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.
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