Separation of deterministic signals using independent component analysis (ICA)
- 531 Downloads
Independent Component Analysis (ICA) represents a higher-order statistical technique that is often used to separate mixtures of stochastic random signals into statistically independent sources. Its benefit is that it only relies on the information contained in the observations, i.e. no parametric a-priori models are prescribed to extract the source signals. The mathematical foundation of ICA, however, is rooted in the theory of random signals. This has led to questions whether the application of ICA to deterministic signals can be justified at all? In this context, the possibility of using ICA to separate deterministic signals such as complex sinusoidal cycles has been subjected to previous studies. In many geophysical and geodetic applications, however, understanding long-term trend in the presence of periodical components of an observed phenomenon is desirable. In this study, therefore, we extend the previous studies with mathematically proving that the ICA algorithm with diagonalizing the 4th order cumulant tensor, through the rotation of experimental orthogonal functions, will indeed perfectly separate an unknown mixture of trend and sinusoidal signals in the data, provided that the length of the data set is infinite. In other words, we justify the application of ICA to those deterministic signals that are most relevant in geodetic and geophysical applications.
KeywordsICA separation of deterministic signals 4th order cumulant
Unable to display preview. Download preview PDF.
- Botai O.J., 2011. Analysis of Geodetic Data and Model Simulated Data to Describe Nonstationary Moisture Fluctuations over Southern Africa. Ph.D. Thesis, Faculty of Natural and Agricultural Sciences, University of Pretoria, South Africa (http://upetd.up.ac.za/thesis/available/etd-10212011-153344/unrestricted/00front.pdf).Google Scholar
- Botai O.J., Combrinck L., Sivankumar V., Schuh H. and Böhm J., 2010. Extracting independent local oscillatory geophysical signals by geodetic tropospheric delay. In: D. Behrend and K.D. Baver (Eds.), International VLBI Service for Geodesy and Astrometry 2010 General Meeting Proceedings. NASA/CP-2010-215864, Greenbelt, MD, 345–354 (http://ivscc.gsfc.nasa.gov/publications/gm2010/botai).
- Cardoso J.F. and Souloumiac A., 1993. Blind beamforming for non-Gaussian signals. IEEE Proc. F, 140, 362–370, DOI: 10.1.1.8.5684.Google Scholar
- Chatfield C., 1989. The Analysis of Time Series: An Introduction. Chapman and Hall, Boca Raton, 352 pp. ISBN-10: 1584883170.Google Scholar
- Hyvärinen A., 1999. On independent component analysis. Neural Comput. Surv., 2, 94–128.Google Scholar
- Koch K.R., 1988. Parameter Estimation and Hypothesis Testing in Linear Models. Springer, New York.Google Scholar
- Kusche J., Rietbroek R. and Forootan E., 2010. Signal separation: the quest for independent mass flux patterns in geodetic observations. AGU Fall Meeting, 17 December 2010, San Francisco, USA (http://adsabs.harvard.edu/abs/2010AGUFM.G51C0683K).
- Nikias C. and Petropulu AP., 1993. Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework. Prentice Hall, 528 pp., ISBN:9780136782100.Google Scholar
- Swami A., Mendel J.M. and Nikias C.L., 1995. Higher-Order Spectral Analysis Toolbox. The MathWorks Inc., Natick, MA (http://www.uic.edu/classes/idsc/ids594/research/BBC/hosa.pdf).Google Scholar