Estimating an abrupt perturbation of a dynamical system and identification of its parameters (Q1363252)

Discrete time linear stochastic systems are considered. There are permanent disturbances of white noise type and an abruptly appearing disturbance of unknown constant value which is applied to the system during an unknown time interval. One can use observations corrupted by random errors to estimate the level and the time interval of the disturbance. Instead of the traditional method of generalized likelihood ratio, the author suggests a new scheme based on a combination of a multimodel approach and stochastic dichotomy method [see the author, Lect. Notes Pure Appl. Math. 142, 41-56 (1993; Zbl 0790.93031)]. The main idea is rather simple. A set of possible values of uncertain parameters is discretized and the corresponding set of possible models is analyzed to check their adequacy to the observations with a sufficiently high probability. An iterative procedure is designed to decrease the size of uncertainty region. It is shown that the method can be realized in real time and it was used for the estimation of the distance to a moving target that performs a maneuver with unknown constant acceleration.