Title :
PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances
Author :
Li, Li ; Hu, Jianming ; Chen, Yudong ; Zhang, Yi
Author_Institution :
Dept. of Autom., Tsinghua Univ., Beijing
fDate :
7/1/2009 12:00:00 AM
Abstract :
In this paper, the validity of PCA eigenspectrum based Hurst exponent estimator proposed in[J. B. Gao, Y. Cao, and J.-M. Lee, ldquoPrincipal Component Analysis of 1/f alpha noise,rdquo Phys. Lett. A, vol. 314, no. 5-6, pp. 392-400, 2003] for single fBm signal is proved. Moreover, how to apply this estimator for fBm signals corrupted with some other signals are discussed. Theoretical analysis and experiments show that it can also be used for 1) mixed fBm signals with different Hurst exponents, 2) fBm signals corrupted with additive Gaussian white noise when the signal-to-noise ratio (SNR) is not too small, and 3) fBm signals corrupted with additive deterministic sine/cosine signals. However, the estimation accuracy depends on the SNR value for the first two situations.
Keywords :
1/f noise; AWGN; Brownian motion; eigenvalues and eigenfunctions; principal component analysis; spectral analysis; 1/falpha noise; Hurst exponent estimator; PCA eigenspectrum; SNR; additive Gaussian white noise; additive deterministic cosine signal; additive deterministic sine signal; fractional Brownian motion signal; signal-to-noise ratio; Fractal Brownian motion (fBm); Hurst exponent; principal component analysis (PCA);
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2009.2016877