Robust non-linear state-space modeling: From filtering to deep learning approaches


The objective is to mix filtering methods with optimisation and deep learning to design advanced efficient tracking methodologies, with strong theoretical guarantees.


  1. Design hybrid filtering approaches relying on optimisation theory (with theoretical guarantees)
  2. Design hybrid filtering approaches relying on deep learning (e.g., unrolled filtering networks)
  3. Validate the proposed approaches on tracking problems
  4. Investigate application of the methods to computational imaging


Most signal processing applications aim to transform data into interpretable information and enable accurate decision-making processes. In this context, it is necessary to rely on robust, fast, and scalable mathematical tools to design such methods. Optimisation is a family of these tools which has shown to be successful to design scalable algorithms with proved theoretical guarantees. Recently, interesting connections have been unveiled between optimisation and Bayesian filtering methods, sometimes also involving deep learning. In this way, inference in statistical models (that describe probabilistic relations among latent variables and observations) can be sometimes re-interpreted as iterative optimisation techniques. One relevant example of statistical modeling is the state-space models (SSM), that allow to describe temporal stochastic processes that evolve over time.

In this project, the student will aim to develop new tools at the interface of optimisation, deep learning and statistical approaches, in particular focusing on SSMs with nonlinear interactions between variables, with strong theoretical guarantees.

Research theme: 

Principal supervisor: 

Dr Audrey Repetti
Heriot-Watt University, School of Mathematical and Computer Sciences, School of Engineering and Physical Sciences

Assistant supervisor: 

Professor Mike Davies
University of Edinburgh, School of Engineering

Victor Elvira
University of Edinburgh School of Mathematics