Maximum Likelihood Estimates of Vortex Parameters from Simulated Coherent Doppler Lidar Data

The performance of pulsed coherent Doppler lidar in estimating aircraft trailing wake vortices by scanning across the aircraft flight track is evaluated using Monte Carlo lidar simulations of a simple vortex pair in both a nonturbulent and turbulent environment. The performance estimates are based on maximum likelihood estimates of aircraft wake vortex parameters and provide a measure of the ability of the lidar to detect and track wake vortices under the best possible conditions. Two aircraft types are considered: the Boeing 737 and the Boeing 747. Rigorous error analyses are produced by comparing the estimated parameters from numerical simulations of raw lidar data with the known input parameters of the simulation. It is shown that the probability density functions for the estimates are approximately Gaussian and the bias is very small. The main source of the bias was determined to be the movement of the vortex during the lidar scan. The estimation error is increased by the effects of a background turbulent velocity field. The trade-off between lidar pulse energy and pulse repetition frequency for the standard condition of constant laser power is also presented. It is shown that these maximum likelihood estimates provide accurate detection and tracking of the key vortex parameters for a simple vortex model, with and without background turbulence.