Stochastic convergence analysis of cubature Kalman filter with intermittent observations

Abstract

The stochastic convergence of the cubature Kalman filter with intermittent observations (CKFI) for general nonlinear stochastic systems is investigated. The Bernoulli distributed random variable is employed to describe the phenomenon of intermittent observations. According to the cubature sample principle, the estimation error and the error covariance matrix (ECM) of CKFI are derived by Taylor series expansion, respectively. Afterwards, it is theoretically proved that the ECM will be bounded if the observation arrival probability exceeds a critical minimum observation arrival probability. Meanwhile, under proper assumption corresponding with real engineering situations, the stochastic stability of the estimation error can be guaranteed when the initial estimation error and the stochastic noise terms are sufficiently small. The theoretical conclusions are verified by numerical simulations for two illustrative examples; also by evaluating the tracking performance of the optical-electric target tracking system implemented by CKFI and unscented Kalman filter with intermittent observations (UKFI) separately, it is demonstrated that the proposed CKFI slightly outperforms the UKFI with respect to tracking accuracy as well as real time performance.