Gaussian sum filtering using uncorrelated conversion for nonlinear estimation

Abstract

For nonlinear estimation, the Gaussian sum filter (GSF) provides a flexible and effective framework. It approximates the posterior probability density function (pdf) by a Gaussian mixture in which each Gaussian component is obtained using a linear minimum mean squared error (LMMSE) estimator. However, for a highly nonlinear problem with large measurement noise, the estimation performance of the LMMSE estimator is largely limited, since it is the best only within the class of linear estimators. This may further degrade the performance of the GSF, especially if a small number of these components are used. To improve the estimation performance, this paper proposes a Gaussian sum uncorrelated conversion (UC) based filter (GS-UCF), where the recently proposed uncorrelated conversion based filter (UCF) is applied to obtain the Gaussian components for Gaussian sum filtering. The UCF which is the LMMSE estimator using the measurement augmented by its uncorrelated conversions can outperform the original LMMSE estimator. Thus, the first two moments of the Gaussian component obtained by UCF can be more accurate than those obtained by the LMMSE estimator, which further improves the performance of the GSF. As an integration of the UCF and the GSF framework, the obtained filter is named as the Gaussian sum uncorrelated conversion based filter (GS-UCF). Simulation results show the effectiveness of the proposed estimator.