A multiple principal components based adaptive filter

Proportionate normalized least mean squares (PNLMS) is an adaptive filter that has been shown to provide exceptionally fast convergence and tracking when the underlying system parameters are sparse. A good example of such a system is a network echo canceller. Principal components based PNLMS (PCP) extends this fast convergence property to certain nonsparse systems by applying PNLMS while using the principal components of the underlying system as basis vectors. An acoustic echo canceller is a possible example of this type of nonsparse system. Simulations of acoustic echo paths and cancellers indicate that PCP converges and tracks much faster than the classical normalized least mean squares (NLMS) and fast recursive least squares (FRLS) adaptive filters. However, when a basic parameter, like room temperature, changes, the underlying acoustic structure of the room changes as well and principal components of the room responses at one temperature are very different from those at another. This paper addresses this problem by using multiple sets of principle components as basis vectors and performing PNLMS in each basis set. Each set of principle components are derived from the room at a different temperature. The new algorithm, multiple principal components PNLMS (MPCP) is a generalization of PNLMS++. Simulations show the potential effectiveness of the approach.