Efficient Square-Root Sigma-Point Filters Through Iterated Expectation Hybridization

A popular modern nonlinear estimation technique is the sigma-point filter, which estimates the moments of a transformed Gaussian distribution by evaluation of the transformation function at a set of deterministic strategically chosen points chosen by an appropriate integration rule. For more severe nonlinearities, a higher degree rule may be necessary to accurately estimate the moments. However, this comes at the cost of an increased number of evaluation points. A simple way to reduce the number of points is to reduce the dimension of the integration performed. This can be done by exploiting the structure of the dynamics and measurement functions to identify subspaces of the state that can be effectively treated through linearization or that do not contribute to the final result at all. This work presents a simple modification to the standard square-root sigma-point filter algorithm, which allows the exploitation of this subspace structure by leveraging properties of the Cholesky square-root matrix. The modification is particularly simple in the case that the final states of the state vector have no effect on the function result.