Alexander A. Nguyen and Zaher M. Kassas, University of California, Irvine

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Abstract:

A computationally efficient algorithm for selecting the most informative subset of terrestrial signals of opportunity (SOPs) is proposed. The following problem is considered. An aerial vehicle navigates in an environment where global navigation satellite system (GNSS) signals are unavailable. The aerial vehicle is equipped with an on-board receiver that extracts pseudorange observations from an abundant number of M terrestrial SOPs with known locations but unknown dynamic, stochastic clock error states (bias and drift). An extended Kalman filter (EKF) is employed to fuse these pseudorange observations to estimate the aerial vehicle’s states (position and velocity) and the difference between the aerial vehicle-mounted receiver’s clock error states and the clock errors of all SOPs. Due to size, weight, power, and cost (SWaP-C) constraints, the aerial vehicle should select a subset K < M of the available SOPs with which it navigates. Since solving the optimal selection problem is rather involved, a sub-optimal, yet computationally efficient algorithm, termed opportunistic greedy selection (OGS), is proposed. The OGS is formulated by exploiting the additive, iterative properties of the Fisher Information Matrix (FIM), to minimize the aerial vehicle’s average position error variance (i.e., A-optimality criterion). Numerical simulations are presented showing that the proposed OGS algorithm performs comparably with the optimal M choose K selection algorithm, but executes in a small fraction of the time. Furthermore, experimental results are presented for a U.S. Air Force high-altitude aircraft navigating without GNSS signals in an environment comprising M = 57 cellular terrestrial SOPs for 9.39 km in 105 s. It is shown that upon choosing K = 15 SOPs according to the proposed OGS algorithm, the position and velocity root mean square errors (RMSEs) were 11.45 m and 0.80 m/s, respectively. Monte Carlo results are presented arguing that the results achieved from the proposed OGS algorithm are very close to what the global optimal selection algorithm would yield.