Abstract Experience has shown that even carefully designed and tested robots may encounter anomalous situations. It is therefore important for robots to monitor their state so that anomalous situations may be detected in a timely manner. Robot fault diagnosis typically requires tracking a very large number of possible faults in complex non-linear dynamic systems with noisy sensors. Traditional methods either ignore the uncertainty or use linear approximations of non-linear system dynamics. Such approximations are often unrealistic, and as a result faults either go undetected or become confused with non-fault conditions. Probability theory provides a natural representation for uncertainty, but an exact Bayesian solution for the diagnosis problem is intractable. Monte Carlo approximations have demonstrated considerable success in application domains such as computer vision and robot localization and mapping. But, classical Monte Carlo methods, such as particle filters, can suffer from substantial computational complexity. This is particularly true with the presence of rare, yet important events, such as many system faults. This paper presents an algorithm that provides an approach for computationally tractable fault diagnosis. Taking advantage of structure in the domain it dynamically concentrates computation in the regions of state space that are currently most relevant without losing track of less likely states. Experiments with a dynamic simulation of a six-wheel rocker-bogie rover show a significant improvement in performance over the classical approach.