Gn. Milshtein et Oe. Solovyeva, RECURRENT ESTIMATION AND IDENTIFICATION OF THE PARAMETERS IN NONLINEAR DETERMINISTIC SYSTEMS, Journal of applied mathematics and mechanics, 55(1), 1991, pp. 29-36
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/).