Resampling-free Stochastic Integration Filter
Ondřej Straka, Jindřich Duník · 2020
The paper deals with the state estimation of nonlinear stochastic systems with additive Gaussian noises by means of the Gaussian filters leveraging numerical integration rules. The filters were derived under the assumption of the joint state and measurement predictive density being Gaussian, which is violated by the system nonlinearity. Such violation can hardly be monitored by the standard Gaussian filters, which re-generate a new set of points for each involved numerical integration to accommodate their variance increase due to the additive noises. The paper proposes a stochastic integration filter algorithm that modifies the points instead of their resampling and thus admits reusing the points in the next time steps. The distribution of the points can thus bear more information than just the first two moments in case of the standard Gaussian filters. The acquired information is then utilized for the Gaussian assumption monitoring purposes. In the event of the assumption violation, the filter may change its behavior. As a by-product of reusing the points, the computational costs of the proposed filter are significantly reduced compared to the standard stochastic integration filter.