Stochastic Integration Filter: Theoretical and Implementation Aspects

The paper focuses on state estimation of discrete-time nonlinear stochastic dynamic systems with a special focus on the stochastic integration filter. The filter is an representative of the Gaussian filter and computes the state and measurement predictive moments by making use of a stochastic integration rule. As a result, the calculated values of the moments are random variables and exhibit favorable asymptotic properties. The paper analyzes theoretical consequences of using stochastic integration rules and proposes several modifications that improve the performance of the stochastic integration filter. As the filter requires multiple iterations of the stochastic rule, its computational costs are higher in comparison with other Gaussian filters. To reduce the costs, several modifications are proposed in the paper, which are also concerned with numerical stability issues. The proposed modifications are illustrated using both static and dynamic numerical examples used in target tracking.