Page 139 - Advances In Productive, Safe, and Responsible Coal Mining

Communication and tracking system performance 123

distance. This metric is only descriptive within the active TCA because it derives from
a set of IAs.
The 90% CD describes the 90th percentile of IA values from a GTP, an IA mea-
surement in which there is a very high (90%) confidence that a subsequent IA calcu-
lation will be within the 90% CD. The calculation is done by ranking IA measurements
and the IA that is at the 90th percentile rank is the value. This metric value is the clos-
est match to the regulatory guidelines of accuracy required in various parts of the
mine. The important difference is that this is a confidence that a value will be within
the limit; it is not a set measurement. For instance, an IA value at 105ft, in an area
where the 90% CD is 100ft, is not an indication that the 90% CD of that area is in
fact larger than 100ft. A set of measurements that show a 90% CD greater than
100ft is an indication that the 90% CD should be increased for that area.
Values for AA, SDA, and 90% CD as calculated for a particular system/section are
one-dimensional representations of the accuracy of the tracking system. It may also be
important to describe the relative skew in the TSP in two dimensions because tracking
systems report coordinates for a tracked device. The analogy of IA in two-dimensional
space is the error vector (EV), which is the simple difference vector between Cartesian X
and Y components of GTP and TSP. Average error vector (AEV) is the average displace-
ment of a set of TSPs from their corresponding GTP. Average cluster radius (ACR) is
the average of distances a set of TSPs are from their center point, which is determined by
the average error vector. These values are determined by moving each GTP to the origin
and then average TSPs to their corresponding relative locations. The resulting graphs
show bias and spread in the tracking system, which are described by AEV and ACR.
For a set of Ν TSP measurements in the active TCA and corresponding GTPs, AEV
is the vector representing average X and Y coordinates of EVs associated with the
set. ACR is the average of the distance of a TSP from the AEV. It describes a circular
area around the AEV in which the average TSP value would be located.

h
h EV x0 ,EV y0 ¼ TSP x0 GTP x0 , TSP y0 GTP y0
Ν Ν
X X
* EV xi EV yi +
i¼1 i¼1
h AEV x ,AEV y ¼ ,
Ν Ν
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q
X N 2 2
ACR ¼ ð TSP xi AEV x Þ + TSP yi AEV y =N
i¼1
Other important metrics such as reliability, availability, and relative accuracy are dis-
cussed elsewhere.

8.3 Simulation of tracking system performance

Prior to installation and testing of the communications and tracking system, computer
simulations were used to generate anticipated results. These predictions were then
used as the baseline for the system being tested, a partial mesh system with several