Two-stage Approaches for Decomposition of Icesat Waveforms

The Ice, Cloud and Land Elevation Satellite (ICESat) was launched January 13, 2003. The primary purpose of this mission is the determination of inter-annual and long-term changes in polar ice-sheet mass, the causes of changes in mass balance, and the impact of these changes on global sea level. In addition to these objectives, ICESat mission also enables precise measurement of land topography and vegetation structure information [1]. The Geoscience Laser Altimeter System (GLAS) instrument on ICESat provides various data products, of which GLA01 and GLA14 are of interest in this study. The GLA01 Level 1 product provides the transmitted and received waveform from the instrument, while the GLA14 Level 2 product is intended to represent the potential complexities of returns from land. As such, the GLA14 product provides information on the waveform in a way that local relief and land cover interpretations relative to elevation, slope, roughness, and vegetation and/or height of cultural features can be made. GLA14 fits a mixture of a maximum of 6 Gaussian distributions and provides the associated estimated parameters (e.g. centroid, one sigma width, amplitude, and area of each of the Gaussian fits). From these estimated parameters, the Gaussian fit approximation of the waveform can reconstructed in the direction of the laser pointing vector [2]. Decomposing a waveform into distinct components by fitting a mixture of Gaussian distributions is an unsupervised machine learning problem. It impacts the ultimate interpretation of the return waveform, because the resulting parameter estimates of the Gaussian mixture directly affect the understanding of vertical structure within laser footprints. Decomposing the waveform into a mixture of Gaussians involves two separate, but related problems; i) determining the number of mixtures in the waveform, and ii) estimating the parameters of each Gaussian mixture. Estimating parameters of Gaussian mixtures depends heavily on the estimated number and location of Gaussian mixtures. Further, the parameter estimation problem does not have a closed form solution and must be solved iteratively. Therefore, it is critical to obtain a good estimate of number of mixtures and good initial estimates of the parameters of the components of the Gaussian mixture in order to achieve rapid convergence. Even with the limited operation ICESat, the overall computational burden is significant because of the huge number of waveforms being generated by the mission. Presumably, future missions will collect and process waveform data continuously, resulting in dramatically increased computational demands. Additionally, currently operational airborne systems …