A real-time state filtering and prediction scheme which is adaptive, recursive, and suboptimal is proposed for discrete time nonlinear dynamic systems with either Gaussian or non-Gaussian noise. The proposed scheme (PR) estimates states adaptively whenever both the observation is available and there exists a non-zero and finite number of real state roots of the observation model, otherwise the PR estimates states non-adaptively. The PR state transition and observation functions are as general as the state transition and observation functions for particle filters. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple hypothesis testing. The PR first detects state estimate divergence points along the time axis, and then state estimate divergences are prevented by introducing new admissible state quantization levels; whereas the extended Kalman filter (EKF), sampling importance resampling (SIR) particle filter (bootstrap filter), and auxiliary sampling importance resampling (ASIR) particle filter produce diverging state estimates from actual state values for many dynamic models. The PR uses state transition functions in order to calculate transition probabilities from gates to gates. If these transition probabilities are somehow available, then state transition functions are not needed for state estimation with the PR; whereas state transition functions are necessary for state estimation with both particle filters and the EKF. The PR is very suitable for state estimation with either constraints imposed on state estimates or missing observations. The PR is more general than grid-based estimation approaches. Monte Carlo simulations have shown the effectiveness of the PR, that is, the PR performance is better than the performances of the EKF, SIR, and ASIR particle filters for many nonlinear models with white Gaussian noise, four examples of which are presented in the paper. (C) 2012 Elsevier Inc. All rights reserved.