A measure of the tracking capability of recursive stochastic algorithms with constant gains

A criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time-varying systems; the optimal gain for a given disturbance is also calculated. This criterion is seen to have some connection with the Fisher information matrix, and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances. Examples of applications are given in the areas of identification theory and data communication theory.