Estimation Algorithm Based on the Stochastic Approximation Method

This paper presents a state estimation algorithm of a single variable nonlinear system to which the stochastic approximation is applied. First, under a weaker condition than any previous one, it is shown that the estimation error by this algorithm converges to zero in the mean square for a disturbance free message process. Further, it is clarified that, under a still weaker condition, the estimation error variance for a nonlinear message process with a disturbance which may be correlated with a measurement noise has a finite upper bound which is previously given by statistical parameters of a disturbance and a measurement noise, if known. Finally, some digital simulations for simple nonlinear systems demonstrate that the convergence rate of this algorithm is very fast and that the error variance converges to a smaller value than a theoretical one.