Constrained approximation in the Hellinger distance

We consider the Georgiou-Lindquist problem of approximating a spectral density function with spectra that are consistent with given state-covariance. Rather than the Kullback-Leibler pseudo-distance, however, we employ the Hellinger distance. We characterize the optimal solution and provide an iterative scheme for the Lagrange multiplier matrix that allows to solve numerically the dual problem.