Multiestimates for Linear-Gaussian Continuous Systems under Communication Constraints
It is well-known that a state estimation problem is an important part of the more general problem of control under incomplete information. In many cases control strategies are built on the base of various algorithms of state estimation. In this work, estimation problems for linear systems are considered under mixed disturbances. It is supposed that the determined disturbances are constrained by convex and compact restrictions, and the random disturbances are standard Wiener processes. Random information sets named for brevity multiestimates are defined. The entered multiestimates in the absence of random components coincide with information sets from the theory of guaranteed estimation. The structure of multiestimates is considered, and it is shown that they are the sum of a random vector and a determinate set, which depend on a set of parameters. In turn, the given set of parameters unequivocally defines the conditional and unconditional probability of inclusion of the multiestimate in a covering set. Special cases are considered, and the question on the form of the covering set is discussed. A modified problem is considered under communication constraints in which the limited capacity of the digital data link and random errors in a communication channel is taken into consideration. Relations between the accuracy of restoration of multiestimate's parameters, the length of a transferred word, and a transmission frequency are received in the noiseless case. A number of results are illustrated on an example.