Minimizing Trilateration Errors in the Presence of Uncertain Landmark Positions

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Minimizing Trilateration Errors in the Presence
ofUncertain Landmark Positions

• Alexander Bahr John J. Leonard
• abahr,jleonard_at_mit.edu

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Motivation Underwater Navigation

• No GPS, except when surfacing
• Low feature density (!)
• Low resolution sensor (SONAR)
• Low dead-reckoning performance in open
  ocean

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Cooperative Underwater Navigation a 2D problem
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Acoustic Communication and Ranging

• Acoustic modem (Woods Hole Oceanographic
  Institution)
• Maximum range 200 m - 8 km
• Maximum data rate 3 bytes/s - 1 kByte/s
• 1 Channel (no FDMA scheme possible)
• Range estimate between transmitting and receiving
  vehicle through globally synchronized modems
  (Pulse Per Second signal)
• Obtained for free Range r between vehicles

32 bytes every 10 s
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Cooperative Underwater Navigation

• Broadcast
• Position (x,y,z), uncertainty (sx, sy)
• Maybe course, speed, waypoint, etc.
• For free with broadcast range

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Cooperative Navigation Scenario

• Broadcast
• Position (x,y,z), Uncertainty (sx, sy)
• Other useful information
• course, speed, waypoint, etc.
• For free with broadcast range

x,y,z,?x,?y
x,y,z,?x,?y
x,y,z,?x,?y
x,y,z,?x,?y
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Problem Formulation
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Metrics for Position Error

• Possible error metrics
• semi-minor to semi-major axis ratio
• ellipse area
• Circular Error Probability (CEP)

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Optimal Trilateration Position
Looking for the optimal trilateration position
Knowing enables us to 1.) compute a new
quality metric
Similar to Geometric Dilution of Precision
(GDOP), BUT taking uncertain landmarks into
account
2.) use ? and as part of the cost function
for path planning
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Optimal Trilateration Position
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Future work

• Directly compute position for minimal
  trilateration error
• Application Planning paths which are optimized
  for cooperative navigation

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• Thank you

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Overview

• Motivation
• Problem Formulation
• Metrics
• Results
• Future Work