We derive a maximum a posteriori estimator for the linear observation model,
where the signal and noise covariance matrices are both uncertain. The
uncertainties are treated probabilistically by modeling the covariance matrices
with prior inverse-Wishart distributions. The nonconvex problem of jointly
estimating the signal of interest and the covariance matrices is tackled by a
computationally efficient fixed-point iteration as well as an approximate
variational Bayes solution. The statistical performance of estimators is
compared numerically to state-of-the-art estimators from the literature and
shown to perform favorably
