Hierarchical Dirichlet processes for tracking maneuvering targets

We consider the problem of state estimation for a dynamic system driven by unobserved, correlated inputs. We model these inputs via an uncertain set of temporally correlated dynamic models, where this uncertainty includes the number of modes, their associated statistics, and the rate of mode transitions. The dynamic system is formulated via two interacting graphs: a hidden Markov model (HMM) and a linear-Gaussian state space model. The HMM´s state space indexes system modes, while its outputs are the unobserved inputs to the linear dynamical system. This Markovian structure accounts for temporal persistence of input regimes, but avoids rigid assumptions about their detailed dynamics. Via a hierarchical Dirichlet process (HDP) prior, the complexity of our infinite state space robustly adapts to new observations. We present a learning algorithm and computational results that demonstrate the utility of the HDP for tracking, and show that it efficiently learns typical dynamics from noisy data.