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The problem of estimating a quaternion random signal is addressed under the condition of ℂη-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...
A series representation for continuous-time quaternion random signals is given. The series expansion is based on augmented statistics and provides uncorrelated scalar real-valued random variables. The proposed technique implies a dimension reduction of the four-dimensional original problem to a one-dimensional problem. As a particular case, the quaternion Karhunen-Loève expansion is obtained. Finally,...
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