  Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the
classical angular synchronization problem consists of recovering unknown angles
$\theta_1^*,\dots,\theta_n^*$ from a collection of noisy pairwise measurements
of the form $(\theta_i^* - \theta_j^*) \mod 2\pi$, for all $\{i,j\} \in
\mathcal{E}$. This problem arises in a variety of applications, including
computer vision, time synchronization of distributed networks, and ranking from
pairwise comparisons. In this paper, we consider a dynamic version of this
problem where the angles, and also the measurement graphs evolve over $T$ time
points. Assuming a smoothness condition on the evolution of the latent angles,
we derive three algorithms for joint estimation of the angles over all time
points. Moreover, for one of the algorithms, we establish non-asymptotic
recovery guarantees for the mean-squared error (MSE) under different
statistical models. In particular, we show that the MSE converges to zero as
$T$ increases under milder conditions than in the static setting. This includes
the setting where the measurement graphs are highly sparse and disconnected,
and also when the measurement noise is large and can potentially increase with
$T$. We complement our theoretical results with experiments on synthetic data.
