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Lopes, Wilder B.; Al-Nuaimi, Anas; Lopes, Cassio G.
IEEE signal processing letters, 2016-June, 2016-6-00, 20160601, Volume: 23, Issue: 6Journal Article
This letter exploits geometric (Clifford) algebra (GA) theory 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 3-D 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 3-D 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.
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