SCIENCE@home

Elliptic and hyperbolic localizations using minimum measurement solutions

Sanaa S. A. Al-Samahi,Sanaa S. A. Al-Samahi,Yang Zhang,Dominic K. C. Ho

Published 2020 in Signal Processing

ABSTRACT

Abstract Localization of an object using a number of sensors is often challenged by outlier observations and solution finding. This paper derives a new algebraic positioning solution using a minimum number of measurements, and from which to develop an outlier detector and an object location estimator. Two measurements are sufficient in 2-D and three in 3-D to yield a solution if they are consistent. The derived minimum measurement solution is exact and reduces the computation to the roots of a quadratic equation. The solution derivation leads to simple criteria to ascertain if the line of positions from two measurements intersect. The intersection condition enables us to establish an outlier detector based on graph processing. By partitioning the overdetermined set of measurements first to obtain the individual minimum measurement solutions, we propose a best linear unbiased estimator to form the final location estimate. Analysis supports the proposed estimator in reaching the CRLB accuracy under Gaussian noise. A measurement partitioning scheme is developed to improve performance when the noise level becomes large. We mainly use elliptic time delay measurements for presentation, and the derived results are applicable to the hyperbolic time difference measurements as well. Both the 2-D and 3-D scenarios are considered.

PUBLICATION RECORD

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-48 of 48 references · Page 1 of 1

CITED BY

Showing 1-43 of 43 citing papers · Page 1 of 1