The purpose of this paper is to characterize Medium Scale Trav-
eling Ionospheric Disturbances (MSTIDs), by means of Mixed Integer
Nonlinear Programming (MINLP). The MINLP techniques are used
to for estimating the parameters of the equations that describe the
MSTIDs from a set of observations. A new MSTIDs wave detecting
method, which we will denote as Ambiguity Resolution in Global Navi-
gational Satellite System (GNSS) Ionospheric Interferometry (ARGII)
technique, is designed to model the MSTI...

The purpose of this paper is to characterize Medium Scale Trav-
eling Ionospheric Disturbances (MSTIDs), by means of Mixed Integer
Nonlinear Programming (MINLP). The MINLP techniques are used
to for estimating the parameters of the equations that describe the
MSTIDs from a set of observations. A new MSTIDs wave detecting
method, which we will denote as Ambiguity Resolution in Global Navi-
gational Satellite System (GNSS) Ionospheric Interferometry (ARGII)
technique, is designed to model the MSTIDs wave with the data from
the wide low-density GNSS receivers network. The ARGII techniques
can be set as an special instance of MINLP, because the problem is set
as a series of MSTIDs equations including the unknown wave veloc-
ity (continuous) and cycle ambiguities (integers). The performance of
heuristic and direct search optimization algorithms are evaluated by
solving the MINLP problem with techniques bared an di erent prin-
ciples, and as benchmark we use the solution obtained by exhaustive
enumeration of all possible integer solutions. Among the algorithms
we have implemented in this work are genetic algorithm, simulated
annealing, particle swarm, pattern search and Nelder Mead methods.
The GNSS data used to test the these solvers is observed from the wide
GNSS network in the north of Poland on the day 353, 2013 whose di-
ameter is more than the half of wavelength and therefore will have
phase ambiguities. The evaluating experiments show that the results
computed by the simple improved optimization algorithms especially
the Nelder Mead have not only high correlations with the reference
method (i.e. exhaustive enumeration) but also extremely lower time
complexity compared to the benchmark method. Despite unguaran-
teed global optimal results for the MINLP problems, these methods
show the excellent performance in time complexity when computing
the velocities of MSTIDs with ARGII techniques from large quantity
of the GNSS data.
The purpose of this paper is to characterize Medium Scale Trav-
eling Ionospheric Disturbances (MSTIDs), by means of Mixed Integer
Nonlinear Programming (MINLP). The MINLP techniques are used
to for estimating the parameters of the equations that describe the
MSTIDs from a set of observations. A new MSTIDs wave detecting
method, which we will denote as Ambiguity Resolution in Global Navi-
gational Satellite System (GNSS) Ionospheric Interferometry (ARGII)
technique, is designed to model the MSTIDs wave with the data from
the wide low-density GNSS receivers network. The ARGII techniques
can be set as an special instance of MINLP, because the problem is set
as a series of MSTIDs equations including the unknown wave veloc-
ity (continuous) and cycle ambiguities (integers). The performance of
heuristic and direct search optimization algorithms are evaluated by
solving the MINLP problem with techniques bared an dierent prin-
ciples, and as benchmark we use the solution obtained by exhaustive
enumeration of all possible integer solutions. Among the algorithms
we have implemented in this work are genetic algorithm, simulated
annealing, particle swarm, pattern search and Nelder Mead methods.
The GNSS data used to test the these solvers is observed from the wide
GNSS network in the north of Poland on the day 353, 2013 whose di-
ameter is more than the half of wavelength and therefore will have
phase ambiguities. The evaluating experiments show that the results
computed by the simple improved optimization algorithms especially
the Nelder Mead have not only high correlations with the reference
method (i.e. exhaustive enumeration) but also extremely lower time
complexity compared to the benchmark method. Despite unguaran-
teed global optimal results for the MINLP problems, these methods
show the excellent performance in time complexity when computing
the velocities of MSTIDs with ARGII techniques from large quantity
of the GNSS data.

Citació

Yang, H.; Monte, E.; Hernandez, M. "Internal report. Solving mixed integer non-linear programming problem applied to GNSS data". 2014.