1-5-5 
whereas the global test analyses more than one epoch and 
indicates global trends, i.e. that the train is on a different track. 
The third test, an F-ratio test, determines the probability that the 
train was travelling on a particular track. Since the F-test provides 
a probability, the confidence associated with a particular track 
can be determined. 
The LOM test statistic, T k , highlights instances when a modelling 
or measurement error occurs by rejecting the null hypothesis, H a . 
It is derived from the quadratic product of the predicted residual, 
normalised by their inverse covariance matrix: 
V * = [(f-:r V *) + rQx k x k ) (f-7' v *)] 
(6) 
T k = ( 7 ) 
The null hypothesis proposes that the predicted residuals form a 
zero mean, time uncorrelated sequence with Gaussian 
distribution: 
Ho \ k ~ N(0,Q VtVt ) (8) 
is rejected if 
T t 2 X, 2 ,('n„0) (9) 
where, 
X~ is the upper probability of the chi-square distribution, 
Q is Gaussian white noise matrix, and 
v k v k 
m* is the degrees of freedom. 
The GOM test statistic, X k , can be used to detect unmodelled 
global errors. Rather than sum the LOM statistics, Talbot (1991) 
computes the weighted sum of the LOM statistics: 
(10) 
The null hypothesis, H 0 , proposes that the global model is correct 
and matches the specified models. This hypothesis is rejected if: 
k 
(>>) 
i=1 
The third test, an F-ratio test analyses two possible scenarios in 
an attempt to determine whether the solutions are of equal 
precision. The null hypothesis states that the solutions are 
statistically equivalent, and the alternate hypothesis indicates that 
the solutions are of different precisions. The greater the F k value, 
the greater probability that the scenario with a smaller GOM 
value is the correct solution. This analysis is performed between 
the two solutions with the smallest GOM values. The F value is 
calculated using: 
Larger 
F = -* 
k Smaller 
T k 
(12) 
The null hypothesis is rejected if: 
F t * f 
(13) 
where, 
F H is the upper probability of the F distribution, and 
^Larger ^Smaller ar£ t j, e degrees of freedom of the larger 
and smaller GOM values respectively. 
6 TESTING 
Two tests were performed on a train travelling at velocities of up 
to 80 km/hr over four days, along a section of railway track, 
between Ipswich and Forest Hill, Australia. The test site contains 
many obstructions including bridges, tunnels and areas of dense 
vegetation. The first test provided a map of the track for map 
matching purposes, and the second test was conducted to test the 
performance of the algorithms developed. 
Track Determination for Map Matching 
In order to provide an accurate map database for the map 
matching component of the test, the track centreline was digitized 
from a combined GPS/terrestrial survey of the track. This data set 
was created using dual frequency GPS receivers; two rover units 
located on the train and three reference receivers situated in 
signalling sheds along the track. The signalling sheds were 
selected to ensure that a reference receiver was located within 
10km of the train at all times. The WGS84 coordinates of the 
signalling sheds were determined via a static GPS survey 
connected to four regional permanent marks and four permanent 
GPS tracking stations. Three of the GPS tracking stations form 
part of the Australian Fiducial Network (AFN) and the fourth is 
part of the International GPS Service for Geodynamics (IGS) 
worldwide network of permanent GPS tracking stations. The 
receivers on the train used on the fly (OTF) ambiguity resolution 
techniques to identify the integer biases and provide precise 
coordinates at discrete epochs. 
Having two receivers on the train also enabled an integrity check 
to be performed. The integrity check involved a comparison 
between a GPS carrier phase derived distance and a taped 
distance (Figure 5). This fixed baseline assessment endeavors to 
highlight erroneous solutions. A tolerance of 0.2 m for each 
antenna, equating to a baseline tolerance of 0.4 m was considered 
suitable to indicate such occurrences. If the difference between 
the two carrier phase positions exceeded this tolerance, the two 
positions were ignored in the track determination. The epochs