Time-of-arrival estimation for saturated optical transients using censored probabilistic models

Abstract

The objective of the proposed research is to estimate the time-of-arrival of a transient optical signal subjected to a particular type of nonlinear distortion. The limited dynamic range of optical sensors can result in nonlinear distortion when measuring extreme transient events, such as lightning. To deal with saturated signals, we employ censored probabilistic models to develop maximum-likelihood procedures for estimating the time-of-arrival of lightning strikes, along with associated nuisance parameters. The received signal is modeled as a realization of a Poisson point process characterized by parametric models of a lightning strike's time-varying intensity. The models are extracted from the FORTÉ lighting database via machine learning techniques. Using Monte Carlo simulations, we compare the variances of different algorithms as a function of signal magnitude and saturation threshold. We also compare these variances to analytical performance bounds such as the Cramér-Rao lower bound.