Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.