Nonlinear filtering using measurements affected by stochastic, set-theoretic and association uncertainty

The problem is sequential Bayesian detection and estimation of nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler´s framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements, implemented as a particle filter. The numerical results demonstrate the filter performance: it detects the presence of targets reliably, and using a sufficient number of particles, the support of its posterior spatial PDF is guaranteed to include the true target state.