The purpose of this report is to introduce an adaptive estimation and parameter identification scheme which the authors call Multiple Model Estimation Algorithm (MMEA). The MMEA consists of a bank of Kalman filters with each matched to a possible parameter vector. The state estimates generated by these Kalman filters are then combined using a weighted sum with the a posteriori hypothesis probabilities as weighting factors. If one of the selected parameter vectors coincides with the true parameter vector, this algorithm gives the minimum variance state and parameter estimates. Algorithms for filtering, smoothing, and prediction are derived for linear and nonlinear systems. They are described in a tutorial fashion with results stated explicitly so that they can be readily used for computer implementation. Approaches for the extension of MMEA to a more general class of adaptive estimation problems are outlined. Several further research topics are also suggested.