Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models. Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the state-parameter distribution is simulated forward in time to compute end of life and remaining useful life. The first problem is typically solved through the use of a state observer, or filter. The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance. In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles. Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics.