Explicit State-Estimation Error Calculations for Flag Hidden Markov Models - 2016
State estimation is studied for a special class of flag Hidden Markov Models (HMMs), which comprise 1) an arbitrary finite-state underlying Markov chain and 2) a structured observation process wherein a subset of states emit distinct flags with some chance whereas different states are unmeasured. For flag HMMs, an specific computation of the chance of error for the maximum-likelihood filter and smoother is developed. Conjointly, the form of the optimal filter is further characterized in terms of the time since the last flag, and this result's used to more simplify the error-likelihood computation. Some preliminary graph-theoretic insights into the error chance and its computation are discussed. Finally, these algebraic and structural results are leveraged to handle sensor placement in 2 examples, as well as one on activity-monitoring in an exceedingly home setting that is drawn from field data. These examples indicate that low error-likelihood filtering and smoothing can be achieved with comparatively few sensors.
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