Extended Kalman filter techniques and difference equation for time varying stochastic nonlinearities

In this paper the Extended Kalman filter is designed for time varying dynamic model by linearizing the first order nonlinear system. Taylor's series expansion is applied in the Extended Kalman filter algorithm to identify the dominant element. The projected Extended Kalman filter consists of forecast and data assimilation. The forecast error covariance and posterior error covariance is obtained. The Iterated Extended Kalman filter improves the accuracy by linearizing the most recent estimate with higher computational time. An estimation error and stability conditions of nonlinear system is obtained and shown that estimation error is exponentially bounded with mean square.