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Introduction and Implementations of the Kalman Filter

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ISBN: 9781838805364 9781838805371 9781838807399 Year: Pages: 128 DOI: 10.5772/intechopen.75731 Language: English
Publisher: IntechOpen
Subject: Computer Science
Added to DOAB on : 2019-10-03 07:51:53

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Sensor data fusion is the process of combining error-prone, heterogeneous, incomplete, and ambiguous data to gather a higher level of situational awareness. In principle, all living creatures are fusing information from their complementary senses to coordinate their actions and to detect and localize danger. In sensor data fusion, this process is transferred to electronic systems, which rely on some ""awareness"" of what is happening in certain areas of interest. By means of probability theory and statistics, it is possible to model the relationship between the state space and the sensor data. The number of ingredients of the resulting Kalman filter is limited, but its applications are not.

Ambisonics

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Book Series: Springer Topics in Signal Processing ISBN: 9783030172077 Year: Pages: 210 DOI: 10.1007/978-3-030-17207-7 Language: English
Publisher: Springer Nature
Subject: Music --- Mathematics --- Agriculture (General)
Added to DOAB on : 2020-02-04 11:21:14
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This open access book provides a concise explanation of the fundamentals and background of the surround sound recording and playback technology Ambisonics. It equips readers with the psychoacoustical, signal processing, acoustical, and mathematical knowledge needed to understand the inner workings of modern processing utilities, special equipment for recording, manipulation, and reproduction in the higher-order Ambisonic format. The book comes with various practical examples based on free software tools and open scientific data for reproducible research. The book’s introductory section offers a perspective on Ambisonics spanning from the origins of coincident recordings in the 1930s to the Ambisonic concepts of the 1970s, as well as classical ways of applying Ambisonics in first-order coincident sound scene recording and reproduction that have been practiced since the 1980s. As, from time to time, the underlying mathematics become quite involved, but should be comprehensive without sacrificing readability, the book includes an extensive mathematical appendix. The book offers readers a deeper understanding of Ambisonic technologies, and will especially benefit scientists, audio-system and audio-recording engineers. In the advanced sections of the book, fundamentals and modern techniques as higher-order Ambisonic decoding, 3D audio effects, and higher-order recording are explained. Those techniques are shown to be suitable to supply audience areas ranging from studio-sized to hundreds of listeners, or headphone-based playback, regardless whether it is live, interactive, or studio-produced 3D audio material.

Advanced DSP Techniques for High-Capacity and Energy-Efficient Optical Fiber Communications

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ISBN: 9783039217922 9783039217939 Year: Pages: 150 DOI: 10.3390/books978-3-03921-793-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-01-07 09:08:26
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The rapid proliferation of the Internet has been driving communication networks closer and closer to their limits, while available bandwidth is disappearing due to an ever-increasing network load. Over the past decade, optical fiber communication technology has increased per fiber data rate from 10 Tb/s to exceeding 10 Pb/s. The major explosion came after the maturity of coherent detection and advanced digital signal processing (DSP). DSP has played a critical role in accommodating channel impairments mitigation, enabling advanced modulation formats for spectral efficiency transmission and realizing flexible bandwidth. This book aims to explore novel, advanced DSP techniques to enable multi-Tb/s/channel optical transmission to address pressing bandwidth and power-efficiency demands. It provides state-of-the-art advances and future perspectives of DSP as well.

Fractional Order Systems

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ISBN: 9783039216086 9783039216093 Year: Pages: 114 DOI: 10.3390/books978-3-03921-609-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century

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ISBN: 9783038977469 Year: Pages: 260 DOI: 10.3390/books978-3-03897-747-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-04-05 11:17:10
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Iterative Methods for Solving Nonlinear Equations and Systems

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ISBN: 9783039219407 9783039219414 Year: Pages: 494 DOI: 10.3390/books978-3-03921-941-4 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-01-07 09:08:26
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Keywords

point projection --- intersection --- parametric curve --- n-dimensional Euclidean space --- Newton’s second order method --- fixed point theorem --- nonlinear equations --- multiple zeros --- optimal iterative methods --- higher order of convergence --- nonlinear operator equation --- Fréchet derivative --- ?-continuity condition --- Newton-like method --- Frédholm integral equation --- nonlinear equations --- Padé approximation --- iterative method --- order of convergence --- numerical experiment --- fourth order iterative methods --- local convergence --- banach space --- radius of convergence --- nonlinear equation --- iterative process --- non-differentiable operator --- Lipschitz condition --- high order --- sixteenth order convergence method --- local convergence --- dynamics --- Banach space --- Newton’s method --- semi-local convergence --- Kantorovich hypothesis --- iterative methods --- Steffensen’s method --- R-order --- with memory --- computational efficiency --- non-linear equation --- basins of attraction --- optimal order --- higher order method --- computational order of convergence --- nonlinear equations --- multiple roots --- Chebyshev–Halley-type --- optimal iterative methods --- efficiency index --- Banach space --- semilocal convergence --- ?-continuity condition --- Jarratt method --- error bound --- Fredholm integral equation --- Newton’s method --- global convergence --- variational inequality problem --- split variational inclusion problem --- multi-valued quasi-nonexpasive mappings --- Hilbert space --- sixteenth-order optimal convergence --- multiple-root finder --- asymptotic error constant --- weight function --- purely imaginary extraneous fixed point --- attractor basin --- drazin inverse --- generalized inverse --- iterative methods --- higher order --- efficiency index --- integral equation --- efficiency index --- nonlinear models --- iterative methods --- higher order --- nonlinear equations --- optimal iterative methods --- multiple roots --- efficiency index --- iterative methods --- nonlinear equations --- Newton-type methods --- smooth and nonsmooth operators --- heston model --- Hull–White --- option pricing --- PDE --- finite difference (FD) --- iteration scheme --- Moore–Penrose --- rectangular matrices --- rate of convergence --- efficiency index --- nonlinear equations --- conjugate gradient method --- projection method --- convex constraints --- signal and image processing --- nonlinear monotone equations --- conjugate gradient method --- projection method --- signal processing --- nonlinear systems --- multipoint iterative methods --- divided difference operator --- order of convergence --- Newton’s method --- computational efficiency index --- system of nonlinear equations --- Newton method --- Newton-HSS method --- nonlinear HSS-like method --- Picard-HSS method --- convexity --- least square problem --- accretive operators --- signal processing --- point projection --- intersection --- planar algebraic curve --- Newton’s iterative method --- the improved curvature circle algorithm --- systems of nonlinear equations --- King’s family --- order of convergence --- multipoint iterative methods --- nonlinear equations --- Potra–Pták method --- optimal methods --- weight function --- basin of attraction --- engineering applications --- Kung–Traub conjecture --- multipoint iterations --- nonlinear equation --- optimal order --- basins of attraction

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