Recursive estimation of nonlinear functions of the return power in a lidar system entails use of a nonlinear filter. This also permits processing of returns in the presence of multiplicative noise (speckle). The use of the extended Kalman filter is assessed here for estimation of return power, log power, and speckle noise (which is regarded as a system rather than a measurement component), using coherent lidar returns and tested with simulated data. Reiterative processing of data samples using system models comprising a random walk signal together with an uncorrelated speckle term leads to self-consistent estimation of the parameters.
Barry J. Rye and R. Michael Hardesty, "Nonlinear Kalman filtering techniques for incoherent backscatter lidar: return power and log power estimation," Appl. Opt. 28, 3908-3917 (1989)