We consider the problem of tracking the state of a process that evolves over time in a distributed setting, with multiple observers each observing parts of the state, which is a fundamental information processing problem with a wide range of applications. We propose a cloud-assisted scheme where the tracking is performed over the cloud. In particular, to provide timely and accurate updates, and alleviate the straggler problem of cloud computing, we propose a coded distributed computing approach where coded observations are distributed over multiple workers. The proposed scheme is based on a coded version of the Kalman filter that operates on data encoded with an erasure correcting code, such that the state can be estimated from partial updates computed by a subset of the workers. We apply the proposed scheme to the problem of tracking multiple vehicles. We show that replication achieves significantly higher accuracy than the corresponding uncoded scheme. The use of maximum distance separable (MDS) codes further improves accuracy for larger update intervals. In both cases, the proposed scheme approaches the accuracy of an ideal centralized scheme when the update interval is large enough. Finally, we observe a trade-off between age-of-information and estimation accuracy for MDS codes.