Multiresolution Coverage Computation for Space-Based Space Surveillance Systems Using Octrees

Space-based space surveillance has the potential to enhance the tracking and characterization of space objects by extending coverage and improving observability relative to ground-based systems. A key first step in designing satellite systems for space surveillance is to formulate an objective function that accurately captures spatial coverage characteristics under realistic observation conditions. For optical systems, this problem is usually posed as maximizing the above-the-horizon coverage of the satellites over a dual-altitude band target region, so that observations are always made against a space background. This problem has previously been studied in some limited analytical cases in two dimensions, and more recently in three dimensions using numerical methods. This article proposes a novel multiresolution approach to satellite coverage analysis in three dimensions. The method allows for the specification of geometric constraints in a highly general fashion using constructive solid geometry. The coverage is represented efficiently using a linear octree. Multiplicities of coverage for an arbitrary number of satellites are computed by projecting the individual octrees onto the Morton space-filling curve, thereby enabling an efficient partition of the space by multiplicity via a simple interval nesting problem. The method’s capabilities are demonstrated in an application problem involving a multiplane space surveillance constellation.