Near-optimal deterministic filtering on the unit circle

We present a near-optimal deterministic filter for systems that evolve on the unit circle. Unlike suboptimal filtering algorithms that rely on approximations of the system, the proposed approach preserves the non-linear system model. This leads to an explicit bound on the optimality gap in terms of the tracking error. Specifically, the optimality gap is bounded by a term that is fourth-order in the tracking error. A simulation demonstrates that the filter can track a signal on the unit circle in the presence of large disturbances. An optimal algorithm for recursive estimation of static (non-dynamic) data on the unit circle appears as a special case of the proposed filter.