Convex Relaxation Methods for Unified Near-Field and Far-Field TDOA-Based Localization

This paper develops two convex relaxation solutions for the unified localization of a signal source using time difference of arrival measurements, regardless of whether the source is in the near field for coordinate positioning or in the far field for the direction of arrival estimation. The previou...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on wireless communications 2019-04, Vol.18 (4), p.2346-2360
Main Authors: Wang, Gang, Ho, K. C.
Format: Article
Language:English
Subjects:
Convergence
Direction of arrival
Direction-of-arrival estimation
Economic models
Estimation
Formulations
fractional programming (FP)
Iterative solution
Localization
Mathematical programming
Maximum likelihood estimators
modified polar representation
Optimization
Position errors
Position sensing
Programming
Representations
semidefinite/second-order cone programming (SD/SOCP)
Sensors
Three-dimensional displays
time difference of arrival (TDOA)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper develops two convex relaxation solutions for the unified localization of a signal source using time difference of arrival measurements, regardless of whether the source is in the near field for coordinate positioning or in the far field for the direction of arrival estimation. The previous study on unified estimation only derived an iterative solution, which is sensitive to initialization. Albeit a coarse initialization was supplied to start the iteration, it may not be sufficient to ensure convergence to the global solution especially when the source is close to the sensors. The proposed solutions come from two novel formulations for optimization, one using the weighted least squares with the modified polar representation of the source position as variable and the other applying fractional programming with the Cartesian coordinate representation instead. Both the optimization problems are solved by first performing semidefinite relaxation and then tightening the relaxed problem by including a set of second-order cone constraints. The two formulations are created from different approaches. Nevertheless, we are able to prove that both the formulations reduce to solving exactly the same mixed semidefinite/second-order cone program and thus establish their equivalence. Furthermore, the proposed solution method is extended to the more practical scenario when sensor position errors are present. The results from both the simulated and real experiments show that the proposed method achieves almost the same performance of the iterative maximum likelihood estimator under ideal initialization.
ISSN:1536-1276
1558-2248
DOI:10.1109/TWC.2019.2903037