Gaussian Decomposition of Laser Altimeter Waveforms

We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.