Stochastic observability and fault diagnosis of additive changes in state space models

We derive a Kalman filter based on data from a sliding window. This is used for a new approach to fault detection and diagnosis, where the state estimate from past data is compared to the state estimate of some of the future data. We suggest a method to judge the quality of diagnosis in a simple way. For fault estimation in the diagnosis, the general concept of stochastic observability in linear systems is introduced. Its role in the design step is illustrated on a problem of estimating the true velocity of a car.