Least squares recursive differential-corection estimation in nonlinear problems

A general formulation of recursive filtering in non-linear problems is presented. The time dependence of variables and parameters to be estimated is described by a set of nonlinear differential equations for which an exact explicit solution may not be available. Another source of nonlinearities may be the relationships between observations and the variables and parameters required for complete description of the observed process. These nonlinearities are handled by first-order perturbation theory plus iteration. The approach used to derive the filter equations is a simple extension of classical least squares or regression theory. Trajectory estimation examples are used to illustrate the techniques.