Indoor Absolute Positioning System

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:

No line-of-sight restrictions
Drift-free measurements
Building-wide coverage
Accuracy/bandwidth suitable for application (several Hz, 2-4 inch accuracy for robots)
Any number of sensor units, all providing measurements in a common frame
Mobile component is small, low power
No baselines needed for attitude
No FCC restrictions

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:

Kuipers, Raab, Blood - Polhemus and Ascension Technologies
Useful for motion capture applications, but not for building-wide robotics:
- Very limited coverage area.
- Sensitive to some materials in the environment
Our approach offers several key advantages of these techniques.

	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

Each beacon produces fields according to its own "code"
Each code can be represented by a unique sequence of +1’s and -1’s (called Gold codes)
Beacon varies polarity of current according to code elements, called "chips"
CDMA shown to have significant advatnages over TDMA and CDMA techniques
when analyzed to account for sensing and eddy current noise

(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)
	=		+

Correlation between beacon codes and decaying exponentials of various amplitudes and time
constants is pre-computed.
In real time, the information in the "late" correlator values can be used to "look up"the error the eddy field
cause to the "on-time" correlator value.
Iron is a much harder material to correct for because it has a fundamental impact on the field lines.
However, the thesis presents several correction techniques that have been developed.

	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 position: 3.7 cm bias, 1.3 cm standard deviation attitude: 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