A Unified Approach to The Orbital Tracking Problem

Abstract

Consider an object in orbit about the earth for which a sequence of angles-only measurements is made. This paper looks in detail at a one-step update for the filtering problem. Although the problem appears very nonlinear at first sight, it can be almost reduced to the standard linear Kalman filter by a careful formulation. The key features of this formulation are (1) the use of a local or adapted basis rather than a fixed basis for three-dimensional Euclidean space and the use of structural rather than ambient coordinates to represent the state, (2) the development of a novel "normal:conditional- normal" distribution to described the propagated position of the state, and (3) the development of a novel "Observation- Centered" Kalman filter to update the state distribution.A major advantage of this unified approach is that it gives a closed form filter which is highly accurate under a wide range of conditions, including high initial uncertainty, high eccentricity and long propagation times.