Title :
Maximum Likelihood Positioning of Network Nodes Using Range Measurements
Author :
Weiss, Anthony J. ; Picard, Joseph S.
Author_Institution :
Tel Aviv Univ., Tel Aviv
Abstract :
Given a network of stations with incomplete and possibly imprecise inter-station range measurements, it is required to find the relative positions of the stations. Due to its asymptotic properties maximum likelihood estimation is discussed. Although the problem is quadratic, the proposed solution is based on solving a linear set of equations. For precise measurements we obtain explicitly the exact solution with a small number of operations. For noisy measurements the method provides an excellent initial point for the application of the Gerchberg-Saxton iterations. Proof of convergence is provided. The case of planar geometry is coached using complex numbers which reveals a strong relation to the celebrated problem of phase retrieval. We provide a compact, matrix form of the Cramer-Rao bound, small error analysis and evaluation of the computational load. Numerical examples are provided to corroborate the results.
Keywords :
ad hoc networks; iterative methods; maximum likelihood estimation; Cramer-Rao bound; Gerchberg-Saxton iterations; asymptotic properties; inter-station range measurements; maximum likelihood positioning; network nodes; noisy measurements; planar geometry; Distance measurement; Electric variables measurement; Equations; Least squares approximation; Linear matrix inequalities; Maximum likelihood estimation; Monitoring; Position measurement; Resists; Temperature sensors;
Conference_Titel :
Wireless Communication Systems, 2006. ISWCS '06. 3rd International Symposium on
Conference_Location :
Valencia
Print_ISBN :
978-1-4244-0398-1
Electronic_ISBN :
978-1-4244-0398-1
DOI :
10.1109/ISWCS.2006.4362360