3 DEAD RECKONING 
Dead reckoning involves the process of determining the position 
of a subject at any instant by applying the recent history of 
velocity and heading measurements to the last well-determined 
position (point of departure or subsequent fix) (NMEA, 1992). 
The determination of subsequent positions requires a continuous 
source of velocity and heading information. 
The sensors which comprise a dead reckoning system provide 
either velocity or heading information. Generally, the vehicle’s 
odometer is chosen to provide the velocity, as it is simple and 
cheap source of information. However, the determination of 
vehicle’s heading is more complicated due to many external 
forces which combine to effect the accuracy. Heading is measured 
either with a gyroscope or magnetic compass, each instrument 
having their own limitations. As an alternative to a heading 
measurement, rate of change of direction can be measured with 
rate gyroscopes. The use of rate gyroscopes in a dead reckoning 
system requires the raw observations to be integrated over time to 
compute a heading (Schwarz et al., 1993). 
Dead reckoning devices are prone to drifts and biases, producing 
measurements of uncertain accuracies. The accuracy of each 
component is often expressed as a percentage of distance or time 
travelled; low cost systems incur errors of approximately 2-5%, 
i.e. 2-5 m of error after travelling 100 m. As long as adequate 
error modelling and calibration is performed, even low cost 
inertial sensors with systematic and major error characteristics 
can be used within integrated navigation systems (Vieweg, 1994). 
However, a complete loss of GPS derived positions for extended 
time periods can compromise error budgets, since a 5% system 
can accumulate 100 m of error after 2 km of travel. 
4 DGPS/DEAD RECKONING INTEGRATION 
It is clear that no single sensor can provide continuous, accurate 
vehicle position information. Therefore, multisensor integration is 
required to provide the vehicle with complementary, sometimes 
redundant information on its position and trajectory. Kalman 
filtering techniques were utilised in the integration of the DGPS 
and dead reckoning measurements to obtain an optimal estimate 
of the current state of the system and a prediction of the future 
state of the system (Figure 2). The state consisted of nine 
parameters, including three positions components (e, n, u), three 
velocities (è,n,û) and three accelerations (ë,ri,ü). The Kalman 
filter uses the statistical characteristics of a measurement model to 
recursively estimate the state and it’s covariance. Because of its 
recursive nature, the filter is highly suited to real-time 
applications. It can be used without storing any historical data, 
and thus improves computational efficiency. 
Initialise Filter 
Figure 2. Flowchart of the Kalman filter process 
5 MAP MATCHING 
To increase the integrity of the positioning system, especially 
during periods of long GPS outages, map matching techniques 
can be applied. The map matching module plays an important 
role in vehicle location and navigation systems. It employs a 
digital map to increase the positioning system’s integrity, 
reliability and accuracy. Map matching systems have been 
developed to correlate the filtered position or trajectory of a 
vehicle with a position associated with a location on a map (Zhao, 
1997). When the observations and statistics indicate that the 
vehicle is on a certain position on the map, the position of the 
vehicle may be adjusted to some absolute position on the map. 
Map matching is being extensively used for in-car navigation 
systems and has the potential to be particularly effective in the 
railway industry, given that the train is constrained to the track, 
thus significantly limiting the possible scenarios. 
A conventional map matching algorithm compares the trajectory 
of the vehicle against known roads close to the previously 
mapped position. To determine the location of the train with 
respect to the track, multiple model estimation algorithms were 
utilised. These adaptive algorithms were first presented by Magill 
(1965) and are often referred to as multiple hypothesis tests. 
These tests utilise a parallel bank of Kalman filters, each 
representing another hypothesis, or in this scenario, another track. 
A Kalman filter solution is performed for each filter within the 
bank, and the individual filter estimates and probabilities are 
retained. In the original filter proposed by Magill (1965), the 
unknown factor was the covariance quantity, requiring a 
significant amount of numerical calculations for each filter. 
However, in this modified technique, the unknown factor is the 
perpendicular offset to track that only appears in the measurement 
model (Figure 3). The gain and covariance structures of the filter 
are uniform for the full parallel bank, thus reducing the 
computing requirements, and enabling real-time operations to be 
feasible (Wanless and Lachapelle, 1988). Figure 4 depicts the 
map matching process used.