Linear and nonlinear smoothing algorithms for widely factorizable signals

The fixed-point smoothing estimation problem is analyzed for a class of improper complex-valued signals, called widely factorizable, characterized because the correlation of the augmented vector formed by the signal and its conjugate is a factorizable kernel. For this type of signal, widely linear processing is the most suitable approach considering the complete information of the augmented correlation function. Then, from only the knowledge of the second order properties of the augmented vectors involved, linear and nonlinear smoothing algorithms are provided without the necessity of postulating a state-space model. Moreover, in the linear case, recursive formulas for computing the fixed-point smoothing estimation error are proposed.

► WL fixed-point smoothing algorithms are given for both linear and nonlinear systems. ► Only second-order statistics information is used and no state-space model is needed. ► Superiority of WL algorithms over conventional SL ones is numerically illustrated.