Control theory | Signal estimation | Stochastic differential equations
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 a computer with finite memory. A finite dimensional approximated nonlinear filter may be more based on heuristics, such as the extended Kalman filter or the assumed density filters, or more methodologically oriented such as for example the Projection Filters, some sub-families of which are shown to coincide with the Assumed Density Filters. In general, if the separation principle applies, then filtering also arises as part of the solution of an optimal control problem. For example, the Kalman filter is the estimation part of the optimal control solution to the linear-quadratic-Gaussian control problem. (Wikipedia).
Introduction to Frequency Selective Filtering
http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Separation of signals based on frequency content using lowpass, highpass, bandpass, etc filters. Filter g
From playlist Introduction to Filter Design
Hybrid sparse stochastic processes and the resolution of (...) - Unser - Workshop 2 - CEB T1 2019
Michael Unser (EPFL) / 12.03.2019 Hybrid sparse stochastic processes and the resolution of linear inverse problems. Sparse stochastic processes are continuous-domain processes that are specified as solutions of linear stochastic differential equations driven by white Lévy noise. These p
From playlist 2019 - T1 - The Mathematics of Imaging
Etienne Pardoux: Uniqueness of the filtering equations in the space of measures
HYBRID EVENT Recorded during the meeting " Probability/PDE Interactions: Interface Models and Particle Systems " the April 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by world
From playlist Probability and Statistics
Introduction to the paper https://arxiv.org/abs/2002.06707
From playlist Research
Low Pass Filters & High Pass Filters : Data Science Concepts
What is a low pass filter? What is a high pass filter? Sobel Filter: https://en.wikipedia.org/wiki/Sobel_operator
From playlist Time Series Analysis
"Data-Driven Optimization in Pricing and Revenue Management" by Arnoud den Boer - Lecture 3
In this course we will study data-driven decision problems: optimization problems for which the relation between decision and outcome is unknown upfront, and thus has to be learned on-the-fly from accumulating data. This type of problems has an intrinsic tension between statistical goals a
From playlist Thematic Program on Stochastic Modeling: A Focus on Pricing & Revenue Management
"Diffusion Approximation and Sequential Experimentation" by Victor Araman
We consider a Bayesian sequential experimentation problem. We identify environments in which the average number of experiments that is conducted per unit of time is large and the informativeness of each individual experiment is low. Under such regimes, we derive a diffusion approximation f
From playlist Thematic Program on Stochastic Modeling: A Focus on Pricing & Revenue Management
Duality between estimation and control - Sanjoy Mitter
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
Silvia Villa - Generalization properties of multiple passes stochastic gradient method
The stochastic gradient method has become an algorithm of choice in machine learning, because of its simplicity and small computational cost, especially when dealing with big data sets. Despite its widespread use, the generalization properties of the variants of stochastic
From playlist Schlumberger workshop - Computational and statistical trade-offs in learning
Part1. Data assimilation using particle filters... - Crisan - Workshop 2 - CEB T3 2019
Crisan (Imperial College London, UK) / 13.11.2019 Data assimilation using particle filters for class of partially observed stochastic geophysical fluid dynamics models. Part I ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actua
From playlist 2019 - T3 - The Mathematics of Climate and the Environment
2 Ruediger - Stochastic Integration & SDEs
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Sebastian Ertel - An Ensemble Kalman-Bucy filter for correlated observation noise
Sebastian Ertel (Technical University of Berlin) presents, "An Ensemble Kalman-Bucy filter for correlated observation noise", 8/7/22.
From playlist Statistics Across Campuses
Sri Namachchivaya - Stability, dimensional reduction and data assimilation in random dynamical sy
PROGRAM: Nonlinear filtering and data assimilation DATES: Wednesday 08 Jan, 2014 - Saturday 11 Jan, 2014 VENUE: ICTS-TIFR, IISc Campus, Bangalore LINK:http://www.icts.res.in/discussion_meeting/NFDA2014/ The applications of the framework of filtering theory to the problem of data assimi
From playlist Nonlinear filtering and data assimilation
Data Driven Methods for Complex Turbulent Systems ( 3 ) - Andrew J. Majda
Lecture 3: Data Driven Methods for Complex Turbulent Systems Abstract: An important contemporary research topic is the development of physics constrained data driven methods for complex, large-dimensional turbulent systems such as the equations for climate change science. Three new approa
From playlist Mathematical Perspectives on Clouds, Climate, and Tropical Meteorology
Sri Namachchivaya - Stability, dimensional reduction and data assimilation in random dynamical sy
PROGRAM: Nonlinear filtering and data assimilation DATES: Wednesday 08 Jan, 2014 - Saturday 11 Jan, 2014 VENUE: ICTS-TIFR, IISc Campus, Bangalore LINK:http://www.icts.res.in/discussion_meeting/NFDA2014/ The applications of the framework of filtering theory to the problem of data assimi
From playlist Nonlinear filtering and data assimilation
I discuss causal and non-causal noise filters: the moving average filter and the exponentially weighted moving average. I show how to do this filtering in Excel and Python
From playlist Discrete
Sanjoy Mitter - Overview of variational approach to nonlinear filtering
PROGRAM: Nonlinear filtering and data assimilation DATES: Wednesday 08 Jan, 2014 - Saturday 11 Jan, 2014 VENUE: ICTS-TIFR, IISc Campus, Bangalore LINK:http://www.icts.res.in/discussion_meeting/NFDA2014/ The applications of the framework of filtering theory to the problem of data assimi
From playlist Nonlinear filtering and data assimilation
Gang George Yin: "High-Dimensional HJBs: Mean-Field Limits and McKean-Vlasov Equations"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games "High-Dimensional HJBs: Mean-Field Limits and McKean-Vlasov Equations" Gang George Yin, Wayne State University Abstract: In this talk, we will study mean-fiel
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Noncausal filtering of stored data to obtain zero-phase response using the time-reversal property of the DFT, as implemented by the "filtfilt" comma
From playlist Introduction to Filter Design