Space-Based Sensor Coverage of Earth Orbits

In this paper we propose a space-based system for the surveillance of Earth-orbits. The proposed design will have the capability of completely covering spatial tubes (whose widths depends on the sensor ranges) spanning a range of Earth orbits. While the literature on ground-based surveillance is large, the problem we study in this paper (space-based surveillance of Earth orbits) is rarely studied in the past. A surveillance satellite placed in orbit about Earth will only be able to detect objects of interest within its sensors’ footprints. Objects of interest on the same orbit but outside the sensors’ footprints will not be detected due to a difference in angular positions between the satellite and objects of interest. Hence, for that satellite to scan an entire orbit and ensure the detection, with probability one, of any objects on that orbit, it will have to apply control forces to march along the orbit. Hence, in this paper, we develop a simple (and cheap) orbital maneuver to effect the marching of the satellite along the orbit. The maneuver depends on the sensor range and nominal orbit size. This basic design is then extended to multiple satellite systems. Once the basic design is introduced, we investigate the interdependence of three basic design variables: number of satellites used, fuel usage, and time to mission completion. The proposed design starts with two extreme cases: a system design that uses a single satellite but maximum fuel usage and time to mission completion; and a system design with (an analytically computable) maximum number of satellites but with zero fuel usage and time to mission completion. Each of the cases has the ability to detect, with probability one, any objects of interest in orbit within a given range of space orbits. With J2 effect taken into account, the proposed system design will guarantee complete coverage, not only of a tube in space, but of an entire shell containing a wide range of orbits with varying inclination angles. Detailed numerical examples are given for the coverage of Low Earth Orbits and Geostationary Orbit. This paper lays the basis for future work where the authors will consider questions of resource allocation for cases with limited resources (especially severe constraints on the number of satellites used in the mission), and a formal formulation of a multi-objective optimal design problem and solutions where the design parameters are: number of satellites used in the system, fuel-usage and time to mission completion.