Power ratio estimation in incoherent backscatter lidar: direct detection with Gaussian noise

Properties of small sample estimators for the return signal power ratio or log ratio in direct detection incoherent backscatter lidar systems are analyzed. As for heterodyne receivers it is usually preferable to form an estimator from the logarithmic difference of the sample averages rather than their ratio. Calculated values of bias and noise figures are confirmed using simulated data based on constant signal models and compared with the estimates obtained from nonlinear Kalman filters. The latter generally provide the least bias at high noise levels at the cost of greater computational complexity.