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Sequential hypothesis testing for selection of system parameter values from a discrete set has been used by many researchers. We consider recursive (on-line) identification. We have reformulated the problem in terms of a stopping criterion, upper and lower thresholds determined by a priori error probabilities. The main contribution is several expressions for the expected number of observations required to reach the threshold. Therefore not only convergence but rate of convergence is indicated. This is especially useful in considering quantization of a continuous parameter space. A strategy for constructing finer and finer meshes is given for this case, in which only a given number of Kalman filters can he used at one time. Monte-Carlo simulation was used to attempt to define a boundary between this method and that of S??derstr??m.