Technical Report

Position estimation

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  • Acoustic position estimation is used where high accuracy navigation is required over a small area, such as for searching or for collecting gravitational or geomagnetic data. In this position estimation method, a surface ship or submersible periodically sends out a high-frequency acoustic 'ping' at a prearranged frequency. This ping is received by an array of transponders attached to the ocean floor, each of these transponders 'replies' to the ping with another ping at its own prearranged frequency. The ship records the times elapsed from when it sent out its ping to when it received each of the transponder's replies. The ship can then convert these elapsed 'round trip times' into distances, and can compute its position relative to the transpon­der array. However, the relative positions of the transponders must be known. If the ship had some way of accurately determining its position when it deployed the transponders, it would not have needed to deploy them in the first place (since the only purpose of the transponders it to determine the ship's position accurately). Furthermore, even if the ship did know its posi­tion when it deployed a given transponder, there are many forces (such as ocean currents) that would prevent the transponder from descending exactly straight down. This paper presents an algorithm that can determine the relative posi­tions of the transponders in an array from acoustic measurements collected by the ship. This algorithm makes use of a second-order Newton's method with exact linesearch to minimize a.n error function whose domain is the set of coordinates of all the transponder and ship positions involved in the acoustic measurements. This algorithm will be qualitatively compared to an older algorithm that has been used to solve the problem.
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