Recursive state estimation for linear systems with mixed stochastic and set-bounded disturbances

Recursive state estimation is considered for discrete time linear systems with mixed process and measurement disturbances that have stochastic and (convex) set-bounded terms. The state estimate is formed as a linear combination of initial guess and measurements, giving an estimation error of the same mixed type (and causing minimal interference between the two kinds of error). An ellipsoidal over-approximation to the set-bounded estimation error term allows to formulate a linear matrix inequality (LMI) for optimization of the filter gain, considering both parts of the estimation error in the objective. With purely stochastic disturbances, the standard Kalman filter is recovered. The state estimator is shown to work well for an event based estimation example, where measurements are very coarsely quantized.