Robust near-field 3D localization of an unaligned single-coil agent using unobtrusive anchors

Abstract

The magnetic near-field provides a suitable means for indoor localization, due to its insensitivity to the environment and strong spatial gradients. We consider indoor localization setups consisting of flat coils, allowing for convenient integration of the agent coil into a mobile device (e.g., a smart phone or wristband) and flush mounting of the anchor coils to walls. In order to study such setups systematically, we first express the Cramér-Rao lower bound (CRLB) on the position error for unknown orientation and evaluate its distribution within a square room of variable size, using 15 × 10 cm anchor coils and a commercial NFC antenna at the agent. Thereby, we find cm-accuracy being achievable in a room of 10 × 10 × 3 meters with 12 flat wallmounted anchors and with 10 mW used for the generation of magnetic fields. Practically achieving such estimation performance is, however, difficult because of the nonconvex 5D likelihood function. To that end, we propose a fast and accurate weighted least squares (WLS) algorithm which is insensitive to initialization. This is enabled by effectively eliminating the orientation nuisance parameter in a rigorous fashion and scaling the individual anchor observations, leading to a smoothed 3D cost function. Using WLS estimates to initialize a maximum-likelihood (ML) solver yields accuracy near the theoretical limit in up to 98% of cases, thus enabling robust indoor localization with unobtrusive infrastructure, with a computational efficiency suitable for real-time processing.

Practical Accuracy Limits of Radiation-Aware Magneto-Inductive 3D Localization

“…This constrained linear least squares problem has an efficient solution based on an eigenvalue decomposition. For the details we refer to [11], [15]. It shall be noted that we study location estimation from an instantaneous observation h meas without temporal filtering.…”

“…The 5D estimation parameter ψ = [p T ag , φ, θ] T describes the agent deployment; φ and θ are the azimuth and polar angles. The Jacobians comprise derivatives of (1) that follow from an extension of [11,Appendix B] and are omitted for brevity.…”

“…This enables the localization of an agent in a setup with stationary coils of known locations (i.e. anchors) [6]- [11]. In particular, position and orientation estimates can be obtained by fitting a dipole model to measurements of induced voltage or of a related quantity [7]- [11].…”

“…Moreover, we compensate contributions from radiative multipath propagation by exploiting the large wavelength and calibration. A previously proposed algorithm for position and orientation estimation [11] is consequently adapted to this model. Based thereon, we present a system implementation for magneto-inductive 3D localization whereby anchors and agent use flat spiderweb coils tuned to 500 kHz.…”

“…They use triaxial 80-turn coils at 2.5 kHz. In our work [11], we improved the non-linear least squares approach to single-coil agent localization, thereby vastly improving robustness and runtime, and used Cramér-Rao bounds for accuracy projections in thermal noise which was considered as the only limitation. This paper is structured as follows.…”