A Novel filtering approach for the general contact lens problem with range rate measurements

This paper proposes a Novel filtering algorithm for the general contact lens problem, where the measurement uncertainty region takes a thin, curved, contact lens-like shape in the states' Cartesian coordinates. Such problems have severe measurement nonlin-earity and will lead to consistency problems for existing nonlinear filtering techniques such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). This problem is very ill-conditioned, which makes it extremely hard and expensive to use a particle filter (PF). In this paper, a General Measurement Adaptive Covariance rule (GMACR) is proposed, for which the consistency of EKF is guaranteed. This leads to a new filtering approach for the general contact lens problem - the General Measurement Adaptive Covariance Extended Kalman Filter (GMAC-EKF). Simulation results show that GMAC-EKF is consistent and has superior tracking accuracy. When the state estimate becomes sufficiently accurate, GMAC-EKF is equivalent to EKF and has the optimal tracking performance. The only drawback of the filter is that it has loss in accuracy at the early stage of the filtering due to the artificially enlarged measurement covariance. A hybrid filter combining the alternative extended Kalman filter and GMAC-EKF is also proposed, which yields the best filtering performance.