Adaptive observers for linear time-variant stochastic systems with disturbances

Motivated by fault detection and isolation problems, we present an approach to the design of state observers for linear time-variant stochastic systems with unknown parameters and disturbances. The novelties with respect to more conventional techniques are: (a) the joint estimation of parameters and disturbances can be carried out; (b) it is a full-stochastic approach: the unknown parameters and disturbances are random quantities and prior information, in terms of means and covariances, can be easily taken into account; (c) the observer structure is not fixed a priori, rather derived from the optimal infinite dimensional one by means of a sliding window approximation; (d) in contrary to descriptor systems techniques, which estimate the state starting from a restricted set of disturbances-free equations, our approach is focused on disturbances estimation, from which state estimates are derived straightforwardly.