A direct algorithm for joint optimal sensor scheduling and MAP state estimation for hidden Markov models

Sensing systems with multiple sensors and operating modes warrant active management techniques to balance estimation quality and measurement costs. Existing literature shows that in the joint sensor-scheduling and state-estimation problem for HMMs, estimator optimization can be done independently of the scheduler at each time step. We investigate the special case when a MAP estimator is used, and show how the joint problem can be converted to a standard Partially Observable MarkovDecision Process (POMDP), which in turn enables us to use POMDP solvers. As this approach is highly redundant, we derive a direct solution, which exploits the separability property while still utilizing standard solvers. When compared to standard techniques, the direct algorithm provides savings by a factor of the state-space dimension. Numerical results are given for an example motivated by wildlife monitoring.