Geometric-Algebra LMS Adaptive Filter and its Application to Rotation Estimation
| Autor: | Lopes, Wilder B., Al-Nuaimi, Anas, Lopes, Cassio G. |
|---|---|
| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/LSP.2016.2558461 |
| Popis: | This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3D point-clouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions. Comment: 4 pages of content plus 1 of references; 4 figures. Supplementary material (codes and datasets) available at www.lps.usp.br/wilder |
| Databáze: | arXiv |
| Externí odkaz: |
|