Invariances, Laplacian-like wavelet bases, and the whitening of fractal processes
IEEE Transactions on Image Processing
Parameter estimation and elimination for stochastic noise from fiber optical Gyro in wavelet domain
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Wavelet packets of fractional Brownian motion: asymptotic analysis and spectrum estimation
IEEE Transactions on Information Theory
A regularised estimator for long-range dependent processes
Automatica (Journal of IFAC)
Identification of Hammerstein-Wiener models
Automatica (Journal of IFAC)
| Hi-index | 754.90 |
Several models have emerged for describing 1/fγ noise processes. Based on these, various techniques for estimating the properties of such processes have been developed. This paper provides theoretical analysis of a new wavelet-based approach which has the advantages of having low computational complexity and being able to handle the case where the 1/fγ noise might be embedded in a further white-noise process. However, the analysis conducted here shows that these advantages are balanced by the fact that the wavelet-based scheme is only consistent for spectral exponents γ in the range γ∈(0, 1). This is in contradiction to the results suggested in previous empirical studies. When γ∈(0, 1) this paper also establishes that wavelet-based maximum-likelihood methods are asymptotically Gaussian and efficient. Finally, the asymptotic rate of mean-square convergence of the parameter estimates is established and is shown to slow as γ approaches one. Combined with a survey of non-wavelet-based methods, these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1/fγ noise processes