Estimation of Widely Factorizable Hypercomplex Signals with Uncertain Observations

The filtering estimation problem under uncertainty conditions is addressed for a class of improper quaternion signals, called widely factorizable, characterized because their augmented correlation function is a factorizable kernel. From the knowledge of the correlation functions involved, a recursive algorithm is designed for the computation of the widely linear (WL) filtering estimate and its associated mean squared error. The main advantage of the proposed solution is that it can be applied in situations where a state-space model is not readily at hand. The benefits of the proposed WL filtering algorithm is analyzed through a simulation example where WL filtering errors are compared with respect to the strictly linear (SL) counterparts, showing the superior behavior of the former over the latter.

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