  This paper concerns a spectral estimation problem in which we want to find a
spectral density function that is consistent with estimated second-order
statistics. It is an inverse problem admitting multiple solutions, and
selection of a solution can be based on prior functions. We show that the
problem is well-posed when formulated in a parametric fashion, and that the
solution parameter depends continuously on the prior function. In this way, we
are able to obtain a smooth parametrization of admissible spectral densities.
Based on this result, the problem is reparametrized via a bijective change of
variables out of a numerical consideration, and then a continuation method is
used to compute the unique solution parameter. Numerical aspects such as
convergence of the proposed algorithm and certain computational procedures are
addressed. A simple example is provided to show the effectiveness of the
algorithm.
