Disertation

Ph.D.

Ústav aplikované matematiky, Fakulta dopravní, ČVUT

Na Florenci 25, Praha 1

2008

Ing. Lenka Pavelková, Ph.D. (ÚTIA - Oddělení adaptivních systémů)

state model, uniform innovations, state filtration, paramete

State estimation is an important subtask of a range decision making problems. Kalman filter is a standard method of its solving. There, a state model with normally distributed innovations is used. An unbounded support of normal distribution may cause troubles in some applications where real quantities are bounded, e.g. in transportation problems. Then, techniques dealing with unknown-but-bounded equation errors can be applied. The resulting min-max type algorithms are useful but the related decision-making tasks are unnecessarily difficult because of missing statistical tools. Above mentioned drawbacks can be avoided by assuming that the involved innovations have a distribution with restricted support. We assume that the innovations of the state model are uniformly distributed. Under this assumption, straightforward use of Bayesian approach provides either batch filtering, i.e., state estimation or batch parameter estimation.