Off-grid DOA estimation through variational Bayesian inference in colored noise environment

This paper provides a direction-of-arrival (DOA) estimation method based on sparse Bayesian learning for a colored noise environment. In this method, the harmonic noise model is absorbed into the covariance matrix model to express the noise objectively. As such, the covariance matrix is parameterized with the signal powers and noise parameters. Given that the existing Bayesian models cannot be directly used for this covariance matrix model, this paper establishes a new probabilistic model. Different priors are assigned for signal power vector and noise parameter vector since signal power vector is sparse but noise parameter vector is not. Based on this probabilistic model, the variational Bayesian inference is applied to estimate signal powers and noise parameters. Moreover, first-order Taylor series expansion is applied to approximate the virtual steering vector as a function of the grid error between the true DOA and the closest grid point. Grid error is estimated in the Bayesian framework and applied to modify the grid, thus alleviating basis mismatch. Simulation results prove that the proposed method achieves high estimation accuracy with a mild computational complexity in a colored noise environment.