7 research outputs found
Minimax rank estimation for subspace tracking
Rank estimation is a classical model order selection problem that arises in a
variety of important statistical signal and array processing systems, yet is
addressed relatively infrequently in the extant literature. Here we present
sample covariance asymptotics stemming from random matrix theory, and bring
them to bear on the problem of optimal rank estimation in the context of the
standard array observation model with additive white Gaussian noise. The most
significant of these results demonstrates the existence of a phase transition
threshold, below which eigenvalues and associated eigenvectors of the sample
covariance fail to provide any information on population eigenvalues. We then
develop a decision-theoretic rank estimation framework that leads to a simple
ordered selection rule based on thresholding; in contrast to competing
approaches, however, it admits asymptotic minimax optimality and is free of
tuning parameters. We analyze the asymptotic performance of our rank selection
procedure and conclude with a brief simulation study demonstrating its
practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio
Time-delay estimation under non-clustered and clustered scenarios for GNSS signals
Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2021.Aplicações que empregam sistemas globais de navegação por satélite, do inglês Global
Navigation Satellite Systems (GNSS) para prover posicionamento acurado estão sujeitos a
degradação drástica não só por intereferências eletromagnéticas, como também componentes
de multipercurso causados por reflexões e refrações no ambiente. Aplicações de segurança
crítica como veículos autonômos e aviação civil, e aplicações de risco crítico como gestão de
pesca, pedágio automático, e agricultura de precisão dependem de posicionamento acurado
sob cenários complicados. Tipicamente quanto mais agrupamento ocorre entre o componente de linha de visada, do inglês line-of-sight (LOS) e componentes de multipercurso ou
não-linha de visada, do inglês non-line-of-sight (NLOS), menos acurada é a estimação da
posição. Abordagens tensorials estado da arte para receptores GNSS baseado em arranjos
de antenas utilizam processamento tensorial de sinais para separar o componente LOS dos
componentes NLOS, assim mitigando os efeitos destes, utilizando decomposição em valores singulares multilinear, do inglês multilinear singular value decomposition (MLSVD)
para gerar um autofiltro de order superior, do inglês higher-order eigenfilter (HOE) com
pré-processamento por média frente-costas, do inglês forward-backward averaging (FBA),
e suavização espacial expandida, do inglês expanded spatial smoothing (ESPS), estimação
de direção de chegada, do inglês direction of arrival (DoA) e fatorização Khatri-Rao, do
inglês Khatri-Rao factorization (KRF), estimação de Procrustes e fatorização Khatri-Rao
(ProKRaft), e o sistema semi-algébrico de decomposição poliádica canônica por diagonalização matricial simultânea, do inglês semi-algebraic framework for approximate canonical
polyadic decomposition via simultaneous matrix diagonalization (SECSI), respectivamente.
Propomos duas abordagens de processamento para estimação de atraso, do inglês time-delay
estimation (TDE). A primeira é a abordagem em lotes utilizando dados de vários períodos
do sinal. Usando estimação em lotes propomos duas abordagens algébricas para TDE, em
que diagonalizaçao é efetivada por decomposição generalizada em autovalores, do inglês
generalized eigenvalue decomposition (GEVD), das primeiras duas fatias frontais do tensor núcleo do tensor de dados, estimado por MLSVD. Esta primeira abordagem, como os
métodos citados, na quais simulações foram feitas com 1 componente LOS e 1 componente
NLOS, assim os dados observados tem posto cheio em todos seus modos, não faz suposições
sobre o posto do tensor de dados. A segunda abordagem supõe cenários nos quais mais de
1 componente NLOS está presente e são agregados (clustered em inglês), assim vários vetores de uma das matrizes-fator que formam o tensor de dados são altamente correlacionaiii
dos, resultando num tensor de dados que é de posto deficiente em pelo menos um modo.
Os esquemas algébricos baseados em tensores propostos utilizam a decomposição poliádica
canônica por decomposição generalizada em autovalores, do inglês canonical polyadic decomposition via generalized eigenvalue decomposition (CPD-GEVD), e a decomposição em
termos de posto-(Lr, Lr, 1) por decomposição generalizada em autovalores, do inglês decomposition in multilinear rank-(Lr, Lr, 1) terms via generalized eigenvalue decomposition
((Lr, Lr, 1)-GEVD) para melhorar a TDE do componente LOS sob cenários desafiadores. A
segunda é a abordagem de processamento adaptativo de amostras individuais utilizando rastreamento de subespaço a cada período de código, epoch em inglês. Usando processamento
adaptativo propomos duas abordagem, uma aplicando FBA expandido (EFBA) e ESPS ao
dados e estimando um HOE, e outra usando usa estimação paramétrica para estimar a DoA.
Estendendo o modelo para um arranjo retangular uniforme, do inglês uniform rectangular
array (URA), o fluxo de dados são tensores de terceira ordem. Para este modelo propomos
três abordagens para TDE baseado em HOE, CPD-GEVD, e ESPRIT tensorial, respectivamente e empregando uma estratégia de truncamento sequencial para reduzir a quantidade de
operações necessárias para cada modo do tensorCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).Applications employing Global Navigation Satellite Systems (GNSS) to provide accurate positioning are subject to drastic degradation not only due to electromagnetic interference, but also due to multipath components caused by reflections and refractions in the
environment. Safety-critical applications such as autonomous vehicles and civil aviation,
and liability-critical applications such as fisheries management, automatic tolling, and precision agriculture depend on accurate positioning under such demanding scenarios. Typically,
the more clustering occurs between the line-of-sight (LOS) component and multipath or
non-line-of-sight (NLOS) components, the more inaccurate is the estimation of the positioning. State-of-the-art tensor based approaches for antenna array-based GNSS receivers apply
tensor-based signal processing to separate the LOS components from NLOS components,
thus mitigating the effects of the latter, using the multilinear singular value decomposition
(MLSVD) to generate a higher-order eigenfilter (HOE) with forward-backward averaging
(FBA) and expanded spatial smoothing (ESPS) preprocessing, direction of arrival (DoA) estimation and Khatri-Rao factorization (KRF), Procrustes estimation and Khatri-Rao factorization (ProKRaft), and the semi-algebraic framework for approximate canonical polyadic
decomposition via simultaneous matrix diagonalization (SECSI), respectively. These approaches use filtering, parameter estimation and filtering, iterative algebraic factor matrix
estimation and filtering, and algebraic factor matrix estimation, respectively. We propose
two processing approaches to time-delay estimation (TDE). The first is batch processing
taking data from several signal periods. Using batch processing we propose two algebraic
approaches to TDE, in which diagonalization is achieved using the generalized eigenvalue
decomposition (GEVD) of the first two frontal slices of the measurement tensor’s core tensor,
estimated via MLSVD. The former approach, like the cited methods, in which simulations
were performed with 1 LOS component and 1 NLOS component, and thus the measured data
has full-rank tensor in all its modes, makes no assumption about the rank of the measurement tensor. The latter approach assumes scenarios in which more than 1 NLOS component
is present and these are clustered, thus several vectors of one of the factor matrices which
forms the tensor data are highly correlated, resulting in a rank-deficient measurement tensor
in at least one mode. These proposed algebraic tensor-based schemes utilize the canonical
polyadic decomposition via generalized eigenvalue decomposition (CPD-GEVD) and the decomposition in multilinear rank-(Lr, Lr, 1) terms via generalized eigenvalue decomposition
((Lr, Lr, 1)-GEVD) in order to improve the TDE of the LOS component in challenging scev
narios. The second approach is adaptive processing of individual samples utilizing subspace
tracking to iteratively estimate the subspace at each epoch. Using adaptive processing we
propose two approaches, one applying FBA and ESPS to the data and estimating a higherorder eigenfilter, and the other using a parametric approach using DoA estimation. By extending the data model for an uniform rectangular array, we have a data stream of third-order
tensors. For this model we propose three approaches to TDE based on HOE, CPD-GEVD,
and standard tensor ESPRIT, respectively and employing a sequential truncation strategy to
reduce the amount of operations necessary for each tensor mode
Spherical Cap Packing Asymptotics and Rank-Extreme Detection
We study the spherical cap packing problem with a probabilistic approach.
Such probabilistic considerations result in an asymptotic sharp universal
uniform bound on the maximal inner product between any set of unit vectors and
a stochastically independent uniformly distributed unit vector. When the set of
unit vectors are themselves independently uniformly distributed, we further
develop the extreme value distribution limit of the maximal inner product,
which characterizes its uncertainty around the bound.
As applications of the above asymptotic results, we derive (1) an asymptotic
sharp universal uniform bound on the maximal spurious correlation, as well as
its uniform convergence in distribution when the explanatory variables are
independently Gaussian distributed; and (2) an asymptotic sharp universal bound
on the maximum norm of a low-rank elliptically distributed vector, as well as
related limiting distributions. With these results, we develop a fast detection
method for a low-rank structure in high-dimensional Gaussian data without using
the spectrum information.Comment: 14 pages; 1 figure. Accepted Jan 31, 2017 by IEEE Transactions on
Information Theor
Design and analysis of adaptive noise subspace estimation algorithms
Ph.DDOCTOR OF PHILOSOPH
Remote Sensing Monitoring of Land Surface Temperature (LST)
This book is a collection of recent developments, methodologies, calibration and validation techniques, and applications of thermal remote sensing data and derived products from UAV-based, aerial, and satellite remote sensing. A set of 15 papers written by a total of 70 authors was selected for this book. The published papers cover a wide range of topics, which can be classified in five groups: algorithms, calibration and validation techniques, improvements in long-term consistency in satellite LST, downscaling of LST, and LST applications and land surface emissivity research