Nonlinear State and Parameter Estimation without Tears

Duration:

Sunday June 5th 08.30-17:30, lunch from 12:30-13:30. One-day (approximately 7 hours) including time for hands-on experience in the use of popular methods for state and parameter estimation in stochastic non-linear systems.

Workshop Objectives:

By the end of this workshop, registrants will be able to

• Identify state/parameter estimation problems
• Choose an appropriate algorithm and solve a given state/parameter estimation problem
• Understand and build upon state-of-the-art research in state/parameter estimation

Abstract:

State and parameter estimation are two quintessential problems that arise in an array of engineering applications. They refer to the estimation of unmeasured variables and parameters from noisy input and output data. These two problems have been studied extensively in the context of stochastic linear systems and their optimal solutions are well-known. In fact, software programs using state-of-the-art algorithms are readily available for linear state and parameter estimation; however, similar optimal solutions for stochastic nonlinear systems have proved to be rather difficult to derive. Although a few analytical solutions exist for specific stochastic nonlinear systems, the majority of algorithms are approximations of unwieldy optimal solutions.

Approximate solutions to these problems can broadly be classified into those that approximate the nonlinearity and those that approximate related density functions. For instance, in extended Kalman filter the nonlinearity is approximated and in particle filters the density functions are approximated. The literature is replete with such approximations and algorithms. This workshop is an attempt to identify the most important and useful algorithms, unify them under the umbrellas of optimization and Bayesian statistics, and present them to an audience interested in engineering applications and research. In particular, the standard nonlinear estimation algorithms such as Kalman filter, Extended Kalman filter, Unscented Kalman filter, Ensemble Kalman filter and Moving Horizon Estimator, Particle filter will be presented using both optimization and Bayesian frameworks. A practitioner's guide to systematically assess the performance of different filtering methods and selecting best strategy for a given problem will also be covered.

Agenda:

Topics to be covered in this workshop will be divided into two main parts. In the first part, a number of state and parameter estimation algorithms will be developed for linear and nonlinear stochastic systems from an optimization perspective. This includes the popular Moving-Horizon Estimation (MHE) algorithm. In the second part, the Bayesian perspective of these algorithms will be discussed. The class of particle filtering methods for state and parameter estimation will also be developed in the second part. Finally, a systematic approach to allow practitioner's to choose the best estimation algorithm will be devised. Registrants will solve hands-on MATLAB exercises and receive take away MATLAB codes to implement these algorithms.

Part 1. State and Parameter Estimation: An Optimization Perspective (by Prof. Sachin C. Patwardhan and Prof. Lorenz T. Biegler)

• Motivation, Historical Introduction, and State and Parameter Estimation
• Maximum Likelihood and Maximum a Posteriori (MAP) Estimation
• Linear Kalman Filtering for State Estimation
• Nonlinear Filtering with Extended Kalman filter, Unscented and Ensemble Kalman filter
• Moving Horizon Estimation, Arrival Cost Approximation, Optimization Tools, M-estimators for Gross Error Detection
• Case Studies

Part 2. State and Parameter Estimation: A Bayesian Perspective (by Prof. R. Bhushan Gopaluni and Dr. Aditya Tulsyan)

• Bayesian Perspective, Bayesian Filtering, State Estimation and Parameter Estimation
• On-line Estimation: Sequential Monte-Carlo (SMC) Methods and Particle Filters
• Off-line Estimation: Expectation-Maximization (EM) Method
• Performance Assessment of Bayesian Methods
• Optimal Bayesian Filtering Strategy for State Estimation
• Case Studies

Presenters:

• R. Bhushan Gopaluni, Associate Professor, Department of Chemical and Biological Engineering (University of British Columbia, Canada)
• Sachin C. Patwardhan, Professor, Department of Chemical Engineering (Indian Institute of Technology Mumbai, India)
• Lorenz T. Biegler, Professor, Department of Chemical Engineering (Carnegie Mellon University, USA)
• Aditya Tulsyan, Postdoctoral Associate, Department of Chemical Engineering (Massachusetts Institute of Technology, USA)