Performance analysis of distributed adaptive filters

This paper investigates the tracking performance of the normalized least mean square (LMS) based distributed adaptive filters, where a set of filters are designed to estimate the unknown time-varying parameters or signals using noisy measurements in a cooperative way. We show that under a general connected topology, the tracking error covariances of the distributed filters can be approximately described and calculated by a simple, linear and deterministic matrix difference equation. Different from most of the existing results, we do not require the regression vectors to satisfy stationarity or independency assumptions, which makes our theory applicable to stochastic systems with feedback.

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