Kalman-like filtering with intermittent observations and non-Gaussian noise

Abstract

The paper concerns the sub-optimal filtering problem when the measurement signal is sent through an unreliable channel and the noise signals are not necessarily Gaussian. In particular, we assume that the measurement packet losses are modeled by an i.i.d. Bernoulli sequence with known probability mass function, and the moments of the (generally) non-Gaussian noise sequences up to the fourth order are known. By mean of a suitable rewriting of the system through an output injection term, and by considering an augmented system with the second-order Kronecker power of the measurements, an optimal solution among the quadratic transformations of the output is provided. Numerical simulations show the effectiveness of the proposed method.