Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 58, Issue 1, Pages 247-252Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2012.2206693
Keywords
Approximate localization; bearing; rigidity
Funding
- Swedish Research Council
- Knut and Alice Wallenberg Foundation
- NICTA
- Australian Government
- Digital Economy
- Australian Research Council through the ICT Centre of Excellence program
- Australian Research Council (ARC) via a Discovery Early Career Researcher Award [DE-120102873]
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Graph theory has been used to characterize the solvability of the sensor network localization problem with ideal (i.e., precisely known) bearing-only measurements between certain pairs of sensors and a limited amount of information about the position of certain nodes, i.e., anchors. In practice, however, bearing measurements will never be exact, and the equations whose solutions deliver sensor positions in the noiseless case may no longer have a solution. This technical brief argues that if the same conditions for localizability that exist in the noiseless case are satisfied and the bearing measurement errors are small enough (as will be formalized later in the technical brief), then the network will be approximately localizable, i.e., sensor position estimates can be found which are near the correct values. In particular, a bound on the position errors is found in terms of a bound on the bearing errors. Later, this bound is used to propose a method to select anchors to minimize the effect of noisy bearing measurements on the localization solution.
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