Stochastic process estimation using the fault-tolerant interval functions

This work deals with the problem of the fault-tolerant estimation of discrete-time stochastic processes. A random walk process is estimated from the fusion of measurement uncertainty intervals provided by a set of sensors. Two algorithms of interval propagation and contraction are proposed. For both algorithms, interval contraction is done using fault-tolerant interval functions rather than the non-robust intersection operator. The first algorithm relies on the propagation of all the measurement intervals since the initial time. When probability distributions are specified for the variables of the system, it allows to predict and monitor the precision and availability of the results, and to offer guarantees on their reliability. The second algorithm, based on a prediction-correction scheme, is a fault-tolerant version of the recursive causal interval estimator.