A heuristic method is proposed to overcome the divergence problems of the minimum variance state and parameter estimator. The algorithm uses adaptive, exponential fading. Rapid fading occurs when data give a poor fit with the model, and slow fading occurs when the data give a good fit. Subject to an observability condition, the estimator is shown to yieldN-step exponential convergence. The usefulness of the algorithm is demonstrated through one extended Kalman filter application. The algorithm has also been applied to industrial processes for state estimation and adaptive control.