Unscented Kalman Filter (UKF) CSCE 774 – Guest Lecture Dr. Gabriel Terejanu Fall 2015.

Slides:

Advertisements

Similar presentations

Introduction to Data Assimilation NCEO Data-assimilation training days 5-7 July 2010 Peter Jan van Leeuwen Data Assimilation Research Center (DARC) University.

Advertisements

Environmental Data Analysis with MatLab Lecture 8: Solving Generalized Least Squares Problems.

EKF, UKF TexPoint fonts used in EMF.

Modeling Uncertainty over time Time series of snapshot of the world “state” we are interested represented as a set of random variables (RVs) – Observable.

State space model of precipitation rate (Tamre Cardoso, PhD UW 2004) Updating wave height forecasts using satellite data (Anders Malmberg, PhD U. Lund.

Kalman Filter CMPUT 615 Nilanjan Ray. What is Kalman Filter A sequential state estimator for some special cases Invented in 1960’s Still very much used.

A Physically-Based Motion Retargeting Filter SEYOON TAK HYEONG-SEOK KO ACM TOG (January 2005) 方奎力.

Introduction to Mobile Robotics Bayes Filter Implementations Gaussian filters.

Probabilistic Robotics: Kalman Filters

Graphical Models for Mobile Robot Localization Shuang Wu.

Chapter 1 Introduction The solutions of engineering problems can be obtained using analytical methods or numerical methods. Analytical differentiation.

Probabilistic Robotics

Kostas Andreadis1, Dennis Lettenmaier1, and Doug Alsdorf2

Comparative survey on non linear filtering methods : the quantization and the particle filtering approaches Afef SELLAMI Chang Young Kim.

Stanford CS223B Computer Vision, Winter 2006 Lecture 11 Filters / Motion Tracking Professor Sebastian Thrun CAs: Dan Maynes-Aminzade, Mitul Saha, Greg.

Estimation and the Kalman Filter David Johnson. The Mean of a Discrete Distribution “I have more legs than average”

Course AE4-T40 Lecture 5: Control Apllication

Probabilistic Robotics Bayes Filter Implementations Gaussian filters.

CHAPTER 3: SIMPLE MODELS

Environmental Data Analysis with MatLab Lecture 7: Prior Information.

G. Hendeby Performance Issues in Non-Gaussian Filtering Problems NSSPW ‘06 Corpus Christi College, Cambridge Performance Issues in Non-Gaussian Filtering.

G. Hendeby Recursive Triangulation Using Bearings-Only Sensors TARGET ‘06 Austin Court, Birmingham Recursive Triangulation Using Bearings-Only Sensors.

Principles of the Global Positioning System Lecture 13 Prof. Thomas Herring Room A;

Host Load Prediction in a Google Compute Cloud with a Bayesian Model Sheng Di 1, Derrick Kondo 1, Walfredo Cirne 2 1 INRIA 2 Google.

Muhammad Moeen YaqoobPage 1 Moment-Matching Trackers for Difficult Targets Muhammad Moeen Yaqoob Supervisor: Professor Richard Vinter.

Colorado Center for Astrodynamics Research The University of Colorado STATISTICAL ORBIT DETERMINATION Project Report Unscented kalman Filter Information.

AMBIENT AIR CONCENTRATION MODELING Types of Pollutant Sources Point Sources e.g., stacks or vents Area Sources e.g., landfills, ponds, storage piles Volume.

Prospects for river discharge and depth estimation through assimilation of swath–altimetry into a raster-based hydraulics model Kostas Andreadis 1, Elizabeth.

Computer vision: models, learning and inference Chapter 19 Temporal models.

Computer Vision Group Prof. Daniel Cremers Autonomous Navigation for Flying Robots Lecture 6.2: Kalman Filter Jürgen Sturm Technische Universität München.

Computer vision: models, learning and inference Chapter 19 Temporal models.

Probabilistic Robotics Robot Localization. 2 Localization Given Map of the environment. Sequence of sensor measurements. Wanted Estimate of the robot’s.

Kalman Filter (Thu) Joon Shik Kim Computational Models of Intelligence.

Complete Pose Determination for Low Altitude Unmanned Aerial Vehicle Using Stereo Vision Luke K. Wang, Shan-Chih Hsieh, Eden C.-W. Hsueh 1 Fei-Bin Hsaio.

Probabilistic Robotics Bayes Filter Implementations Gaussian filters.

Probabilistic Robotics Bayes Filter Implementations.

Overview Particle filtering is a sequential Monte Carlo methodology in which the relevant probability distributions are iteratively estimated using the.

HQ U.S. Air Force Academy I n t e g r i t y - S e r v i c e - E x c e l l e n c e Improving the Performance of Out-of-Order Sigma-Point Kalman Filters.

Assimilating chemical compound with a regional chemical model Chu-Chun Chang 1, Shu-Chih Yang 1, Mao-Chang Liang 2, ShuWei Hsu 1, Yu-Heng Tseng 3 and Ji-Sung.

Introduction to Modeling – Part II

Deguillaume L., Beekmann M., Menut L., Derognat C.

TEMPLATE DESIGN © A high-order accurate and monotonic advection scheme is used as a local interpolator to redistribute.

State Estimation and Kalman Filtering

NCAF Manchester July 2000 Graham Hesketh Information Engineering Group Rolls-Royce Strategic Research Centre.

Unscented Kalman Filter 1. 2 Linearization via Unscented Transform EKF UKF.

Types of Models Marti Blad Northern Arizona University College of Engineering & Technology.

Short Introduction to Particle Filtering by Arthur Pece [ follows my Introduction to Kalman filtering ]

By: Aaron Dyreson Supervising Professor: Dr. Ioannis Schizas

Nonlinear State Estimation

The Unscented Particle Filter 2000/09/29 이 시은. Introduction Filtering –estimate the states(parameters or hidden variable) as a set of observations becomes.

Surface Water Virtual Mission Dennis P. Lettenmaier, Kostas Andreadis, and Doug Alsdorf Department of Civil and Environmental Engineering University of.

Colorado Center for Astrodynamics Research The University of Colorado 1 STATISTICAL ORBIT DETERMINATION Kalman Filter with Process Noise Gauss- Markov.

The Unscented Kalman Filter for Nonlinear Estimation Young Ki Baik.

Estimating emissions from observed atmospheric concentrations: A primer on top-down inverse methods Daniel J. Jacob.

Probabilistic Robotics Bayes Filter Implementations Gaussian filters.

Types of Models Marti Blad PhD PE

Unscented Kalman Filter for a coal run-of-mine bin

Overview of Deterministic Computer Models

PSG College of Technology

Unscented Kalman Filter

Unscented Kalman Filter

Filtering and State Estimation: Basic Concepts

Models of atmospheric chemistry

Surface Water Virtual Mission

Hellenic Open University

Unscented Kalman Filter

Introduction to Modeling – Part II

6.891 Computer Experiments for Particle Filtering

Principles of the Global Positioning System Lecture 13

Kalman Filter: Bayes Interpretation

Presentation transcript:

Unscented Kalman Filter (UKF) CSCE 774 – Guest Lecture Dr. Gabriel Terejanu Fall 2015

Problem Statement 2 Process and measurement noise (temporarily uncorrelated) Initial state statistic summary Measurements

Filtering 3

Review Kalman Filter vs Extended Kalman Filter vs Particle Filter vs Unscented Kalman Filter 4

Main idea of Unscented Transformation 5

Weighted Statistical Linearization (WSL) 6 WSL provides an alternative linear model to the first-order Taylor series expansion

WSL cont. 7

WSL solution 8

UKF - Sigma Points 9

Sigma Points Selection 10 Sigma points are selected to capture the first and the second order moments of the prior distribution.

Notes 11

UKF #1 - Propagate sigma-points through process model 12

UKF #2/#3 – Propagate through measurement model & Data Assimilation 13

UKF - Summary true mean and covariance predicted mean and covariance prior predicted measurement sensor reading true mean and covariance estimated mean and covariance posterior Bayes Update

Application – Atmospheric Dispersion 15 Atmospheric dispersion involves transport (advection) and diffusion of the species released into the atmosphere Dispersion modeling uses mathematical formulations to characterize the atmospheric processes that disperse a pollutant emitted by a source Chernobyl, Soviet Union, April, 26, 1986, radioactive particle plume estimated to be responsible for 4000 extra deaths according to IAEA and WHO

Numerical Results – Puff-based Dispersion Model 16

Puff Splitting and Merging 17 Dispersion over complex terrains Puff splitting: when an initially small puff is grown to the size comparable with the grid spacing of the flow model After splitting, the new puffs can set off in individual directions Puff merging: two puffs, which are sufficiently close to each other, can be merged

Variable State Dimension 18

Simulation Environment 19 Concentration Dosage Chemical Release Example Truth model simulation Dispersion Region 15 x 15 km 2 Grid resolution (concentrations) 200 m Sensors located every 1 km Square Root implementation The results have been averaged over 50 runs Simulation Time: 60 min The Source releases every 1 min for the first 15 min Time Step: 20 sec Wind Speed: 5 m/sec with 20% noise Wind direction changes from 15 deg to 60 deg after 30 min

Results – Plume Concentration 20

Results - Dosage 21

Thank you! 22