The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes

The quaternion least mean square (QLMS) algorithm is introduced for adaptive filtering of three- and four-dimensional processes, such as those observed in atmospheric modeling (wind, vector fields). These processes exhibit complex nonlinear dynamics and coupling between the dimensions, which make th...

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Vydané v:	IEEE transactions on signal processing Ročník 57; číslo 4; s. 1316 - 1327
Hlavní autori:	Took, C.C., Mandic, D.P.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.04.2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Adaptive filters Adaptive multistep ahead prediction Adaptive signal processing Algorithms Applied sciences Benchmarking data fusion via vector spaces Detection, estimation, filtering, equalization, prediction Exact sciences and technology Filtering algorithms Information theory Information, signal and communications theory Least mean squares Least squares approximation Mathematical analysis Miscellaneous multidimensional adaptive filters Multidimensional signal processing quaternion signal processing Quaternions Radar signal processing Signal and communications theory Signal processing Signal processing algorithms Signal, noise Sonar Statistics Telecommunications and information theory Vectors (mathematics) wind modeling Quaternion Adaptive filtering Adaptive filter Algorithm Modeling data fusion via vector spaces Three dimensional model wind modeling Covariance Vector space Multistep method Simulation multidimensional adaptive filters quaternion signal processing Information processing Signal processing Data fusion Adaptive multistep ahead prediction Multiple channel Vector field Least mean squares methods
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	The quaternion least mean square (QLMS) algorithm is introduced for adaptive filtering of three- and four-dimensional processes, such as those observed in atmospheric modeling (wind, vector fields). These processes exhibit complex nonlinear dynamics and coupling between the dimensions, which make their component-wise processing by multiple univariate LMS, bivariate complex LMS (CLMS), or multichannel LMS (MLMS) algorithms inadequate. The QLMS accounts for these problems naturally, as it is derived directly in the quaternion domain. The analysis shows that QLMS operates inherently based on the so called ldquoaugmentedrdquo statistics, that is, both the covariance E { xx H } and pseudocovariance E { xx T } of the tap input vector x are taken into account. In addition, the operation in the quaternion domain facilitates fusion of heterogeneous data sources, for instance, the three vector dimensions of the wind field and air temperature. Simulations on both benchmark and real world data support the approach.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2008.2010600