Semi-Widely Linear Filter with Intermittent Observations and Correlated Noises at the Same Epoch

Abstract

The filtering estimation problem is addressed for a quaternion linear system with intermittent observations and correlated noises at the same epoch. Under $\mathbb {C}^{\eta }$-properness conditions, a semi-widely linear processing is used to derive an online recursive algorithm for the computation of the quaternion signal of interest as well as its mean squared error. The proposed algorithm allows the efficient computation of three and four- dimensional signals with a reduced computational burden. By means of a numerical example, the benefit of our solution with respect to the conventional one is analyzed.