MLAMBDA:
MATLAB Package for Integer Least Squares
Ambiguity Determination, Version 1.0
Users’ Guide
Xiao-Wen Chang and Xiaohu Xie
Scientific Computing Laboratory
School of Computer Science
McGill University
October 2011
Copyright
c
2011 by Xiao-Wen Chang and Xiaohu Xie
1 Introduction
Let the sets of all real and integer m × n matrices be denoted by R
m×n
and Z
m×n
, respectively,
and the sets of real and integer n-vectors by R
n
and Z
n
, respectively.
Given a real least square estimate a ∈ R
n
of the integer ambiguity vector and its covaraince
matrix W ∈ R
n×n
, this Matlab package provides a function to produce p integer least sq uares
estimates of the integer ambiguity vector, i.e., it produces p optimal solutions to the integer least
squares problem (in quadratic form)
min
x∈Z
n
(x − a)
T
W
−1
(x − a), (1)
in the sense that x
(j)
∈ Z
n
is the j-th optimal solution if its corresponding value of the objective
function is the j-th smallest (some of these p values can be equal). Here p is a parameter to be
provided by a user and its default value is 1. This packckage is based on the reduction algroithm
proposed in [2] and the serach algorithm given in [1].
If your integer least squares problem is in the standard form:
min
x∈Z
n
ky − Axk
2
2
, (2)
where A ∈ R
m×n
has full column rank, we strongly su ggest that you use our Matlab package
MILES, which can be downloaded from the same web page, as a transformation from (2) to (1)
may not be numerically reliable.
The purpose of this document is to show how to use this package.
2 System Requirements
The package has been fu lly tested on Windows XP, Linux and Macintosh with Matlab 7.x, and
should work on any p latform supporting Matlab. For the system requirements of runn ing Mat-
lab, please refer to:
http://www.mathworks.com
3 Installing Package
The package is provided as a compressed file with extension “zip”. To extract the package, an
uncompress tool should be used. Suppose that the package is extracted to “C:/MLAMBDA” on
Windows, then you can enter the directory and use the provided functions or examples. If you want
to use the package in a directory rather than “C:/MLAMBDA”, you have to add “C:/MLAMBDA”
to the Matlab path.
4 Citation
MLAMBDA is a freely available software package provided on the Internet. If you are u sing it
in research work in GNSS to be published, please include explicit mention of out work in your
publication. You m ay state something like:
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