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Linear estimation under a minimum mean-square-error criterion in a quasi-stationary environment is considered. A generalized form of the Widrow-Hoff algorithm is employed for the estimation. Performance is measured by the excess error over the minimum meansquare error. A Gaussian assumption is used to determine this performance and determine simple bounds. The transient solution for the algorithm is investigated and a convergence rate determined. These results are used to optimize the algorithm parameters and bound the performance as a function of the environmental rate of change. The Robbins-Monro algorithm for finding the root of a linear regression function suggests the use of fixed step size stochastic approximation algorithms to solve more general quasi-stationary estimation problems.