Unscented transform framework for quantization modeling in data conversion systems

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2017.Esta tese apresenta uma abordagem para o projeto de quantizadores para sinais específicos baseada na Transformada da Incerteza — Unscented Transform (UT) — visando o projeto de conversores de dados. É apresentada uma definição formal da UT em termos da quadratura interpolatória, é demonstrada que a quadratura Gaussiana representa a escolha ótima para maximizar a ordem da transformada e é apresentado um algoritmo para o cálculo eficiente da UT. A UT é apresentada como uma alternativa a métodos de Monte Carlo e é introduzida a Transformada da Incerteza Extendida no contexto do problema de estimação de funções de probabilidade. É apresentado um método para abstrair sinais definidos no tempo em funções de probabilidade e como utilizar a UT para o projeto de quantizadores para sinais específicos.This thesis presents a framework for the design of signal specific quantizers based on the Unscented Transform — UT — for the design of data converters. We formally define the UT in terms of the interpolatory quadrature and we choose the Gaussian quadrature as the optimal scheme for maximizing the order of the transformation. We present an efficient method for computing the UT. The UT is presented as an alternative to Monte Carlo methods in which we introduce an Extended UT for the probability function estimation problem. We show how to abstract a time signal into a probability function and use the UT to design signal specific quantizers

Nonlinear Quantizer Design Based on Clenshaw-Curtis Quadrature

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2019.Esta tese visa propor um novo método para projeto de quantizadores não lineares conservadores de momentos estatísticos, baseado na quadratura de Clenshaw-Curtis. Os conceitos básicos de Conversores Analógico Digital são definidos para contextualização do problema discutido e para servir de base para o entendimento dos parâmetros de quantizadores. Então, uma definição formal da Transformada da Incerteza - Unscented Transform (UT) - é proposta para o contexto deste trabalho, e os conceitos básicos de quadratura são aplicados como uma ferramenta matemática para cálculo da UT. Finalmente, a metodologia de projeto do quantizador é detalhada, apresentando a relação entre os nós e pesos de uma quadratura com os parâmetros de quantizadores. O projeto é então aplicado a uma simulação de estudo de caso para verificação dos cálculos teóricos.This thesis aims to provide a novel method for designing nonlinear moment preserving quantizers based on the Clenshaw-Curtis quadrature. The basic concepts of Analog-to-Digital Converters (ADCs) are defined for contextualization of the discussed problem and to serve as a basis for understanding quantizers parameters. Then, a formal definition of the Unscented Transform (UT) is proposed for this work’s context, and the key concepts of quadrature are applied to it as a mathematical tool for UT calculation. Finally, the design method is detailed, presenting the relationship between quadrature’s nodes and weights and the quantizers parameters. This design is applied to a case study simulation, for validation of theoretical calculations

Unscented Transform and Sparse Grids Applied to Buzzsaw Noise Modeling in Airplane Engines

Trabalho de conclusão de curso (graduação)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2021.Este trabalho apresenta os fundamentos da Transformada da Incerteza (Unscented Trans- form) e do método computacional das Malhas Esparsas (Sparse Grids) para aplicação em simulações de alta dimensionalidade sujeitas a incertezas. O algoritmo proposto é aplicado na obtenção da assinatura de ruído de uma turbina de avião comercial sujeito a alterações nos ângulos nominais das pás (problema com 16 dimensões) com velocidade supersônica da ponta das pás relativamente ao ar em escoamento, sendo a primeira vez que tal técnica é aplicada em aeroacústica, até onde vai o conhecimento do autor. A simulação obtém com sucesso a assinatura de ruído em tempo inferior à uma hora em máquina GNU/Linux com 8GB de memória e processador de 2.5GHz, mostrando a eficácia da técnica em lidar com problemas de alta dimensionalidade. Perspectivas de aprimoramento da técnica e pesquisas futuras são discutidas ao final.This work presents the foundations of the Unscented Transform and of the computational method of Sparse Grids for applications in high-dimensional simulations subject to uncer- tainty. The proposed algorithm is applied in obtaining the noise signature of a commercial airplane turbine subject to changes in the blades angles (a 16 dimensional problem) with supersonic speed of the blade tips relative to the air flow, being the first time this tech- nique is applied in this context, as far as the author knows. The simulation successfully obtained the noise signature with time inferior to an hour in a GNU/Linux machine with 8GB of RAM and a processor @ 2.5GHz, showing the technique effectiveness in deal- ing with high dimensional problems. Perspectives for improvement of the technique and future researches are discussed at the end

Distributed implementations of the particle filter with performance bounds

The focus of the thesis is on developing distributed estimation algorithms for systems with nonlinear dynamics. Of particular interest are the agent or sensor networks (AN/SN) consisting of a large number of local processing and observation agents/nodes, which can communicate and cooperate with each other to perform a predefined task. Examples of such AN/SNs are distributed camera networks, acoustic sensor networks, networks of unmanned aerial vehicles, social networks, and robotic networks. Signal processing in the AN/SNs is traditionally centralized and developed for systems with linear dynamics. In the centralized architecture, the participating nodes communicate their observations (either directly or indirectly via a multi-hop relay) to a central processing unit, referred to as the fusion centre, which is responsible for performing the predefined task. For centralized systems with linear dynamics, the Kalman filter provides the optimal approach but suffers from several drawbacks, e.g., it is generally unscalable and also susceptible to failure in case the fusion centre breaks down. In general, no analytic solution can be determined for systems with nonlinear dynamics. Consequently, the conventional Kalman filter cannot be used and one has to rely on numerical approaches. In such cases, the sequential Monte Carlo approaches, also known as the particle filters, are widely used as approximates to the Bayesian estimators but mostly in the centralized configuration. Recently there has been a growing interest in distributed signal processing algorithms where: (i) There is no fusion centre; (ii) The local nodes do not have (require) global knowledge of the network topology, and; (iii) Each node exchanges data only within its local neighborhood. Distributed estimation have been widely explored for estimation/tracking problems in linear systems. Distributed particle filter implementations for nonlinear systems are still in their infancy and are the focus of this thesis. In the first part of this thesis, four different consensus-based distributed particle filter implementations are proposed. First, a constrained sufficient statistic based distributed implementation of the particle filter (CSS/DPF) is proposed for bearing-only tracking (BOT) and joint bearing/range tracking problems encountered in a number of applications including radar target tracking and robot localization. Although the number of parallel consensus runs in the CSS/DPF is lower compared to the existing distributed implementations of the particle filter, the CSS/DPF still requires a large number of iterations for the consensus runs to converge. To further reduce the consensus overhead, the CSS/DPF is extended to distributed implementation of the unscented particle filter, referred to as the CSS/DUPF, which require a limited number of consensus iterations. Both CSS/DPF and CSS/DUPF are specific to BOT and joint bearing/range tracking problems. Next, the unscented, consensus-based, distributed implementation of the particle filter (UCD /DPF) is proposed which is generalizable to systems with any dynamics. In terms of contributions, the UCD /DPF makes two important improvements to the existing distributed particle filter framework: (i) Unlike existing distributed implementations of the particle filter, the UCD /DPF uses all available global observations including the most recent ones in deriving the proposal distribution based on the distributed UKF, and; (ii) Computation of the global estimates from local estimates during the consensus step is based on an optimal fusion rule. Finally, a multi-rate consensus/fusion based framework for distributed implementation of the particle filter, referred to as the CF /DPF, is proposed. Separate fusion filters are designed to consistently assimilate the local filtering distributions into the global posterior by compensating for the common past information between neighbouring nodes. The CF /DPF offers two distinct advantages over its counterparts. First, the CF /DPF framework is suitable for scenarios where network connectivity is intermittent and consensus can not be reached between two consecutive observations. Second, the CF /DPF is not limited to the Gaussian approximation for the global posterior density. Numerical simulations verify the near-optimal performance of the proposed distributed particle filter implementations. The second half of the thesis focuses on the distributed computation of the posterior Cramer-Rao lower bounds (PCRLB). The current PCRLB approaches assume a centralized or hierarchical architecture. The exact expression for distributed computation of the PCRLB is not yet available and only an approximate expression has recently been derived. Motivated by the distributed adaptive resource management problems with the objective of dynamically activating a time-variant subset of observation nodes to optimize the network's performance, the thesis derives the exact expression, referred to as the dPCRLB, for computing the PCRLB for any AN/SN configured in a distributed fashion. The dPCRLB computational algorithms are derived for both the off-line conventional (non-conditional) PCRLB determined primarily from the state model, observation model, and prior knowledge of the initial state of the system, and the online conditional PCRLB expressed as a function of past history of the observations. Compared to the non-conditional dPCRLB, its conditional counterpart provides a more accurate representation of the estimator's performance and, consequently, a better criteria for sensor selection. The thesis then extends the dPCRLB algorithms to quantized observations. Particle filter realizations are used to compute these bounds numerically and quantify their performance for data fusion problems through Monte-Carlo simulations

FLEXIBLE LOW-COST HW/SW ARCHITECTURES FOR TEST, CALIBRATION AND CONDITIONING OF MEMS SENSOR SYSTEMS

During the last years smart sensors based on Micro-Electro-Mechanical systems (MEMS) are widely spreading over various fields as automotive, biomedical, optical and consumer, and nowadays they represent the outstanding state of the art. The reasons of their diffusion is related to the capability to measure physical and chemical information using miniaturized components. The developing of this kind of architectures, due to the heterogeneities of their components, requires a very complex design flow, due to the utilization of both mechanical parts typical of the MEMS sensor and electronic components for the interfacing and the conditioning. In these kind of systems testing activities gain a considerable importance, and they concern various phases of the life-cycle of a MEMS based system. Indeed, since the design phase of the sensor, the validation of the design by the extraction of characteristic parameters is important, because they are necessary to design the sensor interface circuit. Moreover, this kind of architecture requires techniques for the calibration and the evaluation of the whole system in addition to the traditional methods for the testing of the control circuitry. The first part of this research work addresses the testing optimization by the developing of different hardware/software architecture for the different testing stages of the developing flow of a MEMS based system. A flexible and low-cost platform for the characterization and the prototyping of MEMS sensors has been developed in order to provide an environment that allows also to support the design of the sensor interface. To reduce the reengineering time requested during the verification testing a universal client-server architecture has been designed to provide a unique framework to test different kind of devices, using different development environment and programming languages. Because the use of ATE during the engineering phase of the calibration algorithm is expensive in terms of ATE’s occupation time, since it requires the interruption of the production process, a flexible and easily adaptable low-cost hardware/software architecture for the calibration and the evaluation of the performance has been developed in order to allow the developing of the calibration algorithm in a user-friendly environment that permits also to realize a small and medium volume production. The second part of the research work deals with a topic that is becoming ever more important in the field of applications for MEMS sensors, and concerns the capability to combine information extracted from different typologies of sensors (typically accelerometers, gyroscopes and magnetometers) to obtain more complex information. In this context two different algorithm for the sensor fusion has been analyzed and developed: the first one is a fully software algorithm that has been used as a means to estimate how much the errors in MEMS sensor data affect the estimation of the parameter computed using a sensor fusion algorithm; the second one, instead, is a sensor fusion algorithm based on a simplified Kalman filter. Starting from this algorithm, a bit-true model in Mathworks Simulink(TM) has been created as a system study for the implementation of the algorithm on chip

Design and implementation of generalized topologies of time-interleaved variable bandpass Σ−Δ modulators

In this thesis, novel analog-to-digital and digital-to-analog generalized time-interleaved variable bandpass sigma-delta modulators are designed, analysed, evaluated and implemented that are suitable for high performance data conversion for a broad-spectrum of applications. These generalized time-interleaved variable bandpass sigma-delta modulators can perform noise-shaping for any centre frequency from DC to Nyquist. The proposed topologies are well-suited for Butterworth, Chebyshev, inverse-Chebyshev and elliptical filters, where designers have the flexibility of specifying the centre frequency, bandwidth as well as the passband and stopband attenuation parameters. The application of the time-interleaving approach, in combination with these bandpass loop-filters, not only overcomes the limitations that are associated with conventional and mid-band resonator-based bandpass sigma-delta modulators, but also offers an elegant means to increase the conversion bandwidth, thereby relaxing the need to use faster or higher-order sigma-delta modulators. A step-by-step design technique has been developed for the design of time-interleaved variable bandpass sigma-delta modulators. Using this technique, an assortment of lower- and higher-order single- and multi-path generalized A/D variable bandpass sigma-delta modulators were designed, evaluated and compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity for ideal and non-ideal topologies. Extensive behavioural-level simulations verified that one of the proposed topologies not only used fewer coefficients but also exhibited greater robustness to non-idealties. Furthermore, second-, fourth- and sixth-order single- and multi-path digital variable bandpass digital sigma-delta modulators are designed using this technique. The mathematical modelling and evaluation of tones caused by the finite wordlengths of these digital multi-path sigmadelta modulators, when excited by sinusoidal input signals, are also derived from first principles and verified using simulation and experimental results. The fourth-order digital variable-band sigma-delta modulator topologies are implemented in VHDL and synthesized on Xilinx® SpartanTM-3 Development Kit using fixed-point arithmetic. Circuit outputs were taken via RS232 connection provided on the FPGA board and evaluated using MATLAB routines developed by the author. These routines included the decimation process as well. The experiments undertaken by the author further validated the design methodology presented in the work. In addition, a novel tunable and reconfigurable second-order variable bandpass sigma-delta modulator has been designed and evaluated at the behavioural-level. This topology offers a flexible set of choices for designers and can operate either in single- or dual-mode enabling multi-band implementations on a single digital variable bandpass sigma-delta modulator. This work is also supported by a novel user-friendly design and evaluation tool that has been developed in MATLAB/Simulink that can speed-up the design, evaluation and comparison of analog and digital single-stage and time-interleaved variable bandpass sigma-delta modulators. This tool enables the user to specify the conversion type, topology, loop-filter type, path number and oversampling ratio

Systems and Methods for the Spectral Calibration of Swept Source Optical Coherence Tomography Systems

This dissertation relates to the transition of the state of the art of swept source optical coherence tomography (SS-OCT) systems to a new realm in which the image acquisition speed is improved by an order of magnitude. With the aid of a better quality imaging technology, the speed-up factor will considerably shorten the eye-exam clinical visits which in turn improves the patient and doctor interaction experience. These improvements will directly lower associated medical costs for eye-clinics and patients worldwide. There are several other embodiments closely related to Optical Coherence Tomography (OCT) that could benefit from the ideas presented in this dissertation including: optical coherence microscopy (OCM), full-field OCT (FF-OCT), optical coherence elastography (OCE), optical coherence tomography angiography (OCT-A), anatomical OCT (aOCT), optical coherence photoacoustic microscopy (OC-PAM), micro optical coherence tomography (µ OCT), among others. In recent decades, OCT has established itself as the de-facto imaging process that most ophthalmologists refer to in their clinical practices. In a broader sense, optical coherence tomography is used in applications when low penetration and high resolution are desired. These applications include different fields of biomedical sciences including cardiology, dermatology, and pulmonary related sciences. Many other industrial applications including quality control and precise measurements have also been reported that are related to the OCT technology. Every new iteration of OCT technology has always come about with advanced signal processing and data acquisition algorithms using mixed-signal architectures, calibration and signal processing techniques. The existing industrial practices towards data acquisition, processing, and image creation relies on conventional signal processing design flows, which extensively employ continuous/discrete techniques that are both time-consuming and costly. The ideas presented in this dissertation can take the technology to a new dimension of quality of service

Projeto de quantizadores não lineares para conversores analógico-digitais com base na transformada da incerteza

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade UnB Gama, 2017.No caso de sistemas de quantização lineares ou uniformes, pode haver grandes erros de quantização para sinais pequenos. Esses erros podem ser tão grandes que a relação sinalruído (\u1d446\u1d441\u1d445) não será suficiente para recuperar toda a informação do sinal. Como alternativa para esse problema pode-se utilizar quantizadores não lineares. O objetivo deste trabalho é a modelagem de um quantizador não linear, que utiliza uma distribuição arcoseno, para aplicação em um conversor analógico-digital com arquitetura Σ-Δ. O projeto foi desenvolvido com auxílio das ferramentas Cadence seguindo a metodologia de projetos \u1d447\u1d45c\u1d45d-\u1d437\u1d45c\u1d464\u1d45b. Na modelagem foi utilizada a linguagem de descrição de ℎ\u1d44e\u1d45f\u1d451\u1d464\u1d44e\u1d45f\u1d452 Verilog-A, que possibilita a análise comportamental e simulação mista. Este trabalho foi dividido em duas partes: modelagem dos quantizadores linear e não linear com distribuição arco-seno e modelagem do modulador Σ-Δ com aplicação dos quantizadores. Na primeira parte modelou-se todos os blocos em Verilog-A e implementou-se um quantizador linear e um quantizador não linear utilizando-se topologia do tipo \u1d453\u1d459\u1d44e\u1d460ℎ. Na segunda parte modelouse todos os blocos do modulador Σ-Δ, aplicando-se os quantizadores projetados anteriormente e fazendo uma comparação de desempenho entre o modulador com quantizador linear e o modulador com quantizador arco-seno.In case of linear or uniform quantization systems, there may be large quantization errors for small signals. These errors can be so large that the signal-to-noise ratio (\u1d446\u1d441\u1d445) will not be sufficient to recover all the signal information. Alternatively to this problem can be used non-linear quantizers. The objective of this work is the modeling of a non-linear quantizer, which uses an arcsine distribution, for application in an analog-digital converter with Σ-Δ architecture. The project was developed with the help of Cadence tools following the \u1d447\u1d45c\u1d45d-\u1d437\u1d45c\u1d464\u1d45b project methodology. In the modeling, the hardware description language, \u1d449 \u1d452\u1d45f\u1d456\u1d459\u1d45c\u1d454 − \u1d434, was used, which allows behavior analysis and mixed simulation. This work was divided in two parts: modeling of linear and non-linear quantizers with arcsine distribution and modeling of the modulator Σ-Δ with application of the quantizers. In the first part, all the blocks were modeled in Verilog-A, implementing a linear quantizer and a non-linear quantizer using a \u1d453\u1d459\u1d44e\u1d460ℎ topology. In the second part all the modulator blocks Σ-Δ were modeled by applying the previously designed quantizers and performing a performance comparison between the linear quantizer modulator and the arcsine modulator