Uncertain Timestamps in Linear State Estimation

We consider a linear state estimation problem, where, in addition to the usual timestamped measurements, observations with uncertain timestamps are available. Such observations could, e.g., come from traces left by a target in a tracking scenario or from witnesses of an event and have the potential to improve the estimation accuracy significantly. We derive the posterior distribution and point estimators for a linear Gaussian smoothing formulation of this problem and illustrate with two numerical examples.