This study focuses on the development and application of a hybrid moving horizon estimator (HMHE) to achieve simultaneous estimation of both continuum and noncontinuum states in a constrained switching dynamic system. One of the major issues in a moving horizon estimation approach is the development of an arrival cost to summarize the effect of past and a prior information. In this work, we have developed a generalized arrival cost, which accounts for both continuum and noncontinuum states. A generalized hybrid state estimator, which can be used as a stand-alone continuum state estimator, or as a simultaneous continuum and noncontinuum state estimator, is developed. The effects of constraints, process, and measurement noise levels, as well as a moving horizon length on the simultaneous estimation of both the continuum and noncontinuum states are analyzed. The effectiveness of the HMHE is demonstrated through simulation studies, while its practical reliability is tested by conducting experimental studies on a distillation column. (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 480-492, 2012