Adaptation with constant gains: analysis for slow variations

Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member. Closed-form expressions for the tracking MSE are obtained for parameters described by ARIMA processes. A key element of the analysis is that adaptation algorithms are expressed as linear time-invariant filters, here called learning filters, that work in open loop for slow parameter variations. Performance analysis can then easily be performed for slow variations, and stability is assured by stability of these learning filters.