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In this paper a generalized multiple-model adaptive estimator (GMMAE) is presented that can be used to estimate unknown model and/or filter parameters, such as the noise statistics in filter designs. The main goal of this work is to provide an increased convergence rate for the estimated model parameters over the traditional multiple-model adaptive estimator (MMAE). Parameter elements generated from a quasi-random sequence are used to drive multiple parallel filters for state estimation. The current approach focuses on estimating the process noise covariance by sequentially updating weights associated with the quasi-random elements through the calculation of the likelihood function of the measurement-minus-estimate residuals, which also incorporates correlations between various measurement times. For linear Gaussian measurement processes the likelihood function is easily determined. A proof is provided that shows the convergence properties of the generalized approach versus the standard MMAE. Simulation results, involving a two-dimensional target tracking problem and a single-axis attitude problem, indicate that the new approach provides better convergence properties over a traditional multiple-model approach.