A general solution to the continuous-time estimation problem under widely linear processing

A general problem of continuous-time linear mean-square estimation of a signal under widely linear processing is studied. The main characteristic of the estimator provided is the generality of its formulation which is applicable to a broad variety of situations, including finite or infinite intervals, different types of noises (additive and/or multiplicative, white or colored, noiseless observation data, etc.), capable of solving three estimation problems (smoothing, filtering or prediction), and estimating functionals of the signal of interest (derivatives, integrals, etc.). Its feasibility from a practical standpoint and a better performance with respect to the conventional estimator obtained from strictly linear processing is also illustrated.