The aim of the Global Muon Trigger is to combine the output of the RPC and
DTBX/CSC based trigger systems and to pass the 4 highest 
muons of the
event to the Global Trigger [6].
In the design of the Global Muon Trigger it is also foreseen to receive so-called quiet bits from the Calorimeter Trigger used to select isolated muons. Since this information is not yet available in the current implementation of the Calorimeter Trigger simulation it was not used for this study.
The first step of the Global Muon Trigger is a unit conversion, where
the 
and 
values (indices) from the RPC and DTBX/CSC trigger
systems are converted to comparable units. As the Global Muon Trigger always
assumes 4 input muons per subsystem (RPC and DTBX/CSC), values 0
indicate empty inputs.
For each of the 8 muon candidates in the Global Muon Trigger a so-called
single-rank is defined as a function of , and the quality
bits provided by the input trigger system. For the time being it is
calculated as a quality weighted by the value.
The next step is to determine if two candidates can be attributed to the same
physical muon. Therefore the spatial coordinates and of all
possible combinations of muon candidates are compared and a so-called
match-quality 
is calculated.
R is then compared to a threshold value and a 4 by 4 matrix
(match-quality matrix) is filled. For this study a threshold value of
2.2 has been used. The resulting matrix has the 4 muon candidates from the
RPC as rows and the 4 muons from the DTBX/CSC as columns. Now each element of
this matrix is compared with all elements of its corresponding row and column.
If the element has the lowest R value of all combinations the two corresponding
muon candidates are assumed to come from the same physical muon.
For each candidate there are two possibilities: either it is seen only by one system, then the Global Muon Trigger has to decide whether it is a fake or a real muon on the basis of the single-rank, or it is seen by both systems. In this case the algorithm has to decide which transverse momentum should be assigned. Therefore a selection matrix (implemented as a lookup table) is used, which takes the single-rank values of the two matching muon candidates as input.
Finally all muon candidates are sorted according to a their ``rank value'' and the 4 ``best'' are passed to the Global Trigger.