The direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research is recently 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 proposes a novel model which incorporates errors caused by the off-grid DOAs. Using this model, an iterative algorithm is developed to solve the DOA estimation problem from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming the same Laplace prior. Like existing sparsity based methods, the new approach applies to arbitrary sensor array and exhibits increased resolution and robustness to noise and source correlation. It is shown that our proposed off-grid DOA model and estimation algorithm can perform DOA estimation with significantly improved accuracy, in terms of estimation bias and mean squared error, and computational efficiency compared with other algorithms. The algorithm can maintain the high estimation accuracy subject to very coarse sampling grid.
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