# Robust filtering and estimation

**Project Leader: **Girish Nair**Primary Contact: **Girish Nair (gnair@unimelb.edu.au)**Keywords: **control and signal processing; sensor networks; signal processing; signals and systems; systems theory**Disciplines: **Electrical & Electronic Engineering**Domains: **Networks and data in society, Optimisation of resources and infrastructure

A basic goal in stochastic filtering/estimation problems is to form an estimate Xest of a parameteror state X from noisy past data Y (time indices omitted). A common distortion criterion is the mean-square error (MSE) under a linearity constraint, which is often unsuitable in nonlinear or discrete-valued settings. An alternative approach in the literature is to maximise the Shannon information I[X; Xest ]. However, this can involve an infinite-dimensional optimisation over distributions.

The aim of this project is to explore estimators that maximise instead the *nonstochastic* information between X and Xest [Nair, IEEE Trans, Automatic Control, 2013; Nair, IEEE Conf. Decision and Control, Osaka, 2015]. This has the potential to yield filters with reduced computational cost for situations with bounded disturbances that are nonstochastic or have poorly known distributions.

A complementary approach is to finding an estimator that satisfies a nonstochastic “unrelatedness” principle, whereby the estimation error is “unrelated” to the data Y in the sense of [Nair, IEEE Trans, Automatic Control, 2013; Nair, IEEE Conf. Decision and Control, Osaka, 2015]. Solving these problems is potentially much simpler than the corresponding probabilistic versions.