Sensor lattices

This paper addresses the sensing uncertainty associated with the many-to-one mapping from a physical state space onto a sensor observation space. By studying preimages of this mapping for each sensor, a notion of sensor dominance is introduced, which enables interchangeability of sensors and a clearer understanding of their tradeoffs. The notion of a sensor lattice is also introduced, in which all possible sensor models are arranged into a hierarchy that indicates their power and gives insights into the construction of filters over time and space. This provides a systematic way to compare and characterize information feedback in robotic systems, in terms of their level of ambiguity with regard to state estimation.