Stochastic stability of the continuous-time unscented Kalman filter

The performance of the modified unscented Kalman-Bucy filter (UKBF) for the nonlinear stochastic continuous-time system is investigated. The error behavior of the UKBF is analyzed. It is proved that the estimation error remains bounded if the system satisfies a detectability condition and both the initial estimation error and the disturbing noise terms are small enough. Furthermore, it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm. Moreover, some selected cases with both bounded and unbounded estimation error are demonstrated by numerical simulations.