This paper presents a real-time recursive state filtering and prediction scheme (PR) for discrete nonlinear dynamic systems with nonlinear noise and random interference, such as undesired random jamming or clutter. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple composite hypothesis testing. The PR outperforms both the sampling importance resampling (SIR) particle filter and auxiliary sampling importance resampling (ASIR) particle filter; whereas Kalman-based nonlinear filters are, in general, inadequate for state estimation of many nonlinear dynamic systems with nonlinear noise and interference. Moreover, the PR is more general than grid-based estimation approaches. It is also very suitable for state estimation with either constraints imposed on state estimates or missing observations. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.