Nonstationary effects in adaptive filtering

Adaptive, or time-varying filters may be characterized as input-dependent operators in which the dependence extends over a finite interval of previous inputs, No. Thus, the filter coefficients at time n are independent of all inputs previous to n - No. The simplest example of an adaptive filter with this property is the block least-squares approach used in speech processing. Continually varying least-squares algorithms and the LMS algorithm, however, may also be modelled using this approach. In this paper, we consider the performance of adaptive filters when the input contains significant energy components in the frequency range of 0 < f < 1/No. Surprising results are obtained for this case and conventional analytical results obtained from a stationary analysis are shown to be inappropriate. Examples taken from magnetometer data processing are presented to illustrate the results.