Quadratic filtering of non-Gaussian systems with intermittent observations

In this paper we consider the problem of state estimation for linear discrete-time non-Gaussian systems with intermittent observations. Intermittent observations result from packet dropouts when data travel along unreliable communication channels, as in the case of wireless sensor networks, or networked control systems. We assume that the receiver does not know the sequence of dropouts, which is common in many circumstances, e.g., wireless sensor networks. We derive the quadratic estimate of the state by means of a recursive algorithm. The solution is obtained by applying the Kalman filter to a suitably augmented system, which is fully observable. The augmented system is constructed as the aggregate of the actual system, and the observable part of a system having as state the second Kronecker power of the original state, namely the quadratic system. To extract the observable part of the quadratic system we exploit the knowledge of the rank of the corresponding observability matrix. This approach guarantees the internal stability of the estimation filter. Simulation results highlight the effectiveness of the proposed approach.