Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid. a posteriori (MAP) optimal estimate that coincides with an optimal solution to the 1 optimization [10]. In the MMV case, the joint sparsity among different (uncorrelated) snapshots is utilized by assuming the same sparse prior for the signals at all snapshots [12]. Correlations between snapshots have also been studied in a recent paper [13]. One merit of SBI is its flexibility in modeling sparse signals that can not only promote the sparsity of its solution, e.g., in [11], but also exploit the possible structure of the signal to be recovered, e.g., in [14]. Since the Bayesian inference is a probabilistic method and based on heuristics to some extent, one shortcoming of SBI is that it offers fewer guarantees on the signal recovery accuracy as compared with, for example, 1 optimization.Recent advancements in array signal processing include compressive (CS-) MUSIC [15] and subspace-augmented (SA-) MUSIC [16]. They are combinations of the conventional MUSIC technique and recent CS methods with guaranteed support recovery performance and can outperform MUSIC and standard CS approaches. Though existing CS-based approaches have shown their improvements in DOA estimation, e.g., their success in the case of limited snapshots, there are still difficulties in practical situations where the true DOAs are not on the sampling grid. On one hand, a dense sampling grid is necessary for accurate DOA estimation to reduce the gap between the true DOA and its nearest grid point since the estimated DOAs are constrained on the grid. On the other hand, a dense sampling grid leads to a highly coherent matrix that violates the condition for the sparse signal recovery. We refer to the model adopted in the standard CS methods as an on-grid model hereafter in the sense that the estimated DOAs are constrained on the fixed grid.An off-grid model for DOA estimation is studied in [17] where the estimated DOAs are no longer constrained in the sampling grid set. The model takes into ac...

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We consider distributed optimization problems in which a number of agents are to seek the optimum of a global objective function through merely local information sharing. The problem arises in various application domains, such as resource allocation, sensor fusion and distributed learning. In particular, we are interested in scenarios where agents use uncoordinated (different) constant stepsizes for local optimization. According to most existing works, using this kind of stepsize rule for update, which is necessary in asynchronous scenarios, will lead to some gap (error) between the estimated result and the exact optimum. To deal with this issue, we develop a new augmented distributed gradient method (termed Aug-DGM) based on consensus theory. The proposed algorithm not only allows for using uncoordinated stepsizes but also, most importantly, be able to seek the exact optimum even with constant stepsizes assuming that the global objective function has Lipschitz gradient. A simple numerical example is provided to illustrate the effectiveness of the algorithm.

Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit signal sparsity, work directly on continuous frequencies, and completely resolve the grid mismatch problem of previous compressed sensing methods. In this work we investigate the frequency recovery problem in the presence of multiple measurement vectors (MMVs) which share the same frequency components, termed as joint sparse frequency recovery and arising naturally from array processing applications. To study the advantage of MMVs, we first propose an 2,0 norm like approach by exploiting joint sparsity and show that the number of recoverable frequencies can be increased except in a trivial case. While the resulting optimization problem is shown to be rank minimization that cannot be practically solved, we then propose an MMV atomic norm approach that is a convex relaxation and can be viewed as a continuous counterpart of the 2,1 norm method. We show that this MMV atomic norm approach can be solved by semidefinite programming. We also provide theoretical results showing that the frequencies can be exactly recovered under appropriate conditions. The above results either extend the MMV compressed sensing results from the discrete to the continuous setting or extend the recent super-resolution and continuous compressed sensing framework from the single to the multiple measurement vectors case. Extensive simulation results are provided to validate our theoretical findings and they also imply that the proposed MMV atomic norm approach can improve the performance in terms of reduced number of required measurements and/or relaxed frequency separation condition.Index Terms-Atomic norm, compressed sensing, direction of arrival (DOA) estimation, joint sparse frequency recovery, multiple measurement vectors (MMVs).

The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1-D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2-D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to study the MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic 0 norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on the relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared with the existing atomic norm and subspace methods.

Location-based services (LBS) have attracted a great deal of attention recently. Outdoor localization can be solved by the GPS technique, but how to accurately and efficiently localize pedestrians in indoor environments is still a challenging problem. Recent techniques based on WiFi or pedestrian dead reckoning (PDR) have several limiting problems, such as the variation of WiFi signals and the drift of PDR. An auxiliary tool for indoor localization is landmarks, which can be easily identified based on specific sensor patterns in the environment, and this will be exploited in our proposed approach. In this work, we propose a sensor fusion framework for combining WiFi, PDR and landmarks. Since the whole system is running on a smartphone, which is resource limited, we formulate the sensor fusion problem in a linear perspective, then a Kalman filter is applied instead of a particle filter, which is widely used in the literature. Furthermore, novel techniques to enhance the accuracy of individual approaches are adopted. In the experiments, an Android app is developed for real-time indoor localization and navigation. A comparison has been made between our proposed approach and individual approaches. The results show significant improvement using our proposed framework. Our proposed system can provide an average localization accuracy of 1 m.

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Abstract-This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., 1 optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.