Optimal linear extrapolation of realizations of a stochastic process with error filtering in correlated measurements

Control problems often require predicting the future state of the controlled plant given its present and past state. The practical relevance of such prediction problems has spurred many studies and led to the development of various methods of solution. These methods can be divided into two large directions: deductive methods, which assume that in addition to the sample the researcher also has some prior information, and inductive methods, where the main heuristic is the choice of an external performance criterion. Each of these directions has its strengths and weaknesses, and is characterized by a specific domain of application. An obvious advantage of the inductive approach is that it requires a minimum of information (in the limit, the problem is solved using a single observed realization, which is not feasible with any other method). However, the heuristic choice of the external criterion, substantially influence the accuracy of extrapolation. Deductive methods, in their turn, ensure a guaranteed, prespecified extrapolation accuracy, but their application requires preliminary, fairly time consuming and costly accumulation of empirical data about the observed phenomenon. The two main directions are mutually complementary, and the use of a particular direction in applications is mainly determined by the volume of datamore » that have been accumulated up to the relevant time.« less