Underground Incrementally Deployed Magneto-Inductive 3-D Positioning Network

Abstract

Underground mines are characterized by a network of intersecting tunnels and sharp turns, an environment which is particularly challenging for radiofrequency based positioning systems due to extreme multipath, non-line-of-sight propagation, and poor anchor geometry. Such systems typically require a dense grid of devices to enable 3-D positioning. Moreover, the precise position of each anchor node needs to be precisely surveyed, a particularly challenging task in underground environments. Magnetoinductive (MI) positioning, which provides 3-D position and orientation from a single transmitter and penetrates thick layers of soil and rock without loss, is a more promising approach, but so far has only been investigated in simple point-to-point contexts. In this paper, we develop a novel MI positioning approach to cover an extended underground 3-D space with unknown geometry using a rapidly deployable anchor network. The key to our approach is that the position of only a single anchor needs to be accurately surveyed-the positions of all secondary anchors are determined using an iterative refinement process using measurements obtained from receivers within the network. This avoids the particularly challenging and time-intensive task in an underground environment of accurately surveying the positions of all of the transmitters. We also demonstrate how measurements obtained from multiple transmitters can be fused to improve localization accuracy. We validate the proposed approach in a man-made cave and show that, with a portable system that took 5 min to deploy, we were able to provide accurate through-the-earth location capability to nodes placed along a suite of tunnels. IndexTerms-Localization, magneto-inductive (MI), underground.

Sensor Fusion for Magneto-Inductive Navigation

“…In [16], the maximum likelihood estimates were found by alternating between optimizing for position and orientation (only the pitch and yaw angles were considered). In [4] and [5], the channel matrix was estimated using least squares, and the range was estimated based on the received signal strength indicator (RSSI). After eliminating the orientation from the dipole field model using algebraic manipulations, the model was inverted to produce estimates of the position direction.…”

“…Similarly, in [11], MI and inertial measurements were fused by using a simultaneous localization and mapping (SLAM) algorithm that exploited local distortions in the magnetic field. Fusion of MI signals from multiple transmitters has been studied in [5]. Although the concept of MI navigation has been around for many decades, no one has yet taken a hard look at the associated general problem of low-level information fusion.…”

“…• We propose a maximum a posteriori (MAP) estimator for the problem of fusing MI measurements and eventual supplementary information to estimate position and orientation. As opposed to previous estimators [4], [5], the proposed estimator is derived based on a conventional optimality criterion and simultaneously computes position and orientation estimates in a one-stage procedure. Moreover, the proposed estimator provides a general framework for tight fusion (all available information is fused before computing any navigation estimates) of MI signals and additional information obtained from e.g., previous MI estimates, motion models, maps, or measurements from other sensors.…”

“…• Numerical comparison reveals that the position and orientation estimator presented in [4] and [5] (and outlined in Appendix A) is the MAP estimator with an uninformative prior, i.e., the maximum likelihood (ML) estimator. • The sum of the position Fisher information along all spatial directions is independent of the direction of the position vector and the orientation.…”

“…This is a nonlinear least-squares problem which can be solved by standard methods, such as the Gauss-Newton algorithm, the Levenberg-Marquardt algorithm, or trust-region methods [31]. The estimator presented in [4] and [5] is equivalent to the ML estimator, and will therefore not be presented as a separate estimator in the performance evaluations.…”