Numerical methods for nonlinear filtering of signals and measurements
Kulikova, Maria; Kulikov, Gennady Yu
Computational Technologies, 21(4) (2016), 64-98
This paper studies numerical methods of contemporary nonlinear Kalman filtering for estimation of unknown vector of state in stochastic continuous-time systems presented by Ito-type stochastic differential equations with discrete measurements. The elaborated methods are analysed and compared in the case of severe conditions of tackling a seventh-dimensional radar tracking problem, where an aircraft executes a coordinated horizontal turn. The latter problem is considered to be a challenging example for testing nonlinear filtering algorithms. This paper explores such effective state estimation methods as the cubature and unscented Kalman filters, including their square-root versions. Implementation particulars and performances of the mentioned techniques are studied for various values of aircraft’s turn rate and sampling time. New variants of the extended and unscented Kalman filters are also presented for treating continuousdiscrete stochastic systems. It is shown that the new methods outperform the traditional extended Kalman filter in the considered air traffic control scenario.