
FASTRAK MANUAL
Rev. G
D-4
JUNE 2012
orientation. Therefore, determining the S/N ratio from a “black box” perspective involves the use
of a precise mechanical positioning instrument with a precision gimbal. Using surveyed
(precisely known) attitude coordinates (azimuth, elevation and roll), a statistically valid number
of measurement samples are taken at each attitude. For each attitude the mean vector sum of
these samples yields the signal (S) component and the vector sum of the one sigma values of the
deviation yields the noise (N) component. The S/N ratio may be expressed as a unitless number
or in db, that is, 20 log
10
S/N.
RESOLUTION
Resolution for electromagnetic 6DOF measurement instruments is generally specified as
angular resolution and translational resolution.
ANGULAR RESOLUTION
Considering that the receiver is an all-attitude (360 degree) device, the angular resolution
is calculated by dividing 360 degrees by the S/N ratio thus yielding its value in degrees.
TRANSLATIONAL RESOLUTION
The translational or positional resolution is a function of the S/N ratio and range. Being a
positional function, there are three orthogonal vectors whose vector sum multiplied by any given
range number yields the required translational resolution as shown in
. One vector is
defined along the axis of the range and is therefore a function of the inverse cube of the range.
The remaining two orthogonal vectors (a & b) are a function of the tangent of the angle derived
by dividing 180 degrees by the S/N ratio. Unlike angular resolution which uses 360 degrees
divided by the S/N ratio, 180 degrees is used for these translational resolution component vectors
because with an electromagnetic system there are two possible solutions to the 6DOF
measurement problem. This two solution possibility constitutes a potential system ambiguity.
Obviously for a position measurement, only one solution is permitted and valid. The units for
translational resolution are either English (inches) or metric (cm.).
Figure D-3 Translational Resolution.