Linear and nonlinear filters based on the improper Karhunen–Loève expansion

Suboptimal linear and nonlinear continuous-discrete filters for improper complex valued signals are given. The estimators are derived from a generalized improper Karhunen–Loève expansion of the signal involved and take the form of recursive algorithms which can easily be implemented in practice. Two examples show that the technique is feasible.

► To introduce an improper Karhunen–Loève expansion on any interval of the real line.
► To provide widely linear estimation algorithms based on the above series expansion.
► To extend the results obtained in the linear problem under a nonlinear philosophy.
► To illustrate the performance of the proposed estimators with different simulations.