In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is formulated as the marginalized maximum likelihood (or type-II ML) estimation of the variance hyperparameters of a joint sparsity inducing Gaussian prior on the source signals. We derive conditions under which the resulting nonconvex constrained optimization perfectly recovers the nonzero support of a joint-sparse Gaussian source ensemble with arbitrarily high probability. The support error probability decays exponentially with the number of MMVs at a rate that depends on the smallest restricted singular value and the nonnegative null space property of the self Khatri-Rao product of the sensing matrix. Our analysis confirms that nonzero supports of size as high as$O(m^{2})$are recoverable from$m$measurements per sparse vector. Our derived sufficient conditions for support consistency of the proposed constrained type-II ML solution also guarantee the support consistency of any global solution of the multiple sparse Bayesian learning (M-SBL) optimization whose nonzero coefficients lie inside a bounded interval. For the case of noiseless measurements, we further show that a single MMV is sufficient for perfect recovery of the$k$-sparse support by M-SBL, provided all subsets of$k + 1$columns of the sensing matrix are linearly independent.

In this letter, we address the problem of reconstructing the common nonzero support of multiple joint sparse vectors from their noisy and underdetermined linear measurements. The support recovery problem is formulated as the selection of nonnegative hyperparameters of a correlation-aware, joint sparsity inducing Gaussian prior. The hyperparameters are recovered as a nonnegative sparse solution of covariance-matching constraints formulated in the observation space by solving a sequence of proximal regularized convex optimization problems. For proximal regularization based on Von Neumann Bregman matrix divergence, an exponentiated gradient (EG) update is proposed, which when applied iteratively, converges to hyperparameters with the correct sparse support. Compared to existing multiple measurement vector support recovery algorithms, the proposed multiplicative EG update has a significantly lower computational and storage complexity and takes fewer iterations to converge. We empirically demonstrate that the support-recovery algorithm based on the proposed EG update can solve million variable support recovery problems in tens of seconds. Additionally, by leveraging its correlation-awareness property, the proposed algorithm can recover supports of size as high as O(m2) from only m linear measurements per joint sparse vector.

In this work, we consider the estimation of multiple jointly sparse vectors (or signals) from noisy, undetermined, linear measurements acquired by multiple nodes connected in a network. We propose a decentralized Bayesian algorithm, which is able to exploit the joint sparsity structure across the nodes. In the proposed algorithm, each node seeks the maximum a posterior probability (MAP) estimate of a local sparse signal vector by learning the parameters of a sparsity inducing signal prior, which is assumed to be common to the nodes, in a distributed fashion. Through simulations, we show that our algorithm significantly outperforms DCS-SOMP, an existing algorithm, in terms of number of measurements required per node for exact recovery of the common support. We also propose a tuning procedure to accelerate the convergence of our algorithm.

Enhancing GNSS acquisition and tracking sensitivity is critical to improving the GNSS user experience in indoor situations. This paper describes various techniques to enhance GNSS signal acquisition and tracking sensitivity and increasing the robustness and availability of position fixes. Specifically, a technique called Staggered Coherent Integration is proposed which enables up to 1 dB improvement in sensitivity compared to conventional techniques. Also discussed are challenges in tracking the weak signals seen in indoor conditions and techniques to improve sustained tracking under these conditions. Analysis and simulation results are shown to demonstrate the effectiveness of the techniques described.