A semidefinite programming approach for robust elliptic localization
arxiv(2024)
摘要
This short communication addresses the problem of elliptic localization with
outlier measurements, whose occurrences are prevalent in various
location-enabled applications and can significantly compromise the positioning
performance if not adequately handled. In contrast to the reliance on
M-estimation adopted in the majority of existing solutions, we take a
different path, specifically exploring the worst-case robust approximation
criterion, to bolster resistance of the elliptic location estimator against
outliers. From a geometric standpoint, our method boils down to pinpointing the
Chebyshev center of the feasible set determined by the available bistatic
ranges with bounded measurement errors. For a practical approach to the
associated min-max problem, we convert it into the well-established convex
optimization framework of semidefinite programming (SDP). Numerical simulations
confirm that our SDP-based technique can outperform a number of existing
elliptic localization schemes in terms of positioning accuracy in Gaussian
mixture noise, a common type of impulsive interference in the context of
range-based localization.
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