Gn. Milshtein et Oe. Solovyeva, THE CONSTRUCTION OF FILTERS IN NONLINEAR DETERMINISTIC SYSTEMS, Journal of applied mathematics and mechanics, 58(6), 1994, pp. 971-982
The method of residuals (see, e.g. [1-31]) is used to serve the proble
m of estimation when both object and observations involve noise, and t
he input determination problem [3-5] is considered. These estimation p
roblems are solved by minimizing a certain functional, and this in tur
n involves solving a boundary-value problem at each instant of time. D
epending on the recurrent method used to solve the relevant family of
boundary-value problems, one obtains different representations of opti
mal non-linear filters for the estimated quantities. The choice of a s
pecific representation depends on the degree to which the object with
whose help the filter is being designed is well conditioned. A locally
optimal filter of a design similar to that of filters for linear prob
lems is constructed.