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Switching Kalman Filter
The switching Kalman filtering (SKF) method is a variant of the Kalman filter. In its generalised form, it is often attributed to Kevin P. Murphy,K. P. Murphy, "Switching Kalman Filters", Compaq Cambridge Research Lab Tech. Report 98-10, 1998Kalman Filtering and Neural Networks. Edited by Simon Haykin. but related switching state-space models have been in use. Applications Applications of the switching Kalman filter include: Brain–computer interfaces and neural decoding, real-time decoding for continuous neural-prosthetic control,Wu, Wei, Michael J. Black, David Bryant Mumford, Yun Gao, Elie Bienenstock, and John P. Donoghue. 2004. Modelling and decoding motor cortical activity using a switching Kalman filter. IEEE Transactions on Biomedical Engineering 51(6): 933-942. and sensorimotor learning in humans.Heald JB, Ingram JN, Flanagan JR, Wolpert DM. Multiple motor memories are learned to control different points on a tool. ''Nature Human Behaviour''. 2, 300–311, (2018). It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman Filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory. This digital filter is sometimes termed the ''Stratonovich–Kalman–Bucy filter'' because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow. Kalman filtering has numerous te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filtering Problem (stochastic Processes)
In the theory of stochastic processes, filtering describes the problem of determining the state of a system from an incomplete and potentially noisy set of observations. While originally motivated by problems in engineering, filtering found applications in many fields from signal processing to finance. The problem of optimal non-linear filtering (even for the non-stationary case) was solved by Ruslan L. Stratonovich (1959, 1960), see also Harold J. Kushner's work and Moshe Zakai's, who introduced a simplified dynamics for the unnormalized conditional law of the filter known as Zakai equation. The solution, however, is infinite-dimensional in the general case. Certain approximations and special cases are well understood: for example, the linear filters are optimal for Gaussian random variables, and are known as the Wiener filter and the Kalman-Bucy filter. More generally, as the solution is infinite dimensional, it requires finite dimensional approximations to be implemented in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Differential Equations
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes. Random differential equations are conjugate to stochastic differential equations. Background Stochastic differential equations originated in the theory of Brownian motion, in the work of Albert Einstein and Smoluchowski. These early examples were linear stochastic differential equations, also called 'Langevin' equations after French physicist Langevin, describing the motion of a harmonic oscillator subject to a random force. The mathematical theory of stocha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Estimation
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing'' includes audio, video, speech, image, sonar, and radar as examples of signal. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information. In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling. Signaling theory, in evolutionary biology, proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Filters
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components (resistors, capacitors, inductors, and linear amplifiers) will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies (their frequency response), they are s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Filters
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothing Problem (stochastic Processes)
The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time using incremental incoming measurements. It is one of the main problems defined by Norbert Wiener.1942, ''Extrapolation, Interpolation and Smoothing of Stationary Time Series''. A war-time classified report nicknamed "the yellow peril" because of the color of the cover and the difficulty of the subject. Published postwar 1949 MIT Press. http://www.isss.org/lumwiener.htm Wiener, Norbert (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. New York: Wiley. . A smoother is an algorithm that implements a solution to this problem, typically based on recursive Bayesian estimation. The smoothing problem is closely related to the filtering problem, both of which are studied in Bayesian smoothing theory. A smoother is often a two-pass process, composed of forward and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoffrey E
Geoffrey, Geoffroy, Geoff, etc., may refer to: People * Geoffrey (name), including a list of people with the name * Geoffroy (surname), including a list of people with the name * Geoffrey of Monmouth (c. 1095–c. 1155), clergyman and one of the major figures in the development of British history * Geoffrey I of Anjou (died 987) * Geoffrey II of Anjou (died 1060) * Geoffrey III of Anjou (died 1096) * Geoffrey IV of Anjou (died 1106) * Geoffrey V, Count of Anjou (1113–1151), father of King Henry II of England * Geoffrey II, Duke of Brittany (1158–1186), one of Henry II's sons * Geoffrey, Archbishop of York (c. 1152–1212) * Geoffroy du Breuil of Vigeois, 12th century French chronicler * Geoffroy de Charney (died 1314), Preceptor of the Knights Templar * Geoffroy IV de la Tour Landry (c. 1320–1391), French nobleman and writer * Geoffrey the Baker (died c. 1360), English historian and chronicler * Geoffroy (musician) (born 1987), Canadian singer, songwriter and multi-in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Haykin
Simon Haykin (born in 1931 as Sahir Sabir Hakim ) is an electrical engineer noted for his pioneering work in Adaptive Signal Processing with emphasis on applications to Radar Engineering and Telecom Technology. He is currently Distinguished University Professor at McMaster University in Hamilton, Ontario, Canada. Education and career Haykin received BSc (First-Class Honours) (1953); Ph.D. (1956), and DSc. (1967), degrees-all in Electrical Engineering from University of Birmingham, UK (England). He is a Fellow of the Royal Society of Canada, and a Fellow of the Institute of Electrical and Electronics Engineers for contributions to signal processing, communications theory, and electrical engineering education. In 2002 he became a recipient of Henry Booker Gold Medal from URSI and in 1999 received Hon. Degree of Doctor of Technical Science from ETH Zurich, Switzerland, and many other medals and prizes. In mid-1980s, Haykin shifted the thrust of his research effort in the direction o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zoubin Ghahramani
Zoubin Ghahramani FRS ( fa, زوبین قهرمانی; born 8 February 1970) is a British-Iranian researcher and Professor of Information Engineering at the University of Cambridge. He holds joint appointments at University College London and the Alan Turing Institute. and has been a Fellow of St John's College, Cambridge since 2009. He was Associate Research Professor at Carnegie Mellon University School of Computer Science from 2003–2012. He was also the Chief Scientist of Uber from 2016 until 2020. He joined Google Brain in 2020 as senior research director. He is also Deputy Director of the Leverhulme Centre for the Future of Intelligence. Education Ghahramani was educated at the American School of Madrid in Spain and the University of Pennsylvania where he was awarded a double major degree in Cognitive Science and Computer Science in 1990. He obtained his Ph.D. from the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology, su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrics
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8–22 Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1p. 1–34Abstract (2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used today. A basic tool for econometrics is the multiple linear regression model. ''Econometric the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
