  In applications such as free-space optical communication, a signal is often
recovered after propagation through a turbulent medium. In this setting, it is
common to assume that limited information is known about the turbulent medium,
such as a space- and time-averaged statistic (e.g., root-mean-square), but
without information about the state of the spatial variations. It could be
helpful to gain more information if the state of the turbulent medium can be
characterized with the spatial variations and evolution in time described.
Here, we propose to investigate the use of data assimilation techniques for
this purpose. A computational setting is used with the paraxial wave equation,
and the extended Kalman filter is used to conduct data assimilation using
intensity measurements. To reduce computational cost, the evolution of the
turbulent medium is modeled as a stochastic process. Following some past
studies, the process has only a small number of Fourier wavelengths for spatial
variations. The results show that the spatial and temporal variations of the
medium are recovered accurately in many cases. In some time windows in some
cases, the error is larger for the recovery. Finally we discuss the potential
use of the spatial variation information for aiding the recovery of the
transmitted signal or beam source.
