The construction of filters in non-linear deterministic systems

The method of residuals (see, e.g. [1–31]) is used to solve the problem of estimation when both object and observations involve noise, and the input determination problem [3–5] is considered. These estimation problems are 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 non-linear niters for the estimated quantities. The choice of a specific 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 problems is constructed.