Auto-Regressive Moving Average Models on Complex-Valued Matrix Lie Groups

The present contribution aims at extending the classical scalar autoregressive moving average (ARMA) model to generate random (as well as deterministic) paths on complex-valued matrix Lie groups. The numerical properties of the developed ARMA model are studied by recurring to a tailored version of t...

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Bibliographic Details
Published inCircuits, systems, and signal processing Vol. 33; no. 8; pp. 2449 - 2473
Main Author Fiori, Simone
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2014
Springer Nature B.V
Subjects
Bundles
Circuits
Circuits and Systems
Computer simulation
Data processing
Electrical Engineering
Electronics and Microelectronics
Engineering
Instrumentation
Lie groups
Mathematical analysis
Mathematical models
Random variables
Scalars
Signal,Image and Speech Processing
Tangents
Lie-group theory
Processing of data taking values on Lie groups
Random matrix generation and random path generation on Lie groups
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ISSN0278-081X
1531-5878
DOI10.1007/s00034-014-9745-1

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Summary:The present contribution aims at extending the classical scalar autoregressive moving average (ARMA) model to generate random (as well as deterministic) paths on complex-valued matrix Lie groups. The numerical properties of the developed ARMA model are studied by recurring to a tailored version of the Z-transform on Lie groups and to statistical indicators tailored to Lie groups, such as correlation functions on tangent bundles. The numerical behavior of the devised ARMA model is also illustrated by numerical simulations.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-014-9745-1