FASTRAK MANUAL
Rev. G
D-1
JUNE 2012
APPENDIX D. ‘Accuracy and Resolution’ White Paper
ACCURACY AND RESOLUTION IN ELECTROMAGNETIC
6 DEGREE-OF-FREEDOM (6DOF) MEASUREMENT SYSTEMS
APB 8500-001A
INTRODUCTION
The classical definitions of resolution and accuracy as articulated by Cook and
Rabinowicz in “Physical Measurement and Analysis,” Addison-Wesley Publishing Company,
1963, are:
Resolution: the smallest amount of the quantity being measured
that the instrument will detect.
Accuracy: the fractional error in making a measurement.
Clearly, confusion over these issues in light of the burgeoning need to measure both the
position and orientation of a freely movable object in space with respect to a fixed reference, can
lead to inconclusive results and lost effort in application measurements.
From the outset of electromagnetic 6 Degree-Of-Freedom (6DOF) measurement
technology, regardless of the application, the subjects of accuracy and resolution have been
confusing in light of claims by competing technologies and product manufacturers. This
Application Note attempts to clarify accuracy and resolution and to illustrate their total
applicability to the classical definitions.
THEORY OF OPERATION
The position of a point in space may be fully described by its relationship to any fixed
and convenient three axis (x, y, z) coordinate system. Orientation means direction in relationship
to that position and may be fully described by three parameters or angles known as azimuth
(yaw), elevation (pitch), and roll.
A typical Polhemus system consists of a fixed magnetic-dipole transmitting antenna
called a transmitter; a freely movable magnetic-dipole receiving antenna called a receiver; and
associated electronics as shown in
. Both the transmitter and receiver antennas
consist of three mutually orthogonal loops (coils). The loop diameters are kept very small
compared to the distance separating the transmitter and receiver so that each loop may be
regarded as a point or infinitesimal dipole. Exciting a loop antenna produces a field consisting of
a far-field component and a near or induction-field component. The far-field intensity is a
function of loop size and excitation frequency and decreases with the inverse of the distance
(1/r). The induction-field or “quasi-static” field component intensity is not frequency dependent
and decreases by the inverse cube of the distance (1/r
3
). The quasi-static field is not detectable at
long distances; in fact, its strength dominates at short distances and the far-field is negligible.