Rosa M. Fernandez-Alcala, Jesus Navarro-Moreno, Juan C. Ruiz-Molina, and Nuria Ruiz-Fuentes
Gaussian signals, Quadratic estimation, Quaternion widely linear processing
A new solution to the problem of estimating any functional of a Gaussian signal observed in the presence of an additive noise is provided from the information supplied by both the observation process and its square, at a finite discrete instant of time. This problem is addressed in the quaternion domain and under a widely linear processing, by using a Karhunen-Lo\`eve series expansion. The proposed solution takes the form of a suboptimum estimator which allows the estimation of a functional of the signal through a recursive algorithm. From the own expression of this suboptimum estimator, its superiority over the complex widely linear solution is guaranteed. Moreover, by way of illustration, a simulation example is developed.
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