An exact sequential solution procedure for a class of discrete-time nonlinear estimation problems

An exact procedure is developed for sequentially updating the optimal solution for a general discrete-time nonlinear least-squares estimation problem as the process length increases and new observations are obtained. The optimal sequential estimation equations are derived by means of an imbedding on two physically meaningful parameters, namely, the duration of the dynamical process and the value of the final observation. The optimal sequential estimation equations are contrasted with the approximate sequential estimation equations which would be obtained via extended Kalman filtering.