RECURRENT ESTIMATION AND IDENTIFICATION OF THE PARAMETERS IN NONLINEAR DETERMINISTIC SYSTEMS

Estimation of the phase states and parameters of non-linear determinis tic systems of differential equations is reduced to the determination of initial data which minimize a certain functional which depends on o bservations and prior information. Equations are derived for an optimu m non-linear filter whose realization demands repeated integration of auxiliary systems of differential equations. A modified, simpler filte r, which is nearly optimum in many quite typical situations, is constr ucted. consideration is given to the problem of estimation based on pa rtly-known initial data, a special case of which is identifying the pa rameters of a system whose phase states are known at the initial time. In the linear case, if there is no a priori information, the results obtained here represent a deterministic version of Kalman filtering. T he most constructive results in estimation have been obtained for line ar systems (for general approaches see /1/, for recurrent filtration g iven known a priori information of a statistical nature about the init ial data and noise in the object and in the observations, see /2/, for a deterministic version of recurrent estimation along game-theoretic lines, assuming known restrictions on noise, see /3/, and for a determ inistic version of Kalman filtering see /4, 5/).