Abstract
To better describe statistical characteristics of asymmetric distributions often encountered in nonlinear systems, this paper aims at providing effective third-degree moment approximation by a new deterministic sample, named tau-point set. The set is not limited to a particular structure such as in the unscented transformation. It is computationally stable and can be asymmetric, which makes its moment approximation better than some state-of-the-art methods. The construction of a tau-point set is formulated first as a constrained third-order symmetric tensor decomposition problem. Inspired by the idea of homotopy, a simple problem with an easy (or known) solution is proposed, and then a novel approach initialized adaptively in filtering is developed for solving the decomposition problem by tracing analytic zero paths emanating from a solution of the simple problem. The tau points are used to approximate the moments in the linear minimum mean square error (LMMSE) estimation framework. Thus a new filter is developed and demonstrated to outperform some popular nonlinear filters through examples.
Published Version
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