Multiple-model filters have been used in literature to estimate unknown parameters; typically the estimate converges to the best value amongst the assumed values. However, the best value may not be the true value. A promising solution is proposed in this paper through the concept of an adaptive multiple-model filter. The adaptive multiple-model filter changes the models adaptively according to the model performance after the posterior probabilities corresponding to the models converge. The models may need to be changed several times before arriving at the true value of the parameter. Time for convergence time to the best value is critical to fast parameter estimation and the performance of the estimator itself. A novel quantum-inspired scheme based on the extended Grover's algorithm is presented that accelerates parameter convergence. Newton's method is used in the outer loop to find the true parameter value. It is proved that the quantum-inspired scheme can give an exponential boost to the convergence of the posterior probabilities corresponding to different models. Simulation results are provided that show the potential of the adaptive multiple-model filter in achieving accurate parameter estimation.