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Optimality analysis of sensor-target localization geometries

Published: 01 March 2010 Publication History

Abstract

The problem of target localization involves estimating the position of a target from multiple noisy sensor measurements. It is well known that the relative sensor-target geometry can significantly affect the performance of any particular localization algorithm. The localization performance can be explicitly characterized by certain measures, for example, by the Cramer-Rao lower bound (which is equal to the inverse Fisher information matrix) on the estimator variance. In addition, the Cramer-Rao lower bound is commonly used to generate a so-called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate, i.e. an estimate which achieves the lower bound. The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized. Deeming such sensor-target geometries to be optimal with respect to the chosen measure, the optimal sensor-target geometries for range-only, time-of-arrival-based and bearing-only localization are identified and studied in this work. The optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor-target configuration is not, in general, unique. The importance of understanding the influence of the sensor-target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples.

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Information & Contributors

Information

Published In

cover image Automatica (Journal of IFAC)
Automatica (Journal of IFAC)  Volume 46, Issue 3
March, 2010
159 pages

Publisher

Pergamon Press, Inc.

United States

Publication History

Published: 01 March 2010

Author Tags

  1. Angle-of-arrival (AOA)
  2. Bearing-only
  3. Cramer-Rao bound
  4. Fisher information
  5. Geometry
  6. Localization
  7. Optimal localization geometries
  8. Optimal sensor placement
  9. Positioning
  10. Range-only
  11. Sensor network
  12. Target tracking
  13. Time-difference-of-arrival (TDOA)
  14. Time-of-arrival (TOA)

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  • (2024)Reactive navigation of nonholonomic robots for search and tight circumnavigation of group objects through singular inter-object gapsRobotics and Autonomous Systems10.1016/j.robot.2024.104649174:COnline publication date: 1-Apr-2024
  • (2024)A Robust Bias Reduction Method with Geometric Constraint for TDOA-Based LocalizationWireless Personal Communications: An International Journal10.1007/s11277-024-11541-1138:2(945-971)Online publication date: 1-Sep-2024
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  • (2023)Optimality analysis of range sensor placement under constrained deployment regionWireless Networks10.1007/s11276-023-03357-x29:6(2797-2812)Online publication date: 29-Apr-2023
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