Low Complexity Sequential Search With Size-Dependent Measurement Noise

Abstract

This paper considers a target localization problem where at any given time an agent can choose a region to query for the presence of the target in that region. The measurement noise is assumed to be increasing with the size of the query region the agent chooses. Motivated by practical applications such as initial beam alignment in array processing, heavy hitter detection in networking, and visual search in robotics, we consider practically important complexity constraints/metrics: time complexity, computational and memory complexity, and the complexity of possible query sets in terms of geometry and cardinality. Two novel search strategy, dyaPM and hiePM, are proposed. Pertinent to the practicality of our solutions, dyaPM and hiePM are of a connected query geometry (i.e. query set is always a connected set) implemented with low computational and memory complexity. Additionally, hiePM has a hierarchical structure and, hence, a further reduction in the cardinality of possible query sets, making hiePM practically suitable for applications such as beamforming in array processing where memory limitations favors a small and predefined query sets. Through a unified analysis with Extrinsic Jensen Shannon (EJS) Divergence, dyaPM is shown to be asymptotically optimal in search time complexity (asymptotic in both resolution (rate) and error (reliability)). On the other hand, hiePM is shown to be near-optimal in rate. In addition, both hiePM and dyaPM are shown to outperform prior work in the non-asymptotic regime.