Revisiting the filtering problem (IAC-19,A6,7,6,X50344)

Consider a space object in orbit about the earth and suppose a sequence of angles only measurements is available at known times. The objective of the filtering problem is to successively update the predicted distribution of the state of the orbiting object. Each overall step of the filtering algorithm includes two parts: a propagation step and an update step. These tasks are simplest if the distribution of the propagated state vector and the measurement can be described in terms of Gaussian distributions, so that a variant of the classic Kalman filter can be used. It is well-known that ECI coordinates are unsuited for this purpose since the distribution of propagated position vector can have a pronounced banana shape (and hence is non-Gaussian) for large propagation times. A better coordinate system is given by equinoctial coordinates, which perform well in many (but not all) circumstances. Equinoctial coordinates depend on a “reference plane”, typically taken to be the equatorial plane. In this paper we explore the use of a recently developed new set of coordinates called “Adapted STtructural (AST)” coordinates. They are essentially a local or adapted version of equinoctial coordinates. The reference plane is now taken to be the orbital plane of the current best estimate of the state. There are also a few other differences between AST and equinoctial coordinates. One of the benefits of the AST coordinate system is that it can be used with a nonlinear Kalman filter to track space debris. In this paper we perform a detailed analysis on different tracking algorithms. In particular, we show that in certain circumstances under high eccentricity, the iterated extended (IEKF) and unscented (IUKF) Kalman filters can outperform the more conventional extended (EKF) and unscented (UKF) Kalman filters.