  We address the recovery of sparse vectors in an overcomplete, linear and
noisy multiple measurement framework, where the measurement matrix is known
upto a permutation of its rows. We derive sparse Bayesian learning (SBL) based
updates for joint recovery of the unknown sparse vector and the sensing order,
represented using a permutation matrix. We model the sparse matrix using
multiple uncorrelated and correlated vectors, and in particular, we use the
first order AR model for the correlated sparse vectors. We propose the
Permutation-MSBL and a Kalman filtering based Permutation-KSBL algorithm for
low-complex joint recovery of the uncorrelated and correlated sparse vectors,
jointly with the permutation matrix. The novelty of this work emerges in
providing a simple update step for the permutation matrix using the
rearrangement inequality. We demonstrate the mean square error and the
permutation recovery performance of the proposed algorithms using Monte Carlo
simulations.
