General ℒ(p,q)-metric estimator of arbitrary complex impulsive interference in linear systems

A general L^(p,q)-metric p, q>0 on a probability space is defined, and the corresponding optimality criterion is derived. This criterion is applied to the problem of complex impulsive interference estimation in linear systems represented by scalar state-space equations. The closed-form expression of the a posteriori density of the state (interference) is computed recursively for both arbitrary i.i.d. state noise and any discrete-type measurement noise (multilevel complex signal). Optimal L^(p,q)-metric interference estimators based on different values of p and q are developed. As a test, the proposed algorithms are applied to estimate highly impulsive state processes driven by noise with symmetric α-stable distribution