NIRK-based accurate continuous-discrete extended Kalman filters for estimating continuous-time stochastic target tracking models

Journal of Computational and Applied Mathematics, 316 (2017), 260-270
http://dx.doi.org/10.1016/j.cam.2016.08.036

This paper presents three state estimators grounded in the variable-stepsize Gauss- and Lobatto-type Nested Implicit Runge–Kutta (NIRK) formulas of orders 4 and 6 and designed for treating continuous-time stochastic systems arisen in radar tracking. Our filters are built within the Extended Kalman Filtering (EKF) framework and based on accurate numerical integrations of the corresponding Moment Differential Equations (MDEs). Automatic local and global error regulation mechanisms implemented in these methods allow the committed discretization error to be under control and made negligible in automatic mode. The latter raises the state estimation accuracy of the constructed filters, significantly. This also leads to the advanced notion of Accurate Continuous–Discrete Extended Kalman Filtering (ACD-EKF) developed by Kulikov and Kulikova in 2013–2016. Our novel methods are constructed within the same approach, but possess the improved accuracy and efficiency in comparison to their predecessors due to both more effective error control mechanisms implemented for integrating MDEs and more accurate iterations used for treating arisen nonlinear equations in the revised filters. Numerical experiments with the updated state estimators and their comparison to the cited earlier-designed ACD-EKFs are fulfilled in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in Matlab. This examination suggests that the novel state estimation algorithms outperform their predecessors and possess a promising potential for solving target tracking tasks in real-world applications