Jth Moment Extended Kalman Filtering for Estimation of Nonlinear Dynamic Systems
Two flavors of an analytical approach (called the Jth Moment Extended Kalman Filtering, JMEKF) to estimate the state of a nonlinear dynamical system from vector measurements, developed by the authors recently are compared. The main distinction in the two flavors lies in the method of computing the time evolution of arbitrarily high order statistical moments between the classical Kalman update stages of the filter. The first flavor involves the state transition tensor approach (originally due to Park and Scheeres ) and the second flavor explicitly derives the statistical moment evolution equations using perturbation theory. Updating all, not only the first two, of the propagated statistical moments constitutes the JMEKF framework for estimation of nonlinear systems. This brief review is followed by a discussion outlining the assumptions in the assumed structure and associated convergence issues. The connection between probability theory and the associated statistical propagation developed in this paper is explored by an elementary exposition to entities called cumulants and characteristic functions. The tensor transformation between moments and cumulants is presented in a vector matrix form for ease in computations. To overcome the local nature of the Taylor expansions involved in the propagation and update of the JMEKF framework, a smooth particle approach is suggested. Several building blocks required for such a scheme are developed. The generation of the local density function process from evolved moments is detailed where multiple nominal expansion nominal solutions in the phase space are considered to reconstruct the evolved density function. 2008 by Majji, M., Junkins, J. L., and Turner, J. D.,.
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AIAA Guidance, Navigation and Control Conference and Exhibit