A modification of Ljung's theorem with application to the analysis of extended Kalman filtering

AbstractExtended Kalman filtering is applied to estimate the parameters of a linear dynamic stochastic system given in a state space description. The equation describing the dynamics of the system is implicit i.e. the equation yields a linear transform of the new state vector. The inverse mapping is estimated recursively. To analyze the convergence properties an extension of Ljung's scheme is suggested in which a mixed (stochastic and deterministic) recursion is used