A real-time algorithm for separating locally-stationary random processes in the presence of noise

The forward separation of two locally stationary random autoregressive (AR) processes is presented. Current adaptive filter schemes focus on rapid minimum-mean-square-error (MSE) convergence as a measure of quality. Given an environment that is generally nonstationary, the MSE filters must be constructed with finite memory to allow timely adaptation to process changes. This approach unavoidably results in the MSE modeling of locally stationary noise events, which occur synchronously with the underlying information process. The removal of these noise events is analogous to the classical problem of separating general stochastic processes from colored noise. For the case presented, the task is made more difficult by coloring the noise as though it were a spectrally distinct process. The synchronous process occurrence is described analytically, and a real-time heuristic separation algorithm for multiple processes is proposed, with emphasis on retaining causality and computational efficiency