Partitioned Update Binomial Gaussian Mixture Filter

Gaussian Mixture Filters (GMFs) are approximations of the Bayesian filter for nonlinear estimation. A GMF consists of a weighted sum of Gaussian components. Each component is propagated and updated with a Kalman-type filter. When the nonlinearity is small in the update step, the required number of components to yield an accurate approximation is small and vice versa. In this paper, we propose multiple improvements to GMF that reduce the computational load and increase the estimation accuracy. The new filter processes measurements so that the least nonlinear measurements will be applied first, this reduces the need for new components. After splitting a Gaussian component, the update is done so that the measurement function is evaluated only in nonlinear directions, which reduces computational load. Finally we propose a new faster algorithm for reducing the number of components after measurements are applied. Results show that the proposed improvements make the algorithm faster and improve the estimation accuracy with respect to a GMF that is used as a basis for development.