An estimate of the tracking ability of adaptive algorithms

A study is made of a fairly general algorithm for tracking properties that can be described in a linear regression form (including autoregressive models and the like). An explicit expression for the mean square error between the estimated and the true (time-varying) parameter is established. For slow adaptation this expression can be arbitrarily well approximated by a much simpler expression. The treatment differs from related studies, using weak convergence theory, averaging, etc., in that the results are not asymptotic in nature and they are applicable also to the transient phase, as well as over unbounded time intervals