Joint Estimation of Trajectory and Dynamics from Paired Comparisons

Recent literature has developed methods for localizing a low-dimensional vector $w$ from paired comparisons of the form “ $w$ is closer to $\pmb{p}$ than $\pmb{q}$, ” where $\pmb{p}$ and $q$ are selected from a fixed set of landmark points and $w$ does not change over time. In this work, we consider a time-varying extension of this problem, in which $w$ evolves according to some unknown dynamics model. We consider the task of actively selecting informative paired comparisons between landmark points to jointly estimate the state trajectory and identify the true dynamics model from a finite set of candidate models. Leveraging information-theoretic insights, we propose selecting pairs that simultaneously maximize information gain about both the trajectory and dynamics model, and propose a Bayesian method for tracking and system identification. We demonstrate the efficacy of our approach with numerical simulations, showing that our method is able to jointly estimate the state trajectory and identify the correct dynamical model.

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