Detection and estimation of partially-observed dynamical systems: an outer-measure approach

In real environments, it is seldom that physical dynamical systems can be observed without detection failures and without disturbances from the background. Yet, a vast majority of the literature regarding Bayesian inference for such systems ignore these undesired effects and assume that pre-processing can be applied to remove them. To some extent, this goes against the Bayesian philosophy which promotes the integration of the different aspects of the problem into a joint formulation. However, such a formulation usually involves a precise modelling of these adverse effects as well as the setting of the corresponding parameters, which is not always feasible or realistic. In this article, we propose to use outer measures of a certain form to allow for additional flexibility in the modelling of these effects within the Bayesian paradigm. It is shown that detection and estimation of partially-observed dynamical systems can be performed with little to no knowledge about the background disturbances and with only an upper bound on the probability of detection failure. It is conformed in simulations that such an approach can compete with standard methods even when the latter are given the true parameter values.