  This paper addresses the problem of decentralized, collaborative state
estimation in robotic teams. In particular, this paper considers problems where
individual robots estimate similar physical quantities, such as each other's
position relative to themselves. The use of pseudomeasurements is introduced as
a means of modelling such relationships between robots' state estimates, and is
shown to be a tractable way to approach the decentralized state estimation
problem. Moreover, this formulation easily leads to a general-purpose
observability test that simultaneously accounts for measurements that robots
collect from their own sensors, as well as the communication structure within
the team. Finally, input preintegration is proposed as a
communication-efficient way of sharing odometry information between robots, and
the entire theory is appropriate for both vector-space and Lie-group state
definitions. To overcome the need for communicating preintegrated-covariance
information, a deep autoencoder is proposed that reconstructs the covariance
information from the inputs, hence further reducing the communication
requirements. The proposed framework is evaluated on three different simulated
problems, and one experiment involving three quadcopters.
