Probabilistic processing of interval-valued sensor data

When dealing with sensors with different time resolutions, it is desirable to model a sensor reading as pertaining to a time interval rather than a unit of time. We introduce two variants on the Hidden Markov Model in which this is possible: a reading extends over an arbitrary number of hidden states. We derive inference algorithms for the models, and analyse their efficiency. For this, we introduce a new method: we start with an inefficient algorithm directly derived from the model, and visually optimize it using a sum-factor diagram.