Spacecraft Trajectory Estimation Using a Sampled-Data Extended Kalman Filter with Range-Only Measurements

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The problem of estimating the full state of a dynamical system based on limited measurements is of extreme importance in many applications. For the case of a linear system with known dynamics, the classical Kalman filter provides an optimal solution (Jazwinski, 1970 and Gelb, 1974). However, state estimation for nonlinear systems remains a problem of research interest. There are two main approaches to approximate nonlinear filtering. The first approach is based on a linearization of the nonlinear dynamics and measurement mapping. For example, the extended Kalman filter uses the nonlinear dynamics to propagate the state estimate while using the linearized dynamics and linearized output map to propagate the pseudo-error covariance. The extended Kalman filter is often highly effective, and documented applications cover an extraordinarily broad range of disciplines. The second approach to approximate nonlinear state estimation foregoes an explicit update of the state estimate error covariance in favor of a collection of filters whose response is used to approximate the state estimate error covariance. These statistical approaches include the particle, unscented, and ensemble Kalman filters (Julier et al., 2000; Daum, 1995; and Houtekamer and Mitchell, 1998). The present paper is concerned with state estimation for satellite trajectory estimation, which, for unforced motion, is equivalent to orbit determination (Tapley, 2004)