My research is focused on exploiting Geometric (Clifford) Algebra theory – which generalizes linear algebra and vector calculus for hypercomplex variables – in order to devise new adaptive filtering strategies. I have been advised by Prof. Dr. Cássio Guimarães Lopes at the Signal Processing Laboratory of the University of São Paulo, Brazil.
The collaboration with the Media Technology Chair of the TU München (TUM) started in October 2013. Their research in computer vision (CV) has some interesting problems which can be pursued via an adaptive filtering approach. We have been particularly interested in applying adaptive filtering theory to devise new algorithms for 3D registration of point clouds (PCDs). During my year-long research stay at TUM (May 2014 - May 2015) under the supervision of Prof. Dr.-Ing. Eckehard Steinbach, several results showing the benefits of using AFs in PCD registration were obtained. The collaboration remained active in 2015 and two papers, containing theoretical and practical results, have been submitted and are currently under review.
In this work a new strategy for combination of adaptive filters is introduced and studied. Inspired by incremental schemes and cooperative adaptive filtering, the standard convex combination of parallel-independent filters is rearranged into a series-cooperative configuration, while preserving computational complexity. Two new algorithms are derived employing recursive least-squares (RLS) and least-mean-squares (LMS) algorithms as the component filters. In order to assess the performance of the incremental structure, tracking and steady-state mean-square analysis is derived. The analysis is carried out assuming the combiners are fixed, so that the universality of the new structure may be studied decoupled from the supervisor’s dynamics. The resulting analytical model shows good agreement with simulation results.
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