Robot location estimation in the situation calculus

Location estimation is a fundamental sensing task in robotic applications, where the world is uncertain, and sensors and effectors are noisy. Most systems make various assumptions about the dependencies between state variables, and especially about how these dependencies change as a result of actions. Building on a general framework by Bacchus, Halpern and Levesque for reasoning about degrees of belief in the situation calculus, and a recent extension to it for continuous probability distributions, in this paper we illustrate location estimation in the presence of a rich theory of actions using examples. The formalism also allows specifications with incomplete knowledge and strict uncertainty, as a result of which the agent's initial beliefs need not be characterized by a unique probability distribution. Finally, we show that while actions might affect prior distributions in nonstandard ways, suitable posterior beliefs are nonetheless entailed as a side-effect of the overall specification.