The construction of filters in nonlinear deterministic systems (Q1359871)

The method of residuals is used to solve the problem of estimation when both object and observations involve noise. The estimation problem is solved by minimizing a certain functional, and this in turn involves solving a boundary-value problem at each instant of time. Depending on the recurrent method used to solve the relevant family of boundary-value problems, one obtains different representations of optimal nonlinear filters for the estimated quantities. The choice of a specific representation depends on the degree to which the object used to design the filter is well conditioned. Next, one constructs a locally optimal filter whose design is similar to the one of filters for linear problems.