  This paper presents a model-based method for fusing data from multiple
sensors with a hypothesis-test-based component for rejecting potentially faulty
or otherwise malign data. Our framework is based on an extension of the classic
particle filter algorithm for real-time state estimation of uncertain systems
with nonlinear dynamics with partial and noisy observations. This extension,
based on classical statistical theories, utilizes statistical tests against the
system's observation model. We discuss the application of the two major
statistical testing frameworks, Fisherian significance testing and
Neyman-Pearsonian hypothesis testing, to the Monte Carlo and sensor fusion
settings. The Monte Carlo Neyman-Pearson test we develop is useful when one has
a reliable model of faulty data, while the Fisher one is applicable when one
may not have a model of faults, which may occur when dealing with third-party
data, like GNSS data of transportation system users. These statistical tests
can be combined with a particle filter to obtain a Monte Carlo state estimation
scheme that is robust to faulty or outlier data. We present a synthetic freeway
traffic state estimation problem where the filters are able to reject simulated
faulty GNSS measurements. The fault-model-free Fisher filter, while
underperforming the Neyman-Pearson one when the latter has an accurate fault
model, outperforms it when the assumed fault model is incorrect.
