High-resolution ionosphere corrections for single-frequency positioning

The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n=30 coincide with the original B-spline model and improve the positioning accuracy significantly.Peer ReviewedPostprint (published version

Tensor-based tracking schemes for time-delay estimation in GNSS multi-antenna receivers

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2017.Embora os receptores GNSS (Global Navigation Satellite Systems) alcancem atualmente alta precisão ao processar sua localização geográfica sob condições de Linha de Visão (Line of Sight), erros devido a interferência por componentes multipercurso e ruído são as fontes mais degradantes desse sistema. A fim de resolver a interferência multipercurso, receptores baseados em múltiplas antenas tornaram-se o foco de pesquisa e desenvolvimento tecnológico devido ao fato de que podem mitigar a ocorrência de multipercurso fornecendo as melhores estimativas para o atraso do sinal transmitido, que é um parâmetro relevante para determinar a geolocalização do usuário. Neste contexto, abordagens tensoriais baseadas em modelos PARAFAC (PArallel FActor Analysis) têm sido propostas na literatura, proporcionando um ótimo desempenho. Como essas técnicas são baseadas em subespaços, considerando um cenário de rastreamento em tempo real, o cálculo de uma EVD (Eigenvalue Decomposition)/SVD (Singular Value Decomposition) completa para estimativa de subespaço de sinal em cada instante de amostragem não é adequado, devido a razões de complexidade. Portanto, uma alternativa para reduzir o tempo de computação (Time of Computing) de estimativas de subespacos tem sido o desenvolvimento de algoritmos de rastreamento de subespaço. Este trabalho propõe o emprego de dois esquemas de rastreamento de subespaços para fornecer uma redução no desempenho computacional geral das técnicas de estimativa de atraso de tempo baseadas em tensores.Although Global Navigation Satellite Systems (GNSS) receivers nowadays achieve high accuracy when processing their geographic location under conditions of Line of Sight (LOS), errors due to interference by multipath and noise are the most degrading sources of accuracy. In order to solve the multipath interference, receivers based on multiple antennas have become the focus of technological research and development due to the fact they can mitigate multipath occurrence providing best estimates to the transmitted signal time-delay, which is a relevant parameter for determining the user’s geolocation. In this context, tensor-based approaches based on PArallel FActor Analysis (PARAFAC) models have been proposed in the literature, providing optimal performance. As these techniques are subspace-based, considering a real-time tracking scenario, the computation of a full Eigenvalue Decomposition (EVD)/Singular Value Decomposition (SVD) for signal subspace estimation at every sampling instant is not suitable, due to complexity reasons. Therefore, an alternative to reduce the Time of Computing (ToC) of subspace estimations has been the development of subspace tracking algorithms. This work proposes the employment of two subspace tracking schemes to provide a reduction in the overall computational performance of tensor-based time-delay estimation techniques

Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging

Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 millimeter. As NASA pursues the vision of taking humans back to the Moon, new, more precise laser ranging applications will be demanded, including continuous tracking from more sites on Earth, placing new CCR arrays on the Moon, and possibly installing other devices such as transponders, etc. Successful achievement of this goal strongly demands further significant improvement of the theoretical model of the orbital and rotational dynamics of the Earth-Moon system. This model should inevitably be based on the theory of general relativity, fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis. This paper discusses methods and problems in developing such a mathematical model. The model will take into account all the classical and relativistic effects in the orbital and rotational motion of the Moon and Earth at the sub-centimeter level. The new model will allow us to navigate a spacecraft precisely to a location on the Moon. It will also greatly improve our understanding of the structure of the lunar interior and the nature of the physical interaction at the core-mantle interface layer. The new theory and upcoming millimeter LLR will give us the means to perform one of the most precise fundamental tests of general relativity in the solar system.Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton Univ., NJ, 2007

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

GPS measurements of deformation associated with the 1987 Superstition Hills earthquake: Evidence for conjugate faulting

Large station displacements observed from Imperial Valley Global Positioning System (GPS) campaigns are attributed to the November 24, 1987 Superstition Hills earthquake sequence. Thirty sites from a 42 station GPS network established in 1986 were reoccupied during 1988 and/or 1990. Displacements at three sites within 3 kilometers of the surface rupture approach 0.5 m. Eight additional stations within 20 km of the seismic zone are displaced at least 10 cm. This is the first occurrence of a large earthquake (M(sub S) 6.6) within a preexisting GPS network. Best-fitting uniform slip models of rectangular dislocations in an elastic half-space indicate 130 + or - 8 cm right-lateral displacement along the northwest-trending Superstition Hills fault and 30 + or - 10 cm left-lateral displacement along the conjugate northeast-trending Elmore Ranch fault. The geodetic moments are 9.4 x 10(exp 25) dyne-cm and 2.3 x 10(exp 25) dyne-cm for the Superstition Hills and Elmore Ranch faults, respectively, consistent with teleseismic source parameters. The data also suggest the post seismic slip along the Superstition Hills fault is concentrated at shallow depths. Distributed slip solutions using Singular Value Decomposition indicate near uniform displacement along the Elmore Ranch fault and concentrated slip to the northwest and southeast along the Superstition Hills fault. A significant component of non-seismic displacement is observed across the Imperial Valley, which is attributed in part to interseismic plate-boundary deformation

Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography

We study the feasibility of data based machine learning applied to ultrasound tomography to estimate water-saturated porous material parameters. In this work, the data to train the neural networks is simulated by solving wave propagation in coupled poroviscoelastic-viscoelastic-acoustic media. As the forward model, we consider a high-order discontinuous Galerkin method while deep convolutional neural networks are used to solve the parameter estimation problem. In the numerical experiment, we estimate the material porosity and tortuosity while the remaining parameters which are of less interest are successfully marginalized in the neural networks-based inversion. Computational examples confirms the feasibility and accuracy of this approach

Multi-dimensional Channel Parameter Estimation for mmWave Cylindrical Arrays

University of Technology Sydney. Faculty of Engineering and Information Technology.Millimeter-wave (mmWave) large-scale antenna arrays, standardized for the fifth-generation (5G) communication networks, have the potential to estimate channel parameters with unprecedented accuracy, due to their high temporal resolution and excellent directivity. However, most existing techniques have very high complexities in hardware and software, and they cannot effectively exploit the properties of mmWave large-array systems for channel estimation. As a result, their application in 5G mmWave large array systems is limited in practice. This thesis develops new and efficient solutions to channel parameter estimation using large-scale mmWave uniform cylindrical arrays (UCyAs). The key contributions of this thesis are on the following four aspects: We first present a channel compression-based channel estimation method, which reduces the computational complexity substantially at a negligible cost of estimation accuracy. By capitalizing on the sparsity of mmWave channel, the method effectively filters out the useless signal components. As a result, the dimension of the element space of the received signals can be reduced. Next, we extend the channel estimation to the hybrid UCyA case, and design new hybrid beamformers. By exploiting the convergence property of the Bessel function, the designed beamformers can preserve the recurrence relationship of the received signals with a small number of radio frequency (RF) chains. We then arrange the received signals in a tensor form and propose a new tensor-based channel estimation algorithm. By suppressing the receiver noises in all dimensions (time, frequency, and space), the algorithm can achieve substantially higher estimation accuracy than existing matrix-based techniques. Finally, to reduce cost and power consumption while maintaining a high network access capability, we develop a novel nested hybrid UCyA and present the corresponding parameter estimation algorithm based on the second-order channel statistics. Simulation results show that by exploiting the sparse array technique to design the RF chain connection network, the angles of a large number of devices can be accurately estimated with much fewer RF chains than antennas. Overall, this thesis presents several applicable UCyA design schemes and proposes the efficient channel parameter estimation algorithms. The presented new UCyAs can significantly reduce the hardware cost of the system with a marginal accuracy loss, and the proposed algorithms are capable of accurately estimating the channel parameters with low computational complexities. By employing the presented UCyAs and implementing the proposed novel algorithms cohesively, the different communication and deployment requirements of a variety of mmWave communication scenarios can be met