JOINT OPTIMAL ESTIMATION, IDENTIFICATION, AND HYPOTHESIS-TESTING IN DISCRETE DYNAMIC-SYSTEMS

Many important theoretical and practical problems cannot be solved by a separate application of one of the theories of classical estimation, identification, and hypothesis but require the joint use of all of th ese theories simultaneously for their solution. This is connected with a new, more complicated statement of the problem. This paper reveals the structure and obtains equations of the algorithm for joint estimat ion, identification, and hypothesis testing, which is optimal with res pect to the test of the maximum of the a posteriori probability. All t hree estimation methods (filtration, prediction, and smoothing) are co nsidered in a unified form. The problem of optimizing the Bayesian ris k is stated, possible constraints on the domain of unknown parameters are taken into account, important particular cases of the general stat ement of the problem that are of independent interest are studied, and the results are presented in the simplest and most obvious form. The methodology of the use of the theoretical results obtained is illustra ted by examining an example connected with the determination of the fa ct and parameters of a maneuver of an aircraft.