Accurate continuous-discrete unscented Kalman filtering for estimation of nonlinear continuous-time stochastic models in radar tracking

摘要

This paper presents a new state estimation technology grounded in the unscented Kalman filtering for nonlinear continuous-time stochastic systems. The resulting accurate continuous-discrete unscented Kalman filter is based on adaptive solvers with automatic global error control for treating numerically the moment differential equations arising in the mean and covariance calculation of propagated Gaus- sian density. It is intended for an accurate and robust state estimation in nonlinear continuous-discrete stochastic systems of various sorts, including in radar tracking models. This new filter is examined in se- vere conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coor- dinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. For comparison, we also examine such efficient state estimators as the accurate continuous-discrete extended Kalman filter, the continuous-discrete unscented Kalman filter and the mixed-type accurate continuous- discrete extended-unscented Kalman filter designed earlier, but further modified in the present study. The comparison is fulfilled in terms of accuracy and efficiency of estimating the state in the mentioned air traffic control scenario.