Exploration of Two Position Adjustment 

Methods for Underground Mine Tracking 

Systems 

Jingcheng Li, Member ION
 

David P. Snyder
 

Nicholas W. Damiano
 

National Institute for Occupational Safety and Health 

BIOGRAPHY 

Dr. Jingcheng Li is a senior service fellow at Pittsburgh 

Research Lab, The National Institute for Occupational 

Safety and Health. Previously, he was as a senior software 

engineer at Analog Devices Inc. Earlier, he was an 

instructor in the Department of Electrical and Automation 

Engineering at China University of Mining and 

Technology. He received a B.S. in Electrical Engineering 

from China University of Mining and Technology in 

1982, and an M.S. and Ph.D. from Pennsylvania State 

University in Mining Engineering specializing in 

electrical engineering applications in mining engineering 

in 1992 and 1996. 

Mr. David Snyder is a Senior Mine Electrical Engineer 

with the NIOSH Office of Mine Safety and Health. He is 

responsible for the research and development of 

communications and tracking systems for underground 

coal mines. Prior to joining NIOSH, Dave had more than 

20 years experience in wireless telecommunications 

research, development, and engineering. Earlier in his 

career, Dave worked as a mining engineer for operators in 

the central Pennsylvania coal fields including Bethlehem 

Mines. He has a B.S. degree in Mining Engineering from 

Penn State University, an M.S. degree in Electrical 

Engineering from George Washington University, and he 

is a registered Professional Engineer. 

Mr. Nicholas Damiano is an electrical engineer at 

Pittsburgh Research Lab, CDC/NIOSH. Graduating from 

the University of Pittsburgh with a B.S.E.E. in 2002, Nick 

worked for Allegheny Energy, a local power distribution 

company, before entering civil service with the U.S. Dept. 

of Labor, Mine Safety and Health Administration in 

Pittsburgh as an accident investigator for Technical 

Support there. He has more than seven years of combined 

experience in the electrical field including computers, 

power systems, and digital signal processing. 

ABSTRACT 

Currently many underground coal mines worldwide have 

installed or been planning to install a tracking system to 

trace miners mainly for their safety. Although many 

systems have been reported functional, a lack of 

sophisticated and systematic error correction methods 

apparently is still an issue for them; often it results in a 

low system resolution. To improve the system resolutions, 

this paper introduces two position adjustment methods for 

mine tracking systems. The first is an entry-matching 

method that optimally adjusts an off-course tracking 

device to the closest tunnel (entry). The second is a 

distance measurement adjustment method that accurately 

adjusts the position of a tracking device along an entry 

according to a measured distance from the device to a 

reference point. The coplanar node-path network mine 

model is used as the foundation for the development of 

these two methods. 

INTRODUCTION 

Mine tracking systems are used to locate miners in 

underground coal mines during normal operations and in 

an emergency. Several types of mine tracking systems 

have been developed and many systems have been put 

into service worldwide. Among them are RFID (radio 

frequency identification), inertial-based, and radio nodebased systems. A RFID system determines the location of 

a miner using a stationary reader at a known location to 

scan a RFID tag worn by a miner within its range. An 

inertial tracking system relies on its own inertial 

measurement unit (IMU) to attain the data and complete 

its own location calculations. A node-based system uses 

the communication linkage of a stationary transceiver 

(node) and a mobile transceiver (tracking device) to 

estimate the relative location of the device. Although 

current tracking systems are functional, none seems 
 

 

capable of correcting for some common errors, such as a 

tracking device reporting itself inside a solid coal body. 

This paper presents two systematic position adjustment 

methods. The first is an entry-matching method that 

corrects errors by repositioning a tracking device that is 

reporting itself outside an entry to a location in the closest 

entry. The second is a distance measurement adjustment 

method that accurately adjusts the current position of a 

tracking device with a given distance to a reference 

location along the entries. 

MINE MODEL 

The mine model is the foundation for the position 

adjustment methods. The underground coal mine is 

modeled as a coplanar node-path network of its tunnels. 

The main tunnels in the mine are called “entries.” These 

main entries are intersected by other tunnels which are 

called “crosscuts.” Only the length of the entries and 

crosscuts are considered in the network model — their 

widths, heights and undulations are ignored. 

The center lines of the entries and crosscuts are mapped 

onto an x-y plane as the network paths, and the 

intersections of the entries and crosscuts are the network 

nodes. A curved entry or crosscut is modeled as a series 

of line segments. Thus, every entry and crosscut is 

unambiguously identifiable by one or more line segments 

(paths). Every intersection can be identified by the 

matching of the endpoints of two or more line segments 

(nodes). The location of a tracking device is identified by 

its unique (x, y) coordinates on the plane. 

The origin of the x-y coordinates for the mine’s node-path 

network can be set anywhere in the plane. The line 

segments representing all entries and crosscuts become 

deterministic once an x-y plane is selected for a mine. The 

selections of the scales of the x and y axes are also 

arbitrary. Mine entries can be mapped onto the plane in 

their actual or scaled-down lengths. 

Figure 1 displays a portion of a mine to illustrate the 

node–path network. Figure 1 (a) shows a selected x-y 

coordinate system superimposed onto the mine map with 

a scale of 1:1. Figure 1 (b) displays only the mine’s nodepath network. 

There are several essential operational restrictions on the 

mine’s node-path network. A mobile tracking device is 

only allowed to enter the network from predetermined 

fixed points. It must move continuously along and stay on 

the existing line segments. Under ordinary operation, no 

tracking device is allowed to enter the node-path network 

at another arbitrary point, jump from one point to another, 

or jump from one line segment to another. A tracking 

device must be at a point somewhere on a line segment. 

These restrictions are based on the reality that a mine has 

only limited entrances available for any tracking device to 

enter or exit the mine, and the mine entries and crosscuts 

are the only free space for them to travel. These 

restrictions are used in the procedure development of the 

position adjustment methods. 

 

(a) Axes are superimposed on a mine map 

Pillar 

x 

y 

100 feet 

75 feet 

Entry 

Crosscut 

x 

y 

0 

(100, 75) 

(b) Entry line segments on x-y plane 

Figure 1: Node-path network of a mine on the x-y 

plane 

TWO POSITION ADJUSTMENT METHODS 

The first method, the entry-matching method, is based on 

restrictions on the tracking devices in the mine’s nodepath network, and can be used to bring a tracking device 

back to the network if the device is off-track. The second 

method, the distance measurement adjustment method, is 

based on a measured distance between a stationary 

reference location and the tracking device. This method is 

particularly suited for a node-based tracking system. 

Entry-matching Method 

The entry-matching method brings an off-the-line 

tracking device to the closest entry, and it can be used in a 

variety of tracking systems for error correction. It can also 

be used as a damping procedure to minimize the drift 

effects of the IMU in an inertial tracking system. 

Two assumptions are made in the implementation of this 

method. The first is that the tracking system is able to 

save and retrieve the position value of each of its tracking 

devices obtained in the previous calculation. The previous 
 

 

 

0 

y 

x 

(xi, yi) P 

(x0, y0) 

(x1, y1) 

Previous 

position 

Initial mapped location 

 

 

position value will be referenced in determining the 

current optimal position of a tracking device. The second 

assumption is that a mapping tool, which is not included 

in this paper, has already mapped a real three dimensional 

(3-D) location of a tracking device in the mine to a (xi, yi) 

location, called an initial mapped location (IML), on the 

mine’s plane prior to implementation of this method. The 

entry-matching method starts with the IML (xi, yi) and 

ends with an optimal current location (xc, yc) on the 

mine’s coplanar x-y plane. 

This method covers three different IML outcomes 

resulting from mapping a real 3-D location of a tracking 

device onto the x-y plane. The first outcome is that the 

IML (xi, yi) falls on the same entry or line segment with 

the previously saved position (PSP) in the last step, as 

shown in Fig. 2. The IML is, in this case, regarded as the 

optimal current position (xc, yc). The system simply 

updates its position with the IML (xi, yi) values, and 

moves on to the next round of position adjustments. 

Equation (5) can be used to determine whether two points 

share the same entry or line segment on the x-y plane.

Figure 2: IML and PSP share the same line segment 

The second outcome is that the IML of a tracking device 

is near the PSP but off any entry course or line segment 

on the x-y plane. One example is the device reports its 

position inside a coal body. As stated before, this is not 

allowed. The IML needs to be adjusted to the optimal 

location on an entry. The optimal current position of a 

tracking device is the closest point from the IML to the 

closest entry or line segment. The following is a general 

approach to obtain such an optimal position. The tracking 

system first draws, from its IML, perpendicular lines to 

all of the line segments located near the IML on the x-y 

plane. The system then identifies, among all of the 

perpendicular lines, the one with the shortest distance 

from the IML. The intersection to that line segment will 

be regarded as the current optimal position (xc, yc) of the 

tracking device, as shown in Fig. 3, where the dotted lines 

are the perpendicular lines. The tracking system then 

updates and saves the location value. 

Next is the introduction of steps to obtain an intersection 

on a line segment by a perpendicular line, and the 

distance between the IML and that line segment. The line 

segment with two endpoints of (x0, y0) and (x1, y1), shown 

in Fig. 3, is used as an illustration of these steps. The first 

step is to find the slope of that line segment using (1). 

x 

y 

0 

(xi, yi) P 

(x0, y0) 

(x1, y1) 

(xc, yc) 

A 

B 

C 

D 

Figure 3: Find an optimal position from IML 

⎧0 if y0 − y1 =0 ⎪

a = ⎨( y 0 − y1 ) /(x0 − x1 ) if x0 −x1 ≠ 0 (1)

⎪

⎩∞ if x0 −x1 =0

The second step is to obtain the intersection (xc, yc) from 

the IML to that line segment using (2). Note: there are 

many different ways to calculate the intersection; we are 

suggesting one of them. 

⎧⎡xi ⎤ ⎪⎢ ⎥ for a = 0

⎪⎣ y0 ⎦

⎪⎡

⎢ 0 ay 0 + xi + ay ⎤ ⎪ a

2

x − i ⎥ ⎡x ⎪ 2 c ⎤ ⎪⎢ 1+ a ⎥ ⎢ ⎥ = ⎨ for 0 < a < ∞ (2)

y ⎢ ⎥ ⎣ c ⎦ ⎪ ax + a 

2

y − ax + y ⎢ i i 0 0 ⎥ ⎪⎢⎣ 1+ a 

2 ⎥⎦ ⎪

⎪⎡x ⎤ ⎪ 0 ⎢ ⎥ for a = ∞ ⎪⎩⎣ yi ⎦

The third step is to calculate the distance (D) between the 

IML (xi, yi) and the intersection (xc, yc) on the 

perpendicular line A on Fig. 3 using (3). Note: there are 

many different ways to calculate the distance; we are 

suggesting one of them. 

⎧ y i − y0 for a = 0 ⎪

⎪⎪ a(x − x ) + ( y = 0 i yi − 0 ) D ⎨ for 0 < a < ∞ (3)

⎪ 1+ a 

2

⎪

⎪ x 0 − xi ∞ ⎩ for a =

Similarly, lines B, C, and D are drawn perpendicular to 

the rest of the surrounding line segments from the IML 

(xi, yi) as shown in Fig. 3. The intersections of these 

surrounding line segments and the distances to those 

segments from the IML can again be obtained using (1), 

(2), and (3). Evidently, in this example, the shortest 

distance is from the IML (xi, yi) to the intersection (xc, yc) 

on line A. The intersection (xc, yc) is selected as the 

current optimal tracking device position as it shares the 

same line segment with the PSP, P on Fig. 3. 
 

 

 

 

If the IML (xi, yi) has the same short distances to two 

separate line segments, as shown in Fig. 4, the tracking 

system refers to its PSP, P, to determine the current 

position of the tracking device. In this example, the 

position (xc, yc) will be selected as the tracking device’s 

optimal position because it has the shortest distance to the 

PSP, P, from the last step. 

 

 

 

 

0 

(x0, y0) 

y 

(xi, yi) P 

(xc, yc) 

D 

(x1, y1) A 

x 

Figure 4: IML has the same distance to two line 

segments 

The third outcome is when the IML (xi, yi) is farther away 

from the PSP, P, as shown in Fig. 5. To prevent the 

tracking device from executing a sudden long jump from 

one line segment to another, or from one entry to another, 

the tracking system may try to find an average location 

over a number of initial mapped locations, and then 

determine its current optimal (xc, yc) position. Equation 

(4) can be used to calculate an average initial location 

value, (xai, yai), where n is the total number of the initial 

mapped locations. The average initial location value can 

then be used to find an optimal current position on the 

closest entry. After that, the process moves on to the next 

round position adjustments. 

x 

y 

0 

(xi, yi) P 

Figure 5: IML is too far from PSP 

⎡x ai ⎤ ⎡( x i1 + x i2 +...+ xin ) / n ⎤ ⎢ ⎥ = ⎢ ⎥ (4)

⎣ y ai ⎦ ⎣( y i1 + y i2 +...+ yin ) / n⎦

where xai and yai : the average values; xi1 and , xi2 ,Lxin 

y i1 , y i2 L y in : initial mapped values; n : the number of

the initial mapped locations of the tracking device. 

Distance Measurement Adjustment Method 

This method can be applied to those systems that provide 

an estimated distance along the entries between a known 

reference point and the tracking device. A node-based 

tracking system is an example of a system that uses the 

communication linkage of a stationary transceiver (node) 

and a mobile transceiver (tracking device) to estimate the 

radio path distance between them. An inertial tracking 

system can also use this method to correct its tracking 

device if its on-board IMU is capable of “remembering” a 

distance to a reference location and turning points along 

its moving path. 

The fundamental assumptions with this method are that 

the radio signals travel only along the entries, and the 

strongest signal received by a tracking device always 

follows the shortest path. In some node-based tracking 

systems, a tracking device estimates the distance a signal 

travels from a stationary transceiver node by detecting 

received radio signal strengths. In other systems, a

tracking device calculates the distance between itself and 

a node using the radio signal traveling time. 

In general, there exist many paths from a node to a 

tracking device. Fig. 6 gives an example of signal paths 

shown by the dotted lines from the node to the tracking 

device receivers. In the figure, N represents the 

transceiver node and R1, R2, and R3 represent tracking 

device receivers. 

x 

y 

0 

N R2

(xn, yn) (xi, yi) 

R1 R3 

(x1, y1) 

(x0, y0) 

Figure 6: Node transmits navigation signal to receivers 

For convenience in the following discussion, we assume 

that a node under discussion transmits a navigation signal 

that includes two parts; a timing signal and the current 

position of the node. After receiving the signal, a receiver 

calculates the signal traveling time and the signal 

traveling distance (STD), D, from the node, and adjusts its 

position according to the STD. The initial position, (xi, 

yi), of a receiver on a line segment must already be known 

before this method can be used. The distance 

measurement adjustment method starts with the initial 

position (xi, yi) and ends with an updated position (xc, yc) 

of the receiver on the receiver’s line segment. 

In an underground mine environment, the radio signals 

from a node may turn around the corner of a solid coal 

pillar before reaching a receiver as shown in Fig. 6. The 

figure also shows that the signal from node N may follow 

multiple paths to its receivers, and some of the paths may 

have one or more turns. The STD, D, can not be 

immediately used to complete the receiver’s location 

computations if the signal path is not straight. The 

tracking system solves for its receiver’s actual location by 

finding the shortest path to the node with the minimum 

number of turns among all possible radio signal paths. In 

most underground mine environments, the fewer turns a 

path has, the shorter the path is. 
 

 

 

There are three typical signal paths that are covered in the 

second method, and they only differ in the number of 

turns each one has. As shown in Fig. 6, the first one is the 

signal path from the node (N) to the receiver (R1), which 

has no turns. The second is the signal path from the node 

(N) to the receiver (R2), which has only one turn at (x1, 

y1). The third is the signal path from the node (N) to the 

receiver (R3), which has two separate turns at (x1, y1) and 

(x0, y0). The system will take the path with the least 

number of turns. 

The process starts with a search of a straight path from a 

node to a receiver. It examines whether a node and a 

receiver share the same line segment slope and endpoints. 

A generalized case is shown in Fig. 7 where (xn, yn) and 

(xi, yi) are the node position and the initial receiver 

position respectively. If one of the conditions in (5) is 

satisfied, the node and the receiver or, any two points on 

the x-y plane, should be on the same straight line 

segment. 

y − y y − y 

a = n 0 =
 i 0 (5a) 

x n − x0 x i − x 0 

for x n − x0 ≠ 0 and x i − x0 ≠ 0
 

y − y y − y

a = n 0 = i 1 (5b)

x n − x0 x i − x1 

for x n − x0 ≠ 0 and xi − x1 ≠ 0

If the slope, a, of a line segment is infinite, the receiver 

only needs to check whether it shares the same line 

segment endpoints with the node line segment. If so, the 

node and the receiver are on the same line segment or 

entry. 

 

 

 

 

 

0 

N 

x 

(x0, y0) 

(xn, yn) 

(xi, yi) 

(xc, yc) 

R y 

(x1, y1) 

Figure 7: Node and receiver are on the same line 

segment 

When the node and the receiver are on the same line 

segment, the position of the receiver can be simply 

adjusted using the STD, D, from the node along the line 

segment. With the calculated slope, a, the receiver’s 

current position can be calculated from one of the 

equations in (6). The following criteria can be used to 

select a correct equation in (6). I) if a ≥ 0, and yi ≥ yn and 

xi ≥ xn, use (6a); II) if a ≤ 0, and yi ≥ yn and xi ≤ xn, use 

(6b); III) if a ≥ 0, and yi ≤ yn and xi ≤ xn, use (6c); IV) if a 

≤ 0, and yi ≤ yn and xi ≥ xn, use (6d); V) if a = ∞, and yi ≥

yn, use (6e); ) if a = ∞, and yi < yn, use (6f). After that, the 

process moves on to the next round of receiver position 

adjustments. 

⎧⎡x D / 1 a 

2 ⎤ + ⎢ n + ⎪ ⎥ (6a) ⎪⎢ 2 ⎥ aD + ⎪⎣ y n + ( ) / 1 a ⎦

⎪ for a ≥ 0, y ≥ y and x ≥ x ⎪ i n i n 

⎪⎡ ⎤ x − D / 1+ 2

⎪ n a ⎢ ⎥ (6b) ⎪⎢

⎣ y n + + ⎪ aD) / 1 a

2 ⎥ ( ⎦ ⎪ for a ≤ 0, y ≥ i y n and x ≤ x ⎪ i n 

⎪⎡ 2 ⎤ − + ⎪ xn D / 1 a ⎢ ⎥ (6c) ⎡x c ⎤ ⎪⎢ ⎥ ⎢ ⎥ = ⎨⎣ y n − (aD) / 1+ a

2

⎦ ⎣ yc ⎦ ⎪ for a ≥ ⎪ 0, y ≤ i y and x ≤ n i xn 

⎪⎡ ⎤ ⎪ xn + D / 1+ a

2

⎢ ⎥ ⎪ (6d) ⎢ 2 ⎥ ⎪⎣ y n − (aD) / 1 + a ⎦ ⎪ ≤ ⎪ for a 0, y ≤ i y and x ≥ n i xn 

⎪⎡x ⎤ ⎪ n

⎢ ⎥ for a = ∞, and y ≥ i y (6e) ⎪⎣ yn + D n

⎦ ⎪

⎪⎡xn ⎤ ⎢ ⎥ for a = ∞, and y ⎪ ≥ i y (6 f )

⎣ yn − ⎩ D n

⎦

N (xn, yn) D 

x 

y 

0 

R (xi, yi) 

(xc yc) 

(x0i y0) (x1, y1) 

(x2 y2) 

(x3 y3) 

(x4 y4) 

Figure 8: Node and receiver segments share an 

intersection 

The process will be programmed to search for a path with 

one turn after the above search for a zero-turn path fails. 

Fig. 8 shows a generalized case where the signal path has 

a turn at (x4, y4) from the node (N) at (xn, yn) to the 

receiver (R). The receiver’s initial position is at (xi, yi). 

As shown in Fig. 8, (x0, y0) and (x1, y1) are the endpoints 

of the node line segment; (x2, y2) and (x3, y3) are the 

endpoints of the receiver line segment. The intersection of 

the two line segments is (x4, y4). The location of the node 

(xn, yn) is already known from the navigation signal. A 

circle is then drawn at (xn, yn) with the radius of the STD, 

D, to confine the search area. Any potential signal path 

shall fall within the circle because the STD is the longest 

distance for any possible signal path. Within the circle, 

the receiver tries to determine whether there exists a path 
 

from itself to the node through an existing intersection in 

the following steps. 

1) Referring to Fig. 8, use (7a) to obtain the slope of the 

node line segment, and then use (7b) to obtain the slope of 

the receiver line segment. 

an = ( y1 − y0 ) /(x1 − x0 ) (7a) 

ar = ( y3 − y2 ) /(x3 − x2 ) (7b) 

2) Calculate an intersection (x, y) of these two line 

segments using (8). The calculated intersection will be the 

actual intersection if it already exists on both line 

segments, or it will be the calculated intersection of the 

extension of both lines to where they meet. The latter 

indicates that these line segments have no actual common 

connection (not shown in Fig. 8). 

⎡an xn − yn − ar xi + yi ⎤ ⎢ ⎥ ⎡x⎤ a a ⎢ ⎥ ⎢ ⎥ = n − r (8) ⎢ ⎣ y⎦ an yi − a ⎥ n ar xi + an ar xn − ar yn ⎢ ⎥ ⎣ a n − ar ⎦

3) Use the inequality (9) to check whether the calculated 

intersection (x, y) from (8) is within the STD, D. The 

intersection is valid only if equation (9) is satisfied. 

(x − x n ) 2 + ( y − y 

2 2 n ) < D (9)

4) Determine whether the calculated intersection already 

exists on both the node and receiver line segments by 

checking whether its (x, y) coordinates satisfy every 

inequality in (10). The intersection is an actual turning 

point of the signal path only if the checking passes (10). 

min (x 0 , x 1 ) ≤ x ≤ max (x 0 , x 1 )

min ( y 0 , y 1 ) ≤ y ≤ max ( y 0 , y 1 )

min (x 2 , x 3 ) ≤ x ≤ max (x 2 , x 3 ) (10)

min ( y 2 , y 3 ) ≤ y ≤ max ( y 2 , y 3 )

The path with a single turn can be confirmed only after 

steps 3 and 4 are passed (Ideally, it should have x = x4, 

and y = y4). Repeat the same procedures to determine all 

other paths between the node and the receiver within the 

circle. 

All paths start from node position (xn, yn). The next phase 

is to determine the ends of the paths using the following 

three steps. 

1) Find the distance from the node (xn, yn) to the 

intersection (x4, y4) using (11). 

D = (x − x ) 2 2 + ( y − x ) (11) n−4 4 n 4 n 

2) Find the partial STD from point (x4, y4) to the receiver 

along the receiver line segment using (12). 

D = D − D (12) r−4 n−4 

3) As shown in Fig. 8, the partial signal path from (x4, y4) 

to (xi, yi) is a straight line segment, and the procedures 

introduced earlier in finding a zero-turn path can be used 

to calculate the path end point (xc, yc) as follows. 

Substitute D with Dr-4, xn with x4, and yn with y4 in 

equation (6). Then use it to calculate the point (xc, yc). 

After all of the paths with their (xc, yc) end points are 

obtained, the one with the shortest distance to the 

receiver’s initial position (xi, yi) will be used as the real 

signal path. The receiver can update its position with that 

path’s end point accordingly. The process then moves on 

to the next round of the position adjustments. 

The process will search for a signal path with two turns if 

the above search for a one-turn path fails. This case is 

shown in Fig. 9 where the signal path, which is from the 

node (N) at (xn, yn) to the receiver (R), has turns at (x4, y4) 

and (x7, y7). (xi, yi) is the initial position of the receiver. 

N (xn, yn) D 

x 

y 

0 

R (xi, yi) 

(xc yc) 

(x0i y0) (x1, y1) 

(x2 y2) 

(x3 y3) 

(x4 y4) 

(x5 y5) 

(x6 y7) 

(x7, y7) 

Figure 9: Node and receiver line segments share the 

third line segment 

Although Fig. 9 gives only one signal path, multiple paths 

between the node and the receiver may exist, and all of 

them need to be identified. The shortest one among them 

is regarded as the actual path. The following procedures 

can be used to identify a path. Please refer to Fig. 9 for 

symbols. 

1) First, draw a circle at the center of the node position 

(xn, yn) in the radius of the STD, D. The search for every 

path begins from the center. Every (x, y) point of every 

possible path must satisfy the condition confined by 

equation (13). Again, this is because the STD is the 

longest distance for any possible path. 

2 2 2 D ≥ (x − x ) + ( y − y ) (13) n n 
2) Now, use the following criteria to determine the initial 

path’s search direction along the node’s line segment. 

Start from the right if xi ≥ xn, where xi is the initial x 

coordinate value of the receiver, otherwise start from the 

left (if xi < xn). Similarly start from the upper direction if 

yi ≥ yn, otherwise start from the down direction (if yi < 

yn). In the example shown in Fig. 9, the search path 

should obviously start from the right because xi > xn. 

Then find the nearest intersection along the node line 

segment. It is (x4, y4) in this example. Calculate the 

distance between (xn, yn) and (x4, y4) using equation (14) 

if (x4, y4) is in the circle and satisfies equation (13). 

D n−4 = (x − x ) 2 + ( y 

2

4 n 4 − x n ) (14)

3) Calculate the partial STD from (x4, y4) to (xi, yi) using 

equation (15). 

D r −4 = D − D n−4 (15)

Then draw another circle at (x4, y4) with radius of Dr-4; the 

possible position of the receiver should be located within 

both the new and the old circles as shown in Fig. 10. As a 

result of the drawing of the second circle at the center of 

(x4, y4), the partial signal traveling path from (x4, y4) to 

(xi, yi) apparently has only one turn at (x7, y7). The 

procedures for searching for a path with a single turn 

introduced earlier can be applied to find a path from (x4, 

y4) to the receiver. 

N (xn, yn) D 

x 

y 

0 

R (xi, yi) 

(xc yc) 

(x0i y0) (x1, y1) 

(x2 y2) 

(x3 y3) 

(x4 y4) 

(x5 y5) 

(x6 y7) 

(x7, y7) 

Figure 10: The second circle is drawn at (x4, y4) with 

radius Dr-4 

Repeat this procedure and find all other possible paths 

from the node to the receiver within the initial circle. 

Then identify the shortest path among them. It is useful to 

note that the number of turns with a path is equal to the 

number of the circles drawn in the above path-finding 

procedure. 

This method searches for the shortest path starting with 

the least number of turns. Evidently, the core parts of this 

method are those used to calculate the current position of 

a receiver along the straight path. Through the repeated 

turn-eliminating process, the paths with one or more turns 

all have their partial straight lines remaining, and the core 

parts then are used for completion of the position 

calculations. This nested process could be used to create a 

program with a small footprint on computer memory for 

an actual system. 

SUMMARY 

This coplanar node-path network model of an 

underground coal mine can be used in the development of 

more accurate position adjustment methods for tracking 

systems. In this model, the entire mine entry network can 

be digitally mapped onto an electronic coplanar network 

that can be displayed on a self-updating computer 

monitor. The two methods presented are examples of 

using the model to make more accurate position 

calculations. The increased accuracy can greatly improve 

the chances of precisely locating individuals in need and 

reduce the time rescue teams need to locate them. 

ACKNOWLEDGMENTS 

The authors wish to thank Mr. Richard Unger, a lead 

research engineer, at Pittsburgh Research Lab, 

CDC/NIOSH, for his valuable suggestions. The authors 

also wish to thank Mr. Todd M. Ruff, a lead research 

engineer at Spokane Research Lab, CDC/NIOSH, for his 

suggestions. 

REFERENCES 

[1] D. Bernstein, A. Kornhauser, 1996. “An introduction 

to map matching for personal navigation assistants,” New 

Jersey TIDE Center

www.njtude.org/reports/mapmatchintro.pdf. 

[2] A. Hatami, B. Alavi, K. Pahlavan, M. Kanaan, 2006. 

“A Comparative Performance Evaluation of Indoor 

Geolocation Technologies,” Interdisciplinary Information 

Sciences, Vol. 12, No 2, pp. 133-146. 

[3] G. Taylor, G. Blewitt, 1999. “Virtual Differential GPS 

& Road Reduction Filtering by Map Matching,” ION 

GPS’ 99, 14-17 September 1999, Nashville, TN, pp. 

1675-1684. 

[4] J. Geenfield. 2002. “Matching GPS Observations to 

Locations on a Digital Map,” 

www.njtide.org/reports/TRB2002-greenfeld.pdf 

[5] D. Cyganski, et al, 2007. “WPI Precision 

Personnel Locator System,” ION-NTM Session D1: 

Urban and Indoor Navigation Technology, January 

2007, San Diego, CA. pp. 1-9. 

[6] H. Parikh, W. Michalson, R. Duckworth 2004. 

“Performance Evaluation of the RF Receiver for Precision 

Positioning System,” ION GNSS 17th International 

Technical Meeting of the Satellite Division, 21-24 Sept. 

2004, Long Beach, CA. pp. 1908-1917. 
[7] S. Syed, M. Cannon, 2004. “Fuzzy Logic Based-Map 

Matching Algorithm for Vehicle Navigation System in 

Urban Canyons,” Presented at ION National Technical 

Meeting, San Diego, CA, January, 26-28, 2004. 

[8] A. Brown, Y. Lu, “Indoor Navigation Test Results 

Using an Integrated GPS/TOA/Inertial Navigation 

System,” www.navsys.com/Papers/06-09-005.pdf 

[9] C. Basnayake, O. Mezentsev, G. Lachapelle and 

M.E. Cannon, 2005. “An HSGPS, inertial and mapmatching integrated portable vehicular navigation 

system for uninterrupted real-time vehicular 

navigation,” Int. J. Vehicle Information and 

Communication Systems, Vol. 1, Nos. 1/2, pp.131– 

151. 

[10] M. Bittle, P. Brandt, A. Facemire, M. Hunt, M. 

Sweetman, 2007 “Team 2: Mine Tracking System: 

Detailed Design Review,” Senior Design Seminar, West 

Virginia University, 

https://eidr.wvu.edu/files/5444/MineTrackingSystem.pdf 

[11] L. Miller, 2006 “Indoor Navigation for First 

Responders: A Feasibility Study,” National Institute of 

Standards and Technologies,

www.antd.nist.gov/wctg/RFID/Report_indoornav_06021 

0.pdf