Abstract
Fractional Brownian motion (fBm) provides a useful fractal model to represent natural landscapes. The fractal dimension of an fBm is closely related to its spectral exponent, which is the essential parameter of the power spectral density (PSD) of fBm. In this paper, a maximum likelihood (ML) spectral estimation procedure for an fBm defined on a multi-dimensional space is derived. The likelihood function is shown to be represented in terms of a periodogram and the PSD model, instead of a covariance matrix. This representation facilitates the ML estimation in the multi-dimensional case. In an application of this, we estimated the spectral exponent of the moon surface and constructed a detailed simulated moon surface.
