PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances

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.