Computationally efficient sparse-grid Gauss-Hermite filtering

A new nonlinear filtering algorithm based on sparse-grid Gauss-Hermite filter (SGHF) incorporated with the technique of algorithm adapting to dimensions based on their nonlinearity, is presented. The motive of this work is to reduce the computatioanl load of SGHF, while maintaining similar filtering accuracy. This is achieved by implementing adaptive tensor product to construct the multidimensional sparse-grid quadrature points. This reduction in computational burden may increase the scope of application of this filtering algorithm for higher dimensional problems in on-board applications. Performance of the proposed algorithm is illustrated by estimating the frequency and amplitude of multiple superimposed sinusoids.