1-5-2 
1 INTRODUCTION 
The determination of the location and trajectory of vehicles 
promises to become one of the most extensively applied 
applications of Global Positioning System (GPS) technology. The 
near instantaneous knowledge of the position and heading of 
vehicles aids the effective management of trucking fleets, aircraft, 
marine vessels, trains and automobiles. The accuracy generally 
required by these applications can be achieved using the Coarse 
Acquisition (C/A) code in the differential mode of operation. 
However, often the number of visible satellites is less than four 
due to the obstruction of GPS signals, especially when the 
vehicles are in urban or mountainous areas. Under these 
conditions, continuous three-dimensional positions cannot be 
determined from GPS alone, and it is insufficient as a sole 
positioning solution for safety regulated industries, such as train 
signalling. 
Whilst GPS provides accurate positions when sufficient satellites 
are visible, other positioning sensors which are not constrained 
by satellite visibility, such as dead reckoning devices, will 
continually provide positions. Dead reckoning is a technique of 
computing the position of a vehicle from two or more sensors 
which measure the heading and displacement of the vehicle (Kim 
et al., 1996). Unfortunately, dead reckoning devices are prone to 
drifts and biases, producing measurements of uncertain 
accuracies. Without regular calibration, the accuracy of dead 
reckoning data degrades over time. 
The integration of GPS and dead reckoning offers an improved 
solution that not only compensates for poor GPS and dead 
reckoning data, but also provides protection r rom gross errors in 
either sub-system. The result is accurate, hign rate position and 
trajectory information. Also, by utilising the knowledge of the 
road/track locations as an additional measurement or constraint, 
the integrity of the vehicle position estimates can be greatly 
improved. This particular aspect of the system is termed “map 
matching”. Map matching is a particularly useful process in train 
positioning, given that trains are constrained to the tracks. 
Given an integrated DGPS, dead reckoning and map matching 
system, the location of a train can be isolated to a particular track 
from multiple parallel tracks. This paper provides a brief 
overview of Differential GPS (DGPS), dead reckoning and map 
matching techniques, and provides a technique for integrating 
measurements from these sources. 
2 DIFFERENTIAL GPS 
The Global Positioning System is a satellite based radio 
navigation system developed and controlled by the US 
Department of Defense. • The satellites transmit a 
Coarse/Acquisition (C/A) code modulated on the LI carrier 
frequency. This code enables a range measurement to be 
determined between the satellite and the receiver on Earth. The 
range, termed the pseudorange, is based on the time taken for the 
signal to travel from the satellite to the receiver and is biased by 
the misalignment of the satellite and receiver clocks. To compute 
a three dimensional position, observations to at least four 
satellites are required. Three pseudoranges are required to solve 
for the three position components (latitude, longitude, height) and 
the fourth resolves the clock offset. 
Regardless of the observation technique or quality of the GPS 
receiver, for instantaneous positioning using a single GPS 
receiver, the attainable accuracy is 100 m 2DRMS at a 95% 
confidence level (FRNP, 1996). This is due to the intentional 
degradation of the C/A-code, termed Selective Availability (SA) 
(McNeff, 1991; McNeff, 1992). Many of the errors affecting GPS 
observations, including SA, are highly correlated over a localised 
area. To minimise these errors, differential positioning techniques 
are adopted. DGPS positioning involves the simultaneous 
measurement to the same satellites at multiple sites. One receiver 
remains stationary, usually at a point of known coordinates, and 
is termed the reference receiver, whilst other rover receivers 
occupy points of interest. 
Differential corrections are calculated at the reference receiver, 
transmitted to the rover receiver via a communication link and 
applied to the measured pseudoranges. For each satellite in view, 
the reference receiver observes the C/A-code, corrects this range 
for receiver dependent errors (such as the receiver clock error) 
and calculates the difference between this measured range and a 
computed range. The computed range is the distance between the 
satellite and reference station based on the known reference 
station coordinates and the satellite coordinates computed from 
the broadcast ephemeris. The difference between the measured 
and computed range is termed the differential correction (Figure 
1). To improve the achievable accuracy, a range rate correction, 
which is the difference between two consecutive pseudorange 
corrections, is also transmitted. Typically, the rover receiver can 
be positioned to better than 5 m, and a study undertaken at the 
test site by Hailes and Gerdan (1998), resulted in an accuracy of 
approximately 1.4 m 2DRMS at a 95% confidence level.