∈ Λ c j k l t i = 1 expression in which the observability constraint c j is worth 1 if the spatial object 50 considered is observable with respect to this constraint, 0 otherwise. Such a set O k ( t i ) can be determined for each instant t i considered in the observation window, and for each satellite 20.

[0067] As indicated above, it is possible to consider several types of observability constraints. We consider in a non-limiting manner the case where the set Λ is based for example on a set of 4 constraints: Λ = c magnitude , c masquage , c eclipse , c angle garde

[0068] Below we provide non-limiting examples of models that can be used to assess these observability constraints. Contrainte de magnitude visuelle apparente

[0069] There figure 3 schematically represents the phase angle between the Sun 40, a space object 50 and a satellite 20. We denote by d k,l ( t i ) = | r l ( t i ) - r k ( t i )| the distance between the spatial object 50 of index l and satellite 20 index k à the moment t i The phase angle between the Sun-space object direction and the satellite-space object direction is defined by: Φ k , l t i = acos r k t i − r l t i d k , l t i ⋅ r sun t i − r l t i r sun t i − r l t i

[0070] With a Lambertian spherical diffusion model: F spherical ϕ = 2 3 π 2 π − ϕ cos ϕ + sin ϕ the apparent visual magnitude M k , l ( t i ) can then be written: M k , l t i = C − 2.5 log 10 A l ρ l F spherical ϕ k , l t i + 5 log 10 d k , l t i expression in which C is the apparent visual magnitude of the Sun, which is on average -26.74 at the top of the atmosphere ("Top of Atmosphere" or TOA in Anglo-Saxon literature) on Earth.

[0071] The apparent visual magnitude constraint c magnitude is for example checked if the apparent visual magnitude respects a detection threshold of the observation instrument 21.

[0072] As indicated above, it is also possible to take into account the relative angular velocity w k,l ( t i ) of the space object 50 relative to the satellite 20: w k , l t i = r k t i − r l t i × v k t i − v l t i d k , l t i 2

[0073] In such a case, the apparent visual magnitude constraint c magnitude is for example verified if the couple ( M k,l ( t i ), w r,l ( t i )) respects a detection threshold of the observation instrument 21. Typically, the higher the apparent visual magnitude, the lower the relative angular velocity must be so that the space object 50 can be observed / detected by the observation instrument 21, and vice versa). Contrainte de masquage par la Terre

[0074] There figure 4 schematically represents a space object 50, a satellite 20 and the Earth 30, and certain variables making it possible to evaluate the masking constraint by the Earth 30.

[0075] We designate by α k,l ( t i ) the angle between the satellite-space object direction and the satellite-Earth direction: α k , l t i = acos r k t i − r l t i d k , l t i ⋅ − r k t i r k t i

[0076] The distance from the satellite-to-space object direction to the Earth's horizon can then be calculated as follows: d horizon k , l t i = r k t i sin α k , l t i − R earth expression in which R earth corresponds to the radius of the Earth 30 (which can also include the thickness of the atmosphere).

[0077] The Earth masking constraint c masquage can then be considered verified if cos ( α k,l ( t i )) < 0, or if | r k ( t i ))| 2< - ( R earth + d horizon< k,l ( t i )) 2< > d k,l ( t i ) 2< , or even if d horizon< k,l ( t i ) > 0. Contrainte d'éclairement (ou d'absence d'éclipse)

[0078] There figure 5 schematically represents a space object 50, a satellite 20, the Earth 30 and the Sun 40, and certain variables making it possible to evaluate the illumination constraint by the Sun 40.

[0079] We designate by β l ( t i ) the angle between the directions of the Sun and the space object 50 seen from Earth 30: β l t i = acos r sun t i r sun t i ⋅ r l t i r l t i

[0080] The maximum permissible angle, below which the Earth 30 does not obscure the solar rays directed towards the space object 50, is calculated by β l max = π 2 acos R earth r l t i .

[0081] The illumination constraint (or absence of eclipse) c eclipse can therefore be considered verified if β l t i < β l max . Contrainte d'absence d'éblouissement

[0082] There figure 6 schematically represents a space object 50, a satellite 20 and the Sun 40, and certain variables making it possible to evaluate the constraint of absence of glare by the Sun 40.

[0083] We designate by γ k,l ( t i ) the angle between the satellite-space object direction and the satellite-Sun direction: γ k , l t i = acos r sun t i − r k t i r sun t i − r k t i ⋅ r l t i − r k t i r l t i − r k t i

[0084] It is possible to predefine a minimum angle γ min , called the guard angle, above which the observation instrument 21 is not dazzled by the Sun 40.

[0085] The constraint of absence of glare c angle garde can therefore be considered verified if γ k,l ( t i ) > γ min .

[0086] It should be noted that it is also possible, optionally, to consider such guard angles with respect to other stars, for example the Earth 30 and / or the Moon, which amounts to adding other geometric observability constraints.

[0087] As illustrated by the figure 2 , the determination method 70 further comprises a step 72 of determining, over the time window and in a satellite reference frame, called observation reference frame, a spatio-temporal distribution of the spatial objects 50 observable from each satellite 20.

[0088] The spatio-temporal distribution is determined from a set of observable spatial objects and is therefore more relevant for the discovery of new spatial objects. Indeed, the concentrations of known and observable spatial objects can influence the observation law. Unknown spatial objects distributed in space are a priori very dispersed and one could not afford to point in space at random. In addition, adding an observability constraint makes it possible to explore areas, for example, in the vicinity of concentrations of spatial objects, whether these concentrations are observable or not. The first list of spatial objects can indeed come from an extraction of known spatial objects which is then, for example, increased statistically or by simulating physical collisions.That is, statistical or physical augmentation allows, for example, the generation of potential space objects of different sizes and with different trajectories. Thus, known space objects, even those not observable or difficult to observe by the satellite during the observation window, can have an influence on the pointing law.

[0089] The spatio-temporal distribution describes, for example, for each pointing direction relative to the satellite 20 (“spatial” distribution) and each instant (“temporal” distribution) of the time window, a quantity representative of a probability density of the spatial objects potentially observable in this pointing direction from said satellite 20 at this instant of the time window. The quantity given by the spatio-temporal distribution is for example a density strictly speaking, that is to say a number of spatial objects 50 potentially observable (i.e. potentially observable) per unit of solid angle in the pointing direction considered, or even a total number of spatial objects 50 observable in a determined solid angle (corresponding for example to the field of view of the observation instrument 21) in which the pointing direction considered is located, etc.

[0090] The observation reference frame associated with a satellite 20 is for example an orthogonal reference frame centered on the satellite 20, for example centered on a center of mass of said satellite 20. However, the observation reference frame is not linked to a structure of said satellite 20 (and in particular it is independent of the line of sight of the observation instrument), so that orthogonal axes which make up said observation reference frame can vary over time relative to the structure of said satellite 20.

[0091] More particularly, the observation frame associated with a satellite 20 depends for example at any time on the direction of the Sun 40 and the direction of the Earth 30 relative to this satellite 20. Indeed, as indicated above, the Sun 40 and the Earth 30 are determining factors for the observability of space objects. By choosing an observation frame in which the directions of the Sun 40 and the Earth 30 vary little over time in said observation frame, then it is ensured that the directions of the observable space objects 50 are concentrated in limited ranges of solid angles.

[0092] For example, two of the three orthogonal axes of the observation frame are at any time arranged in a plane defined by a satellite-Earth direction (also known as the Nadir direction) and a Sun-satellite direction.

[0093] There figure 7 schematically represents a non-limiting example of an observation reference point comprising: a Z axis oriented along the satellite-Earth direction, an X axis oriented along the orthogonal projection of the Sun-satellite direction in a plane orthogonal to the Z axis, an axis Y orthogonal to the axes X and Z.

[0094] Therefore, with reference to the figure 7 , the Sun 40 and the Earth 30 (or more particularly their respective centers) are at all times in the plane XZ. The Z-axis direction allows the 50 observable spatial objects to be concentrated around the plane XY due to the constraint of masking by the Earth 30. The axis X being the orthogonal projection of the Sun-satellite direction in the plane XY, 50 observable space objects are distributed around the axis Xdue to the constraints of absence of glare and apparent visual magnitude. Consequently, the calibration of the observation reference frame with respect to the Earth 30 and the Sun 40 makes it possible to maintain average observation directions with high added value stationary during the observation window, in particular with respect to the position in orbit of the satellite 20 and the drift of the latter.

[0095] In the Earth-centered frame 30 considered previously, the axes X, Y and Z of the figure 7 can be expressed as follows for satellite 20 of index k at time t i : Z k t i = − r k t i r k t i Y k t i = Z k t i ∧ − r sun t i r sun t i X k t i = Y k t i ∧ Z k t i expressions in which ∧ corresponds to the vector product.

[0096] We can then define a reference frame change matrix allowing us to move from the reference frame centered on the Earth 30 to the observation reference frame, for each satellite 20 of index k and for each instant t i : M loc t i r k r sun = X k t i , Y k t i , Z k t i

[0097] Following step 71 of determining the second list of observable spatial objects, a set O k of 50 observable space objects is associated with each satellite 20 of index k for each instant t i considered in the observation window.

[0098] For each satellite 20 index k, all directions C k ( t i ) from which it is possible to observe a spatial object 50 observable are therefore defined by: ∀ t i , ∀ l ∈ O k t i C k t i = r l t i − r k t i = x k , l t i , y k , l t i , z k , l t i

[0099] These sets of vectors, which all originate from a satellite 20 of index k, constitute the high added value pointing directions on which it may be interesting to align the line of sight of the observation instrument 21 to maximize the chances of detecting new space objects. These vectors can be brought back into the observation frame of the satellite 20 of index k by means of the frame change matrices M loc ( t i ,r k ,r sun ): ∀ t i , ∀ l ∈ O k t i C k loc t i = M loc t i r k r sun x k , l t i , y k , l t i , z k , l t i

[0100] It is advantageously simpler, in this type of reference, to carry out calculations for the pointing law on sets with high added value.

[0101] Other observation reference frames are, for example, conceivable. In particular, it is possible to use an observation reference frame in which two of the three orthogonal axes are at any time arranged in a plane defined by a satellite-Earth direction and a Sun-satellite direction.

[0102] Another non-limiting example of a possible observation reference point is for example such that: the axis X is oriented along the Sun-satellite direction, the Z axis is oriented along the orthogonal projection of the satellite-Earth direction in a plane orthogonal to the axis X, the axis Y is orthogonal to the axes X and Z.

[0103] For example, the spatio-temporal distribution is determined by converting the pointing directions C k loc in polar coordinates D k loc , for example in [azimuth, elevation]. We denote by [ x' k,l ( t i ) ,y' k,l ( t i ) ,z' k,l ( t i )] the coordinates M loc ( t i ,r k ,r sun )[ x k,l ( t i ) ,y k,l ( t i ) ,z k,l ( t i )]. The pointing directions D k loc in polar coordinates [ az k,l ( t i ) ,el k,l ( t i )] are for example obtained as follows: ∀ k , ∀ t i , ∀ x ′ k , l t i , y ′ k , l t i , z ′ k , l t i ∈ C k loc t i , D k loc t i = az k , l t i = atan y ′ k , l t i x ′ k , l t i , el k , l t i = asin z ′ k , l t i x ′ k , l t i , y ′ k , l t i , z ′ k , l t i

[0104] By convention, the azimuth angle sweeps [-180°,180°] and the elevation angle sweeps [-90°,90°].

[0105] For each satellite 20 index k and each set D k loc associated with pointing directions of observable spatial objects 50, it is then possible, following a non-limiting example of implementation, to calculate the spatio-temporal distribution in the form of a histogram by discretizing the pointing directions [azimuth, elevation]. The figure 8 schematically represents an example of space discretized in [azimuth, elevation]. Similarly, the instants t i of the observation window can be discretized. Each grid step of the discretized space has dimensions [ Δaz,Δel ] . These dimensions correspond, for example, in certain implementation modes, to the dimensions of the field of view of the observation instrument 21.

[0106] These histograms HIST k are for example calculated as follows: ∀ k , ∀ t i , ∀ m , ∀ n HIST k az m el n t i = l ∈ O k t i / az k , l t i ∈ az m , az m + Δaz , el k , l t i ∈ el n , el n + Δel

[0107] These histograms HIST k allow the spatial hierarchy of the portions of space presenting the maximum number of spatial objects 50 potentially observable over time. This amounts to creating a map specific to each satellite 20 of index k connecting, at each instant t i and [azimuth, elevation] pair of the space discretized in [ Δaz, Δel ] , a number of observable spatial objects 50. If the observation time window coincides with the start and end of the pointing law, then the histogram HIST k can be directly used to calculate the pointing law, at each instant, as a function of the spatio-temporal distribution.

[0108] When the observation window, extending for example over several orbital periods, over which the observable space objects 50 are determined, is of a duration greater than that of the time window over which one seeks to determine a pointing law, for example of an orbital period, it is for example possible to take into account each orbital period of the observation window, to combine them and reduce them to an orbital period for the calculation of the pointing law. For example, the pointing law can also be calculated over one orbit and repeated over several orbits.

[0109] When the observation window, extending for example over an orbital period, over which the observable space objects 50 are determined, is of shorter duration than that of the time window over which one seeks to determine a pointing law, for example of several orbital periods, it is for example possible to selectively influence the pointing law by favoring the data over the observation window.

[0110] In order to exploit all the 50 spatial objects observable during the observation window, it is for example possible to link for each satellite 20 of index k defined by its positions ( r k ,v k ), the time t i at the position of said satellite in its Earth orbit ρ k ( t i ) = f ( r k ,v k ,t i ) (for example the true anomaly of the satellite on its Earth orbit). Considering positions on orbit discretized by Δρ k , we also introduce the following function which returns the position ρ k ( t i ) in the discretized space: f k t i = ρ k , p / ρ k t i ∈ ρ k , p , ρ k , p + Δρ k

[0111] It is therefore possible to determine all the 50 different space objects which are observable by the satellite 20 of index k from the same position ρ k,p from Earth's orbit, for example according to the following expression: ∀ k , ∀ m , ∀ n , ∀ p MAP k az m el n ρ k , p = u t i HIST k az m el n t i / f k t i = ρ k , p

[0112] In this case, the spatio-temporal distribution grouping together all the observable space objects 50 for all the passages, during the observation window, of the satellite 20 of index k through the same position on its Earth orbit corresponds for example to: HIST ′ k az m el n t i = MAP k az m , el n , f k t i

[0113] This spatio-temporal distribution gives the set of 50 potentially observable space objects for each discrete orbital position according to the discretized pointing directions in [azimuth, elevation].

[0114] It should be noted that other forms are for example possible for the spatio-temporal distribution of the satellite 20 of index k. For example, it is possible to consider continuous and non-discrete pointing directions. In such a case, it is possible to consider for each pointing direction of the spatio-temporal distribution, a quantity representative of a density of potentially observable space objects 50 (for one or more passages through each position on Earth orbit) in a solid angle around each pointing direction, for example a solid angle corresponding to the field of view of the observation instrument 21.

[0115] As illustrated by the figure 2 , the determination method 70 then comprises for example a step 73 of determining a pointing law of the observation instrument 21 of the satellite 20 of index k, on the time window and in the observation frame, as a function of the spatio-temporal distribution of the spatial objects 50 observable from said satellite.

[0116] The spatio-temporal distribution of each satellite 20 defines for this satellite 20, over time, the pointing directions with high added value. As indicated previously, the dense areas of the spatio-temporal distribution can for example be considered as areas in which the probability of detecting new space objects is higher. This results in particular from the fact that many new space objects come from the fragmentation of space objects but are for example too small to be referenced. Furthermore, if certain space objects 50 are space objects deduced from space objects referenced by simulation of the fragmentation of these, then these space objects 50 of the second list correspond to new potentially observable space objects, which one can seek to detect.

[0117] The pointing law is for example optimized to satisfy a criterion for detecting new observable spatial objects. 50 We can indeed distinguish known and referenced objects which will be for example identical to the objects extracted from a reference catalog, from potentially detected new spatial objects. The new spatial objects from a first list increased statistically or physically, are for example marked in memory by a specific label.

[0118] The calculation of the observation law can, for example, be based on the distributions of known space objects and on simulated space objects. Thus, part of the calculations are advantageously based on known data, which potentially avoids excessive drift in the calculations.

[0119] Different detection criteria (also referred to as cost functions in an optimization context) may be used. For example, if the objective over the time window is to monitor one or more new spatial objects 50, the determined pointing law is the candidate pointing law making it possible to observe a determined number of new spatial objects the greatest number of times over the time window. If the objective over the time window is to increase the probability of detecting a maximum number of new spatial objects, the determined pointing law is, for example, the candidate pointing law making it possible to observe, according to the spatio-temporal distribution, the greatest number of different new spatial objects at least once over the time window.The detection criterion may also, in some cases, include a revisit constraint, for example by maximizing the number of new different space objects detected a given number of times. Revisits will indeed allow obtaining additional information, from the photographs taken, to fully determine the orbital parameters of the new space object. However, partial information can also be combined with other sources of information such as other observation satellites from space.

[0120] The estimation of the number of new spatial objects 50 that can be detected by means of a pointing law is carried out by applying the pointing law to the spatio-temporal distribution associated with the satellite 20 considered. Such an evaluation takes into account, for example, the field of view of the observation instrument 21 (possibly already taken into account in the spatio-temporal distribution) to determine the number of new observable spatial objects 50 that are in the field of view when the line of sight is aligned with a given pointing direction.

[0121] The dynamics of the pointing law can for example also be taken into account to evaluate the apparent relative angular velocity of each observable space object 50 with respect to the observation instrument 21.

[0122] Thus, a spatial object 50 is for example considered to be detected when a determined detectability criterion is verified, which notably includes the fact that the spatial object 50 is located in the field of view of the observation instrument 21, and possibly the apparent relative angular velocity (possibly jointly with the apparent visual magnitude).

[0123] The optimization of the pointing law can for example also take into account the feasibility of each pointing law considered. Indeed, the pointing law must be operationally viable, in particular in terms of rotation speed capacity of the line of sight of the observation instrument 21 (the time to move from one pointing direction to another is constrained by the agility of the satellite 20 and / or a pointing mechanism of the observation instrument 21) and avoidance of celestial bodies likely to dazzle the observation instrument 21 when moving from one pointing direction to another. Taking into account constraints on the pointing law in the optimization process therefore advantageously ensures its feasibility.

[0124] An optimization method can for example be implemented to determine a pointing law satisfying the criterion for detecting new spatial objects 50. The choice of a particular type of optimization method can for example be the subject of evaluations and then a selection of the type of optimization. For example, the determination of the pointing law can implement a continuous or discrete automatic optimization method, based for example on genetic, evolutionary, dynamic programming algorithms, etc. The large dimension of the optimization space can make the use of exact methods complex to evaluate in a reasonable time. If necessary, it can then be advantageous to implement exploratory algorithms (for example by gradient descent), which make it possible to converge towards local optima in an efficient manner.

[0125] Regardless of the optimization method used, the determination of the pointing law can, for example, consider a plurality of candidate pointing laws. For each candidate pointing law, the potentially observable spatial objects 50 are then estimated using the spatio-temporal distribution. The selected pointing law is, for example, one of the candidate pointing laws evaluated which satisfies the considered detection criterion.

[0126] In order to reduce the complexity of optimizing the pointing law of each satellite 20, it is for example possible to reduce the degrees of freedom when parameterizing a type of the pointing law. The candidate pointing laws are for example defined by at least one determined parameterizable pointing law, and correspond to different respective candidate values ​​of parameters of the at least one parameterizable pointing law. For example, the at least one parameterizable pointing law comprises one of: a sinusoidal law, in which case the parameters correspond for example to an amplitude and / or a phase and / or a pulsation, a harmonic law, in which case the parameters correspond for example to amplitudes and / or phases and / or pulsations, a polynomial law, for example of predetermined or parameterizable order (bounded if necessary), the parameters corresponding for example to the different coefficients of the polynomial, a continuous law and differentiable up to a certain piecewise order, for example a law based on a spline (for example B-splines), in which case the parameters correspond for example to the order of the spline, to the consecutive dates allowing the nodes of the splines to be positioned, to the values ​​of the coefficients of the splines, etc.

[0127] The pointing law comprises, for example, two pointing laws applied to different dimensions, for example an azimuth pointing law and an elevation pointing law. The pointing law may, for example, also comprise a control of an orientation of the observation instrument 21 in yaw around each pointing direction of said observation instrument 21.

[0128] For example, limiting the pointing law by choosing a type of configurable but limited pointing law, for example with 3 harmonics, advantageously allows for pointing that is less influenced by the spatio-temporal distribution. Indeed, the calculation of the pointing law can, for example, be based on known spatial objects augmented by statistically or physically simulated spatial objects. Thus, the use of a limited pointing law advantageously allows for reducing the influence of the spatio-temporal distribution both because we are not looking for known spatial objects and because the spatial objects increasing the list are probable spatial objects.

[0129] We now describe a non-limiting example of optimization in the case where the pointing law consists of a harmonic law in azimuth and a harmonic law in elevation. The pulsation for each pointing law in azimuth and elevation is considered to be proportional to the orbital pulsation ω k = μ earth / a k 3 Or a k is the semi-major axis of the Earth's orbit of satellite 20 of index k And µ earth is the standard gravitational parameter of the Earth 30. The configurable pointing law is for example defined in azimuth and elevation by: az k t = ∑ i ∈ ℕ α i sin iω k t + ψ i el k t = ∑ j ∈ ℕ δ j sin jω k t + φ j

[0130] Each pointing angle harmonic is characterized by a set of three parameters defining its amplitude, its pulsation and its phase. For a given number of H harmonics, the pointing law therefore has 6H degrees of freedom defining the state vector to be optimized. The resulting pointing law makes it possible to propose a periodic and generic space scanning strategy. The agility of satellite 20 will determine the maximum admissible amplitude / frequency pairs.

[0131] For each satellite 20 of index k, the cost function (detection criterion) aims for example to maximize the number of new 50 different space objects detected at least once: KPI k X = max X Card ∪ az k , el k , t HIST ′ k az k el k t

[0132] It should be noted that the above cost function corresponds to a local detection criterion for each satellite 20 of index k. In the case where the surveillance system comprises several satellites 20, it is possible to separately optimize the pointing law of each satellite 20 according to a local detection criterion. The pointing laws of all the satellites 20 are for example jointly optimized, according to a global detection criterion. For example, by considering N sat satellites, the overall detection criterion aimed at maximizing the number of new 50 different space objects detected at least once can be expressed as follows: KPI X N sat = max X N sat Card ∪ k ∪ az k , el k , t HIST ′ k az k el k t

[0133] In order to explore a wide range of candidate pointing laws, it is possible to use an evolutionary optimization algorithm whose main specific hyper parameters can be, for example: a constraint on the maximum rotation speed of the satellites 20 and / or the pointing mechanisms of the observation instruments 21, a maximum number of harmonics per pointing angle (azimuth, elevation).

[0134] There figure 9 schematically represents an example of spatio-temporal distribution in azimuth and elevation obtained for a satellite 20 in heliosynchronous Earth orbit ("sun-synchronous orbit" or SSO), 6 a.m.-6 p.m. at 500 kilometers altitude. The figure 9 also shows the azimuth and elevation pointing laws obtained in the observation frame by applying an evolutionary algorithm, with for example two harmonics per azimuth and elevation angle admitted (i.e. H = 2) and a maximum rotation speed of 1° / s. The spatio-temporal distribution and the pointing law are determined over a time window corresponding to an orbital period, and are given on the figure 9 depending on the successive positions of satellite 20 in its Earth orbit during the orbital period (from 0° to 360°). On the figure 9 , a dark gray represents a low density of observable space objects, while a light gray represents a high density of observable space objects. figure 9 also represents the anti-Sun direction, that is to say the direction opposite the Sun.

[0135] As can be seen on the figure 9 , by construction of the observation frame, the observable spatial objects 50 are in this example concentrated in azimuth between approximately -100° and approximately 100° and concentrated around an elevation close to 0°. The evolutionary algorithm here proposes a pointing law offering a maximum of azimuth scanning with an amplitude close to 90° and a harmonic of rank 9 coupled with a lower frequency (rank 6) and low amplitude elevation scanning in order to remain concentrated in high density areas.

[0136] There figure 10 schematically represents the main steps of another example of embodiment of a method 80 for determining the pointing law of the observation instrument 21 of a satellite 20, this example not being covered by the scope of the claims.

[0137] The method 80 for determining the pointing law of the figure 10 relies for example on an observation reference frame as described previously, and everything that has been described previously about the observation reference frame is for example applicable for this method 80 for determining a pointing law. The method 80 for determining the pointing law of the figure 10 is for example implemented by a calculation device as described above.

[0138] As illustrated by the figure 10 , the method 80 for determining the pointing law comprises: a step 81 of determining a first excluded band in azimuth and a second excluded band in azimuth determining between them an authorized band in azimuth which corresponds to an angular range as a function of time comprising only pointing directions in azimuth which, during the time window, are observable with respect to the Earth 30 and the Sun 40, a step 82 of determining a first excluded band in elevation and a second excluded band in elevation determining between them an authorized band in elevation which corresponds to an angular range as a function of time comprising only pointing directions in elevation which, during the time window, are observable with respect to the Earth 30 and the Sun 40.

[0139] Indeed, due to the geometric observability constraints with respect to the Earth 30 and the Sun 40 and the observation frame considered, the unobservable areas of space will be concentrated, as will the observable areas of space. This is visible for example on the figure 9 . Indeed, the spatio-temporal distribution clearly shows, in azimuth as in elevation, an upper band and a lower band of black color which correspond to areas in which there are no observable spatial objects 50. In practice, these upper and lower bands of black color correspond to areas in which it is not possible to observe spatial objects 50 due to geometric observability constraints. Consequently, these upper and lower bands can be determined without having to first determine observable spatial objects 50 and spatio-temporal distributions of observable spatial objects 50 (i.e. without performing steps 71 and 72 of the method 70 for determining the figure 2 ). These upper and lower bands correspond to the first and second excluded bands in azimuth and elevation. The areas between these first and second excluded bands correspond, for example, to the authorized bands in azimuth and elevation, which correspond to the observable areas of space over time, which are here continuous in space and time thanks to the use of an observation reference frame centered on the satellite whose axes are positioned according to the positions of the Sun and the Earth.

[0140] It should be noted that it is for example possible to determine authorized bands of variable angular width over time, for example by excluding for the first and second excluded bands only the pointing directions which do not satisfy the geometric observability constraints. It is also possible, according to other examples, to determine authorized bands of constant angular width over time, for example by determining a band of maximum constant width between the first and second excluded bands, in azimuth and in elevation.

[0141] As illustrated by the figure 10 , the determination method 80 then comprises a step 83 of determining an azimuth pointing law comprising only azimuth pointing directions within the authorized azimuth band and an elevation pointing law comprising only elevation pointing directions within the authorized elevation band.

[0142] Because the observable areas are presented in the form of authorized bands (angular ranges over time), it becomes easy to determine a pointing law allowing each authorized band to be scanned, for example, without having to perform optimization as previously. For example, we can also limit the first list of spatial objects using these exclusion bands to arrive at the second list of spatial objects. The second list of spatial objects will then be used, for example, to calculate a spatio-temporal distribution and then the pointing law.

[0143] As indicated above, the authorized bands in azimuth and elevation can be determined without having to first determine observable space objects 50 and space-time distributions of observable space objects 50 as a function of their orbital parameters. However, nothing precludes, according to other examples, determining as previously a space-time distribution, and determining the authorized bands in azimuth and elevation as a function of this space-time distribution. In such a case, it is for example possible to exclude from the authorized bands the pointing directions which, although they satisfy the geometric observability constraints, correspond to sparse areas according to the space-time distribution. Thus, the angular width of each authorized band can vary over time as a function of the positions of the dense areas of the space-time distribution.

[0144] Once a pointing law has been determined for a satellite 20, said pointing law can be applied by the satellite 20 during a time window (and possibly repeated periodically) to search for new space objects 50. The pointing of the observation instrument 21 of the satellite 20 is then controlled according to the pointing law, by aligning the line of sight of said observation instrument 21 with the pointing directions of the pointing law. For example, the pointing law, determined in the observation frame, is converted into another satellite frame more conducive to controlling the line of sight of the observation instrument 21, for example a satellite frame linked to the structure of the satellite 20. This conversion is for example carried out on the ground, and the converted pointing law is transmitted to the satellite 20 by a ground station (not shown in the figures).Several images are thus acquired successively by the observation instrument 21 simultaneously with the control of its pointing according to the pointing law. All or part of the plurality of images may correspond to a video. The plurality of images thus acquired is then processed to search for new space objects 50. This processing of the plurality of images is carried out for example on the ground, after said plurality of images has been transmitted by the satellite 20 to a ground station.

[0145] There figure 11 represents an example of a method based on a pointing law according to the invention. Data are for example provided as input 101 in the form of known space objects associated with their orbital parameters.

[0146] Lists of spatial objects are presented, for example, in the form of databases.

[0147] A next step 102 consists, for example, of a partial extraction from these input data. The extraction may, for example, be based on the Keplerian parameters of interest or other parameters such as mass or size, serving as filters during a selection. The extraction may also comprise the use of a random variable to randomly reduce a database of referenced space objects.

[0148] For example, a distribution calculation 103 is performed on the filtered database. This database serves, for example, as an operational database.

[0149] Alternatively, an augmentation 104 of the database is also carried out. This augmentation is, for example, the result of a simulation of a physical collision between two known space objects which then generates data representative of the space debris resulting from this collision. This augmentation can also, alternatively or in a complementary manner, be the result of statistics from the known space objects, using for example a so-called "Monte Carlo" draw.

[0150] The augmented database 105 is then stored, which will serve as an operational database for calculating the pointing law.

[0151] From the operational database, a distribution of 107 objects is then extracted using selection criteria. The distribution is presented, for example, in the form of a density map. For example, a distribution function can also be obtained by using kernel density estimation (KDE).

[0152] This distribution then allows the calculation of the pointing law 108. The pointing law is for example derived from a specific function respecting constraints such as glare, masking or angular speeds. Illumination combined with the size of spatial objects, or even combined with their speed, is also a criterion that can be taken into account. The choice of the function and its degrees of parameterization are for example taken into account for the development of the pointing law. For example, a cost function is also used to parameterize the pointing law. The cost function allows for example to evaluate the performance of a candidate parameterization or a candidate law, along the path corresponding to the pointing direction, for example by using the Mahalanobis distance integrated on the path to optimize pointing towards potentially high-density or neighboring areas.

[0153] The pointing law can then be programmed on the ground and transmitted aboard the observation spacecraft 109 for execution.

[0154] The law is based on known space objects and it is easy to discard them when searching for new space objects. In addition, a telescope, for example, captures an image that includes a starry background, this starry background allowing particularly precise exploitation and repositioning of the traces of potentially captured new objects. Obtaining several orbital parameters 110 from the observation of these new objects, for example revisited, will make it possible to catalog these new space objects.

[0155] For example, the law is regularly updated based on updated object catalogues and to take into account the updated trajectory of the observation satellite.

Claims

1. Method (70) for determining at least one pointing law of an observation instrument (21) of at least one satellite (20) in terrestrial orbit for detecting new space objects in terrestrial orbit, said pointing law comprising successive pointing directions of said observation instrument for acquiring a plurality of images, over a limited time window, equal to or extended with respect to an observation time window, said determination method comprising: - determining (71), from a first list of space objects associated with their orbital parameters, a second list of space objects that are observable from said at least one satellite on said observation time window, an observability criterion being verified based on at least the orbital parameters of the space objects of the first list and orbital parameters of the at least one satellite, - determining (72) a spatial-temporal distribution of said observable space objects over the observation time window, the spatial-temporal distribution being in the form of a mapping of spatial-temporal densities and describing, for each pointing direction with respect to the satellite and at each instant of the observation time window, a quantity representative of a probability density of the space objects potentially observable in said pointing direction from said satellite at said instant of the observation time window, - determining (73) the pointing law of the observation instrument, comprising successive pointing directions of said observation instrument for acquiring said plurality of images, over said limited time window, equal, or extended with respect to said observation time window, based on said spatial-temporal distribution.

2. Method according to claim 1, wherein said pointing law includes successive pointing directions of said observation instrument extending over at least one orbital period of said satellite and wherein said observation time window extends over a duration equal to or greater than one orbital period.

3. Method according to one of the preceding claims, wherein the first list of space objects associated with their orbital parameters is obtained from an extraction in a catalogue of known space objects, this extraction being then increased by at least one statistical prediction of new space objects from known space objects or by at least one simulation of physical collision between two known space objects.

4. Method according to claim 3, wherein the determination of said pointing law is performed using a cost function relating to the space objects potentially observed by excluding the revisited known space objects and under the constraint of a bounded and configurable mathematical scanning law.

5. Method according to one of claims 3 and 4, wherein the pointing law is selected from a plurality of candidate pointing laws, by an evaluation of each candidate pointing law including an estimation, based on the spatial-temporal distribution, of unknown space objects potentially detected on said observation time window by applying said candidate pointing law, the selected candidate pointing law being that for which a criterion for the detection of new spatial objects is satisfied.

6. Determination method (70) according to claim 5, wherein the criterion is satisfied when the number of different new space objects detected at least once is maximised.

7. Determination method (70) according to claim 5, wherein the criterion is satisfied when the number of different new space objects revisited a given number of times is maximised.

8. Method (70) according to any one of the preceding claims, wherein the spatial-temporal distribution is carried out in a given satellite reference frame, referred to as the observation reference frame, the observation reference frame varying over time according to a direction of the Sun and a direction of the Earth with respect to said satellite, said pointing law also being determined in the observation reference frame.

9. Method for searching for new space objects by at least one satellite in terrestrial orbit, said at least one satellite including an observation instrument, including: - determining a pointing law of the observation instrument of said at least one satellite, according to a method according to any one of the preceding claims, - checking, according to the pointing law, the pointing of the observation instrument, and acquiring images by said observation instrument over at least one orbital period, - a search for new space objects in the images acquired by the observation instrument.

10. Search method according to claim 9, wherein the pointing law is updated at the end of the first observation time window, for a new first observation time window.

11. Space-object search method according to claim 9 or 10, wherein the first list of space objects is supplemented with objects corresponding to new space objects detected (110).

12. Computer program product including instructions that, when executed by at least one processor, configure said at least one processor to implement a method (70) for determining a pointing law according to any one of claims 1 to 8.

13. Computing device including at least one processor and at least one memory, said at least one processor being configured to implement a method (70) for determining a pointing law according to any one of claims 1 to 8.

14. System for monitoring space from space, including: - at least one satellite (20) in terrestrial orbit, said at least one satellite including an observation instrument (21), - a computing device according to claim 13.