A semi-widely linear filtering algorithm for ℂη-proper quaternion signals based on randomly modeled observations

The problem of estimating a quaternion random signal is addressed under the condition of ℂ
^η
-properness. Assuming the signal is not always accessible, observations of the signal are modeled by means of a multiplicative noise given by a sequence of independent Bernoulli random variables. Using the innovation method, a filtering algorithm is developed through a semi-widely linear processing. The superiority of the proposed semi-widely linear filter over the conventional one is illustrated through a simulation example.