Decomposition of laser altimeter waveforms

We develop a method to decompose a laser altimeter return waveform into a s eries of components assuming that the position of each component within the waveform can be used to calculate the mean elevation of a specific reflect ing surface within the laser footprint. For simplicity, we assume each comp onent is Gaussian in nature. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser wavefo rm and obtain initial estimates of the Gaussian half-widths and positions f rom the positions of its consecutive inflection points, Initial amplitude e stimates are obtained using a nonnegative least-squares method (LSM), To re duce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank t he "importance" of each Gaussian in the decomposition using its initial hal f-width and amplitude estimates. The initial parameter estimates of all Gau ssians ranked "important" are optimized using the Levenburg-Marquardt metho d, If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians can be included in the opt imization procedure or initial parameters can be recalculated. The Gaussian decomposition method is demonstrated on data collected by the airborne las er vegetation imaging sensor (LVIS) in October 1997 over the Sequoia Nation al Forest, California.