25 research outputs found
A Modified Levenberg-Marquardt Method for the Bidirectional Relay Channel
This paper presents an optimization approach for a system consisting of
multiple bidirectional links over a two-way amplify-and-forward relay. It is
desired to improve the fairness of the system. All user pairs exchange
information over one relay station with multiple antennas. Due to the joint
transmission to all users, the users are subject to mutual interference. A
mitigation of the interference can be achieved by max-min fair precoding
optimization where the relay is subject to a sum power constraint. The
resulting optimization problem is non-convex. This paper proposes a novel
iterative and low complexity approach based on a modified Levenberg-Marquardt
method to find near optimal solutions. The presented method finds solutions
close to the standard convex-solver based relaxation approach.Comment: submitted to IEEE Transactions on Vehicular Technology We corrected
small mistakes in the proof of Lemma 2 and Proposition
Identification of Piecewise Constant Robin Coefficient for the Stokes Problem Using the Levenberg-Marquardt Method
In this work, we prove the quadratic convergence of the Levenberg-Marquardt method for the inverse problem of identifying a Robin coefficient for the Stokes system, where we suppose that this parameter is piecewise constant on some non accessible part of the boundary and under the assumption that on this part, the velocity of a given reference solution stays far from zero
Earth-Mars trajectories with lunar gravity assist study using the self-adaptive Levenberg-Marquardt Algorithm
As the interest in interplanetary missions is rising, new trajectories and methods should be
studied and analyzed to decrease the costs and increase the capacity of transporting
scientific instruments and payload to Mars.
In this work, a numerical study of interplanetary trajectories between Earth and Mars is
performed, using the Moon to carry out a lunar gravity assist manoeuvre, with the objective
of decreasing the launch energy for the interplanetary transfer and analyze the use of the
self-adaptive Levenberg-Marquardt algorithm as a differential corrector for space mission
design.
The obtained results are compared with the values of the direct transfer achieved with the
same methods and with the estimated values for the next interplanetary transfer Windows
between Earth and Mars. The results are obtained with the astrodynamics two body problem
simplistic model and verified and validated with the open source NASA’s software GMAT for a
more realistic approach. The self-adaptive Levenberg-Marquardt algorithm developed for this
work in the programming language Python 3.6 is tested and used as a differential corrector to
obtain the trajectories for the two-body problem.
The results demonstrate that the self-adaptive Levenberg-Marquardt algorithm is adequate to
design space missions, a lunar gravity assist can be executed in all situations studied and only
in a few cases is not viable. Of the four launch windows analyzed only in one situation the
lunar gravity assist does not diminish the launch energy.
The results show that the energy needed to perform future Mars missions or missions to other
Solar System bodies can be reduced and consequently the payload mass can be increased. The
possible introduction of a new calculation method for space mission design is also shown due
to the observed results.Com o aumento do interesse em missões interplanetárias, novas trajetórias e métodos devem
ser estudados e analisados de maneira a diminuir os custos e aumentar a capacidade de
transportar instrumentação cientÃfica.
Neste trabalho, é realizado um estudo numérico de trajetórias interplanetárias entre a Terra
e Marte, utilizando a Lua para efetuar uma manobra de assistência gravitacional, com os
objetivos de diminuir a energia necessária para a transferência interplanetária e testar e
analisar o uso do algoritmo self-adaptive Levenberg-Marquardt como corretor diferencial para
o desenho de missões espaciais.
Os resultados obtidos são comparados com valores de transferência direta alcançados com os
mesmos métodos e com os valores estimados para as próximas oportunidades de transferência
interplanetária entre Terra e Marte. São obtidos resultados com o problema de dois corpos de
astrodinâmica e verificados e validados com o software aberto GMAT desenvolvido pela NASA
para uma abordagem mais realista. O algoritmo self-adaptive Levenberg-Marquardt
desenvolvido para este trabalho na linguagem de programação Python 3.6 é testado e
utilizado como corretor diferencial para obter as trajetórias para o problema de dois corpos.
Os resultados demonstram que o algoritmo self-adaptive Levenberg-Marquardt é adequado
para planear missões, que a assistência gravitacional lunar pode ser executada em todas as
situações estudadas e que apenas em poucas ocorrências não é viável. Das 4 oportunidades de
lançamento analisadas apenas em uma situação a assistência gravitacional lunar não diminuiu
a energia de lançamento.
Os resultados indicam que a energia necessária para efetuar futuras missões a Marte ou a
outros corpos do sistema solar pode ser reduzida e consequentemente a massa de carga útil
nestas missões pode ser aumentada. A possÃvel introdução de um novo método de cálculo
para desenhar missões espaciais também é demonstrado através dos resultados obtido