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

Maximum-likelihood equations are presented for estimates of the Doppler frequency (speed) and other unknown parameters of signals of laser Doppler anemometers and lidars operating in the one-particle-scattering mode. Shot noise was assumed to be the main interfering factor of the problem. The error correlation matrix was calculated and the Rao — Cramer bounds were determined. The results are confirmed by the computer simulation of the Doppler signal and the numerical solution of the maximum-likelihood equations for the Doppler frequency. The obtained estimate is unbiased, and its dispersion coincides with the Rao — Cramer bound.