Figure 3. The map matching system 
Figure 4. Flowchart of the map matching algorithm used 
(Adapted from Zhao (1997)) 
Many different approaches may be used in the actual 
computations of Figure 4. Within the first step, the filtered 
position and variance-covariance information is a by-product of 
the Kalman filter computations (Figure 2). Once the filtered 
position is known, it is possible to extract all the possible track 
segment scenarios within a given range. This is achieved by using 
a grid cell system. The map database file contains both grid and 
vector based referencing. The track itself consists of a series of 
vectors, linking three dimensional map nodes, which also have 
grid cell attributes. The grid attributes are calculated by 
overlaying a grid on the track and computing a grid cell reference 
for each point using: 
^Grid 
E - E 
^ Position Origin 
Grid Interval 
(1) 
J Grid 
N -N 
Position Origin 
Grid Interval 
(2) 
Given that each node (Figure 3) within the database has a known 
grid reference, and the computed location of the train is known, it 
is possible to compute a grid reference for the filtered position. It 
is then possible to extract all track nodes within a certain number 
of grid cells of the filtered position. Once the relevant track 
segments are extracted, the Kalman gain, (Equation 3), and 
the three dimensional perpendicular offset, or predicted residual, 
F _ T v k (Equation 4), to each parallel track is computed 
(Figure 3). The predicted residual is computed by assuming a 
straight line between any two nodes (Figure 3). 
fQ A t + 7’Qjc Jt * t ] ( 3 ) 
F-T y k = F X k~T X k ( 4 ) 
where, 
fQ,.,. rQr x are the covariance matrix of the filtered 
r x k x k . I x k x k 
state and track respectively, 
A k ,A k are the design matrix, and the transpose of the 
design matrix respectively, and 
F x k , T \ k are the filtered and track coordinate matrices 
respectively. 
Once, the gain and the perpendicular offset are calculated, the 
map matched position, MM x k , is computed using: 
X k F X k 
(5) 
Having constrained the filtered position to each track, three 
statistical tests are performed in an attempt to determine on which 
track the train is travelling. The first two tests developed by 
Teunissen and Salzmann (1989) analyse the predicted residuals to 
see if they match their expected stochastic properties. These tests 
are known as the Local Overall Model (LOM) and Global Overall 
Model (GOM). The local test only analyses one epoch of data at a 
time and highlights solutions containing noise or large biases, 
1-5-4