Both sensor observation data and mathematical models are used to assist in the understanding of physical dynamic systems. However, observational data is often limited in terms of the kind and frequency of observations that can be taken and may only provide access to limited aspects of the system states. Also, any mathematical model used to represent the system dynamics is a reflection of numerous assumptions and simplifications to permit determination of a tractable model. These factors cause overall accuracy to degrade as the model states evolve. The fusion of observational data with state models promises to provide greater understanding of physical phenomenon than either approach alone can achieve. The most critical challenge here is to provide a quantitative assessment of how closely our estimates reflect reality in the presence of model uncertainty, discretization errors as well as measurement errors and uncertainty. The quantitative understanding of uncertainty is essential when predictions are to be used to inform policy making or mitigation solutions where significant resources are at stake.

This workshop will focus on recent development of mathematical and algorithmic fundamentals for uncertainty propagation, forecasting, and model-data fusion for nonlinear systems. The emphasis of this workshop will be on an intuitive understanding of the stochastic processes and practical applications of theory of stochastic processes in estimation and control area. The objectives are to develop a fundamental understanding of stochastic processes and its applications in the area of filtering and control of dynamical systems, to develop an appreciation for the strengths and limitations of state-of-the-art numerical techniques for uncertainty propagation and nonlinear filtering, to reinforce knowledge in stochastic systems with particular emphasis on nonlinear and dynamic problems, and to learn to utilize stochastic system analysis methods as research tools. After the completion of this workshop, audience should be able to apply the discussed methods to real engineering problems with the awareness of potential difficulties that might arise in practice. This workshop would cover topics from basic linear and nonlinear stochastic processes to well-known Kalman filtering methods to recently developed nonlinear estimation methods at a level of detail compatible with the design and implementation of modern control and estimation of dynamical systems. These diverse topics will be covered in an integrated fashion, using a framework derived from stochastic processes, estimation, control, and approximation theory. The reliability and limitations of various methods discussed will be assessed by considering various academic and engineering problems. At the end of this workshop, audience will be able to:

Understand and use the concept of stochastic processes to model engineering systems.
Learn to apply linear uncertainty propagation and filtering techniques to engineering problems.
Understand and derive numerical solution techniques to solve nonlinear uncertainty propagation and filtering problems.
Get exposed to implementation issues such as computational complexity, non-Gaussian uncertainty, reduction of filter dimension, colored noise, discretization etc
The numerical methods to solve the Kolmogorov equation, Perron-Frobenius operator, generalized Polynomial chaos and stochastic collocation methods will be discussed to determine evolution of state pdf due to probabilistic uncertainty in initial or boundary conditions, model parameters and forcing function. Recent advances in sampling methods like Conjugate Unscented Transformation (CUT) will be presented to compute multi-dimensional expectation integrals. A Bayesian framework is used to assimilate the noisy observation data from various sources with uncertain model forecasts to reduce the uncertainty associated with model-state estimates. By accurately characterizing the uncertainty associated with both process and measurement models, this workshop offers systematic design of low-complexity model-data fusion or filtering algorithms with significant improvement in nominal performance and computational effort. Various academic and engineering problems where traditional methods either fail or perform very poorly, will be considered to demonstrate the reliability and limitations of the newly established methods.