A Comparison of Wavelet-Based Schemes for Parameter Estimation

We present the numerical performance of orthogonal and biorthogonal wavelet-based parameterization schemes for solving parameter estimation problems for finding a global solution using the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The two schemes are tested on a two-phase flow problem using the Integrated Parallel Accurate Reservoir Simulators (IPARS) simulator in MATLAB. This work is an extension of the research described in (Velazquez et al., 2008) where wavelet parameterization was limited to the orthogonal Haar wavelet. We extend this work by considering the orthogonal Daubechies, Coiflet, and Symlet families of wavelets, and the biorthogonal Spline family of wavelets. In addition to a comparison of the various wavelet families, an analysis of the performance of each at different levels of decomposition will also be discussed.