Estimation on lumped parameter systems: dynamic optimization approach

State and parameter estimation of lumped systems maybe achieved through output fitting on a finite horizon. Output fitting, if the process noise is not negligible, needs solution of a complex optimization problem. Through the optimization a noise pattern is sought which pus the best fitting. To get more adequate result, constraints on the measurement and process noise may be taken into consideration, which makes the optimization problem more complex. To the stochastic computation a long horizon is desirable; however; the number of variables increases linearly with the length of horizon. A dynamic optimization method, which is based on a series of two-stage optimization and iteration and has been developed for solution of optimum control problems, is suitable for solution of the estimation problem, too. Through the method, the linear or nonlinear state or parameter estimation may be paralleled with computation of linear quadratic control. The introduced parameter estimation method gives also the filtered and estimated states on the horizon. Recursive parameter estimation and filtering algorithms may be repeated at the next sampling instant, and estimates of states, disturbances and parameters on the preceding horizon are used as initial values. Through the computation, the past estimates are updated, according to the new conditions.