An Indoor Absolute Positioning System with
No Line of Sight Restrictions and Building-Wide Coverage

Research by: Eric Prigge in the Aerospace Robotics Laboratory at Stanford University

Research Advisor: Professor Jonathan P. How (Email)
Department of Aeronautics and Astronautics
Space Systems Laboratory
Massachusetts Institute of Technology

Research provides a new positioning system technology especially suited for indoor operations:

Solution: Use Low Frequency Magnetic Fields

  • Current through a coil of wire (‘beacon’) produces magnetic
    field of known shape
  • Sensor measures amplitude of the magnetic field
  • Extremely low frequency (ELF) magnetic fields have excellent characteristics for penetrating line-of-sight obstruction
  • A key benefit of this approach is that the beacons can be combined
    to provide building-wide coverage

Note: similar systems are already in use by the motion capture industry:

Key Research Issues:

Straightforward extension of existing signal structures cannot support the number of beacons
required for a building-wide coverage volume.
This research developed a new signal architecture and new signal processing / solution algorithms that can support a larger number of beacons.
Position estimates can be distorted due to eddy currents and ferromagnetic materials in the environment.
This research developed signal architecture and solution algorithm and two real-time correction techniques


(1) Use Code Division Multiple Access (CDMA) to distinguish between the coils (2) Use correlators from the sensor to estimate the beacon fields in real-time

(3) Use the estimated magnetic field to solve for the position and attitude of the sensor\

  • Position and attitude problems decouple - solve for position first
  • Optimization-based solution techniques of the nonlinear "exact magnitude equations" exhibits
    poor convergence properties.
  • However, these can be accurately approximated with a set of nonlinear functions that are much
    easier to solve, thereby providing a very good starting point for exact equations.
  • Sensor attitude can be determined by solving the following problem:
    • Given two sets of n vectors {B1, B2, ... Bn} (B field as measured by sensors) and {M1, M2, ... Mn} (B field as estimated based on position estimate), where n >= 2
    • Find the rotation matrix C which brings the first set into best least-squares coincidence with the second.
    • Known as Wahba’s problem, for which many solution techniques exist

(4) To compensate for the effects of materials in the field, note that correlation is linear, so

Corr (Sum field,
code 1)
Corr (Beacon field,
code 1)
Corr (Eddy field,
code 1)

Basic Experimental Results

Experimetal Prototype Facility developed at Stanford

Equiped with 8 transmitters
- blue disks on the floor and supported by ladders
- blue grid gives truth measure

Shows sensor on stand in the test area
Laptop displays estimation results.

X-Y statistics

3.7 cm bias, 1.3 cm standard deviation

2.3 deg bias, 0.8 deg standard deviation

Demonstration of the sensing performance inside 2 metal bowls
- 2.4 cm change in position estimation

Galvanized steel garbage can
- 3.6 cm change in position estimation

Demonstration that the sensor performance is not impacted by
200 lbs of concrete and wood

No noticeable change in position estimation

Final test run - artificial office environment with tables and tunnels (metal object lower left)

December 9, 2001