Nonlinear Signal Processing: Optimisation and Tracking on Manifolds

Signal processing is based primarily on linear algebra. Recently though, there has been a push to introduce systematic approaches to signal processing problems based on non-linear mathematics, especially algebraic and differential geometry. Such approaches can result in more accurate and more efficient solutions than traditional approaches. As part of this vision, this project studies optimisation and tracking on curved surfaces. A major application, among many, is to subspace tracking; subspace tracking is a fundamental problem in signal processing, but it has yet to be treated thoroughly in its natural setting, namely, as a filtering problem on the Grassmann manifold.