MILES: MATLAB package for solving Mixed Integer LEast Squares problems

Abstract

In GNSS, for fixing integer ambiguities and estimating positions, a mixed integer least squares problem has to be solved. The MATLAB package MILES provides fast and numerically reliable routines to solve this problem. In the process of solving a mixed integer least squares problem, an ordinary integer least squares problem is solved. Thus this package can also be used to solve an ordinary integer least squares problem alone. An option to compute multiple solutions is provided. This paper gives a description of this package and provides a guide for using it.

High precision GPS positioning with multiple receivers using carrier phase technique and sensor fusion

“…In a practical case the covariance matrix of ∇∆µ k is hard to define only from the measurements of ∇∆φ k . Therefore methods [5], [15], [17] which require this covariance matrix usually produce false positive result from a single epoch measurement.…”

“…The classical solutions, like LAMBDA method [17] or MILES [5] rely on this property only. In some special cases additional sensors (like inertial or magnetic sensors) are present, which can give information to make the result more reliable.…”

Experimental quality evaluation of lattice basis reduction methods for decorrelating low-dimensional integer least squares problems

“…In our experiments, we decide to set the maximum rank of lattice to 60, since finding the exact solution to the shortest vector problem up to such a dimension is still foreseeable [45]. In particular, almost all practical applications of GPS kinematic applications are low-dimensional (see e.g., [26,27]). The condition numbers of the simulated examples range from 10 to 5 × 10 4 .…”

“…Remembering that λ(L) cannot be directly attainable as a result of any reduction algorithm, we will replace it with b 1 . Thus, the left-hand side of (27) exactly becomes the length ratio as defined in (12). In the similar way to defining η B in connection with the Hermite factor, we may define…”

“…http://asp.eurasipjournals.com/content/2013/1/137 errors [15], cryptography [4,16], discrete tomography [17], and global navigation satellite systems (see e.g., [18][19][20][21][22][23][24][25][26][27]). As a result, even an international conference was solely dedicated to celebrate the 25th birthday of the invention of the LLL algorithm at the University of Caen in 2007, with its proceedings containing excellent review and application papers (see e.g., [6,28,29]) published in 2010 [5] (For more information on this event, the reader is referred to the conference website http://lll25.info.unicaen.fr/ and the book of proceedings [5]).…”