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Nonlinear Kalman filtering of long-baseline, short-baseline, GPS, and depth measurements

Abstract
In a recent Moving Ship Tomography experiment we deployed a vertical array of receiving hydrophones 300 times around a 1000 km diameter circle south of Bermuda; six acoustic sources within the circle transmitted every 3 hours. We plan to use the travel times measured along the source/receiver paths to reconstruct the three dimensional sound speed field in the interior of the circle. Accurate location of the hydrophone receivers is crucial to the execution of this plan. A long baseline tracking system consisting of floating buoys and the ship, acoustically measured the range to each hydrophone (~ 1km in depth and ~ 1km in horizontal range). The range to orbiting satellites was measured with GPS. A short base line acoustic system measured range and direction from the ship to a beacon on the cable, and to each buoy. Depths, at various points near the hydrophones were measured using three different pressure sensors. We describe a Kalman filter that combines these primary measurements and some supporting measurements, to form an estimate of the buoy and hydrophone locations. We use an iterated correction step to adjust for the nonlinearities and an outlier detection scheme to make the filter robust.

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