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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Veröffentlicht in:IEEE transactions on signal processing Jg. 57; H. 4; S. 1316 - 1327
Hauptverfasser: Took, C.C., Mandic, D.P.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.04.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.2010600