  In this paper, the line spectral estimation (LSE) problem with multiple
measurement vectors (MMVs) is studied utilizing the Bayesian methods. Motivated
by the recently proposed variational line spectral estimation (VALSE) method,
we develop the multisnapshot VALSE (MVALSE) for multi snapshot scenarios, which
is especially important in array signal processing. The MVALSE shares the
advantages of the VALSE method, such as automatically estimating the model
order, noise variance, weight variance, and providing the uncertain degrees of
the frequency estimates. It is shown that the MVALSE can be viewed as applying
the VALSE with single measurement vector (SMV) to each snapshot, and combining
the intermediate data appropriately. Furthermore, the Seq-MVALSE is developed
to perform sequential estimation. Finally, numerical results are conducted to
demonstrate the effectiveness of the MVALSE method, compared to the
state-of-the-art methods in the MMVs setting.
