Public defence in Automation and Control Engineering, M.Sc. Fatemeh Yaghoobi

The title of the thesis: Computationally efficient and numerically robust state estimation in nonlinear state-space models 

Thesis defender: Fatemeh Yaghoobi
Opponent: Prof. Gustaf Hendeby, Linköping University, Sweden
Custos: Prof. Simo Särkkä, Aalto University School of Electrical Engineering

Many systems we interact with daily—from self-driving cars and industrial robots to aircraft navigation systems and financial markets—require constant monitoring to function properly. However, we often cannot directly measure what's happening inside these systems. 

This research addresses the fundamental challenge of state estimation: reliably inferring the hidden states (like a robot's true position or an industrial process's internal quality) by combining an imperfect mathematical model with noisy, indirect sensor measurements. 

The traditional estimation methods, based on Bayesian filtering and smoothing, often become too slow for modern high-speed applications and can suffer from numerical instability—especially when dealing with large volumes of data—leading to inaccurate results. 

This research makes several significant contributions to the field of inference in state-space models: 

1. Parallel-in-Time Square-Root Algorithms: The thesis derives novel parallel-in-time square-root algorithms for general state-space models. These methods allow estimation problems to be broken down and solved simultaneously across multiple processors (leveraging modern GPUs and TPUs). Crucially, these parallel methods achieve the exact same results as their sequential, time-consuming counterparts, but with vastly reduced computational complexity. The square-root formulation is key to enhancing the numerical stability and accuracy of the results.
2. Handling Integrated Measurements in Industry: The work specifically addresses a difficult class of state-space models common in industrial processes, known as systems with integrated measurements. In these scenarios, quality variables might only be measured periodically via time-consuming laboratory analyses, while other variables are measured instantaneously. The thesis develops computationally efficient sequential and parallel estimation algorithms specifically designed to accurately address these measurement gaps.
3. Optimization-Based Smoothing: The research approaches the smoothing problem (estimating states using all past and future measurements) from a powerful optimization perspective, leading to the derivation of highly efficient recursive Newton solutions. This provides another path to achieve quick, accurate state estimates. 

By addressing both computational efficiency and numerical robustness, this thesis provides practical tools for the next generation of intelligent systems.

Key words: State-space models, Bayesian inference, Robust inference, Parallel computing

Thesis available for public display 7 days prior to the defence at Aaltodoc. 

Contact: fatemeh.yaghoobi@aalto.fi