Learning Hidden Markov Models with Geometrical Constraints
  Hidden Markov models (HMMs) and partially observable Markov decision
processes (POMDPs) form a useful tool for modeling dynamical systems. They are
particularly useful for representing environments such as road networks and
office buildings, which are typical for robot navigation and planning. The work
presented here is concerned with acquiring such models. We demonstrate how
domain-specific information and constraints can be incorporated into the
statistical estimation process, greatly improving the learned models in terms
of the model quality, the number of iterations required for convergence and
robustness to reduction in the amount of available data. We present new
initialization heuristics which can be used even when the data suffers from
cumulative rotational error, new update rules for the model parameters, as an
instance of generalized EM, and a strategy for enforcing complete geometrical
consistency in the model. Experimental results demonstrate the effectiveness of
our approach for both simulated and real robot data, in traditionally
hard-to-learn environments.
