
An
Indoor Absolute Positioning System with
No Line of Sight Restrictions and BuildingWide 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 lineofsight restrictions
 Driftfree measurements
 Buildingwide coverage
 Accuracy/bandwidth suitable for
application (several Hz, 24 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
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
lineofsight obstruction
 A key benefit of this approach
is that the beacons can be combined
to provide buildingwide 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 buildingwide robotics:
 Very limited coverage area.
 Sensitive to some materials
in the environment
 Our approach offers several
key advantages of these techniques.
Key Research Issues:

Straightforward
extension of existing signal structures cannot support the number of beacons
required for a buildingwide 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 realtime correction
techniques 
Approach:
(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 realtime
 Magnitudes of each beacon signal
are recovered from noisy sum measurement
 Naturally rejects steady state
magnetic fields, such as earth’s field
 Attenuates noise that does not
look like a Gold code  motors, lights, etc.
 Signals can be below the noise
level
(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
 Optimizationbased 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 leastsquares
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 precomputed.
 In real time, the information
in the "late" correlator values can be used to "look up"the
error the eddy field
cause to the "ontime" 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.
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. 

XY 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