Iterative RNDOP-Optimal Anchor Placement for Beyond Convex Hull ToA-based Localization: Performance Bounds and Heuristic Algorithms
arxiv(2022)
摘要
Localizing targets outside the anchors' convex hull is an understudied but
prevalent scenario in vehicle-centric, UAV-based, and self-localization
applications. Considering such scenarios, this paper studies the optimal anchor
placement problem for Time-of-Arrival (ToA)-based localization schemes such
that the worst-case Dilution of Precision (DOP) is minimized. Building on prior
results on DOP scaling laws for beyond convex hull ToA-based localization, we
propose a novel metric termed the Range-Normalized DOP (RNDOP). We show that
the worst-case DOP-optimal anchor placement problem simplifies to a min-max
RNDOP-optimal anchor placement problem. Unfortunately, this formulation results
in a non-convex and intractable problem under realistic constraints. To
overcome this, we propose iterative anchor addition schemes, which result in a
tractable albeit non-convex problem. By exploiting the structure arising from
the resultant rank-1 update, we devise three heuristic schemes with varying
performance-complexity tradeoffs. In addition, we also derive the upper and
lower bounds for scenarios where we are placing anchors to optimize the
worst-case (a) 3D positioning error and (b) 2D positioning error. We build on
these results to design a cohesive iterative algorithmic framework for robust
anchor placement, characterize the impact of anchor position uncertainty, and
then discuss the computational complexity of the proposed schemes. Using
numerical results, we validate the accuracy of our theoretical results. We also
present comprehensive Monte-Carlo simulation results to compare the positioning
error and execution time performance of each iterative scheme, discuss the
tradeoffs, and provide valuable system design insights for beyond convex hull
localization scenarios.
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关键词
Dilution of Precision (DOP),Beyond Convex Hull Localization,Range-Normalized DOP (RNDOP),Anchor Placement,Time-of-Arrival (ToA)
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