Maximum likelihood estimates of frequency and other parameters of signals of laser Doppler measuring systems operating in the single-particle scattering mode

摘要

The likelihood equations for combined estimates of the Doppler frequency (velocity) and other unknown parameters of signals of laser Doppler anemometers and lidars operating in the single-particle scattering mode are presented. The problem is solved taking into account the shot noise as the main interfering factor. The correlation error matrix is obtained and the Rao-Kramer bounds are found. The results are confirmed by computer simulations of the Doppler signal and by the numerical solution of the likelihood equation for the Doppler frequency. The obtained estimate is not shifted and its dispersion corresponds to the Rao -Kramer bound.