Aims
The overall aim of the group is to design more accurate and more efficient tracking algorithms for practical problems. More specifically, we are planning to explore areas such as:
- Theory and design of efficient algorithms for a set of core nonlinear deterministic signal processing problems, namely, the computation of coordinate independent properties of functions (eg. root-finding and minimisation)
- Towards a theory of ultra-efficient algorithms for a set of core nonlinear stochastic signal processing problems, namely, stochastic filtering on differential manifolds
- Towards a theory of ultra-efficient algorithms design inspired by the brain.
We will approach these aims systematically, endeavouring to develop a fundamental framework for approaching each problem, as well as specialising this framework to certain practical problems of interest. Particular goals for the group include the following:
- The completion of our work on the foundations of optimisation on manifolds, limited to memoryless algorithms and local convergence properties.
- The development of a foundation for optimisation on manifold algorithms with memory.
- The derivation of global convergence results, allowing development of optimisation and tracking algorithms with guaranteed performance.
- The application of our framework, sometimes in non-trivial ways, to practical problems.
With these aims in mind, and the set of practical goals above, the NSP group is poised to make significant contributions to the Australian and international scientific and technological communities.