  In this paper, a new nonlinear filter based on sparse-grid quadrature method
has been proposed. The proposed filter is named as adaptive sparse-grid
Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the
dimensions equally, whereas the ASGHF assigns a fewer number of points along
the dimensions with lower nonlinearity. It uses adaptive tensor product to
construct multidimensional points until a predefined error tolerance level is
reached. The performance of the proposed filter is illustrated with two
nonlinear filtering problems. Simulation results demonstrate that the new
algorithm achieves a similar accuracy as compared to sparse-grid Gauss-Hermite
filter (SGHF) and Gauss-Hermite filter (GHF) with a considerable reduction in
computational load. Further, in the conventional GHF and SGHF, any increase in
the accuracy level may result in an unacceptably high increase in the
computational burden. However, in ASGHF, a little increase in estimation
accuracy is possible with a limited increase in computational burden by varying
the error tolerance level and the error weighting parameter. This enables the
online estimator to operate near full efficiency with a predefined
computational budget.
