Page 138 - Advances In Productive, Safe, and Responsible Coal Mining

122 Advances in Productive, Safe, and Responsible Coal Mining

a location for the tracked device; this location is the tracking system position (TSP) or
tracking system position estimate (TSPE), used interchangeably. These two positions
can be thought of as where the device really is located (GTP), and where the device is
considered to be located (TSP) at a point in time. The technology used by the tracking
system and its reporting capabilities determine how one collects data from the tracking
system. It is assumed that all tracking systems installed in underground coal mines are
capable of reporting a tracked device’s history over the last 14 days in subminute time
frames.
The most basic metric is tracking coverage area (TCA), which refers to the area
within the mine that the tracking system is working. Because mines are confined
spaces and the tracking system is not required to have 100% coverage, the TCA is
divided into active TCAs and Inferred TCA. Active TCA is where the tracking system
is actively producing TSPs. Inferred TCA is where the TSP is not in communication,
but the general position can be ascertained based on spatial limitations of the mine and
information other than active measurements.
The next fundamental metric is the instantaneous accuracy (IA) of the TSP, which
is the difference between an actual location (GTP) and the tracking system position
estimate (TSP) actively made at that GTP at an instant in time. This is a simple
straight-line distance from any single TSP to the GTP at the same point in time.
The equation for IA is:

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2
IA 0 ¼ ð TSP x0 GTP x0 Þ + TSP y0 GTP y0
If GTP and TSP of a miner’s location are (100,100) and (96,103), respectively, at time
p
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
2
T 0 , then IA at time T 0 is: IA 0 ¼ ð 96 100Þ + 103 100Þ ¼ 4 +3 ¼ 5.
ð
At any location in the mine, over time there are several TSP values that are calcu-
lated by the tracking system. For each TSP value, there is an associated IA; and the
general accuracy of the tracking system for that area is described by average accuracy
(AA), the arithmetic mean of a set of IAs, and standard deviation of accuracy (SDA),
the standard deviation of a set of IA measurements.
Ν
X
IA i
i¼1
AA ¼
Ν
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u Ν
1
u X 2
SDA ¼ t ð IA i AAÞ
Ν 1
i¼1
90% confidence distance (90% CD) is the distance from a tracked device’s actual
location (i.e., GTP) that is greater than 90% of collected IA measurement magnitudes
(“90th percentile”). 90% CD can be specified as a metric based on a standardized,
fixed percentile of measurements, as this section is entitled, but a variant of the con-
cept can also be specified with a percent of TSPs occurring within a standardized