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A novel method is proposed to effectively solve the challenging problem of direction-of-arrival (DOA) estimation for closely spaced correlated signals. A centro-Hermitian extended matrix is exploited to double the number of data samples, and then is transformed into a real-valued data matrix. An improved sparse Bayesian learning scheme is utilised to estimate DOAs by recovering the real-valued jointly row-sparse solution matrix with a reduced computational burden. The proposed method not only provides increased estimation accuracy but also has improved angular separation performance. Simulation results validate the effectiveness of the proposed method.Introduction: Direction-of-arrival (DOA) estimation for highly correlated signals is of great importance in multipath environments such as low-elevation altitude measurement. However, many DOA estimation algorithms suffer significant performance degradation (or fail to work) when the incoming signals are correlated [1]. Moreover, the angular resolution capability decreases when the signals are correlated.It is often desirable to improve angular separation performance while simultaneously enhancing DOA estimation accuracy for closely spaced correlated signals. In [2], an L1-SVD algorithm that exploits the sparse representation of the signal subspace via the singular value decomposition of the received data matrix is developed to obtain a higher resolution and more accurate DOA estimation than the spatial smoothing MUltiple SIgnal Classification (SSMUSIC) algorithm for correlated signals but it is only applicable to well-separated correlated signals with a high signal-to-noise ratio (SNR). When the angular separation of two correlated signals is small, this approach suffers from large biases and may break down. The OGSBI algorithm [3] formulated from a Bayesian perspective improves the DOA estimation accuracy in comparison with L1-SVD. However, there are three disadvantages to this approach. First, if there is no a priori information on the number of signals, OGSBI cannot be used. Secondly, it suffers from a substantial degradation of performance in situations of small angular separation of two correlated signals. Finally, biases do not disappear even when two correlated signals are more than about 10°apart.In this Letter, we develop a new powerful unitary sparse Bayesian learning approach with real-valued processing to DOA estimation for strongly correlated signals, which exhibits the following benefits: (a) it needs less snapshots to achieve a precision better than those of SSMUSIC, L1-SVD and OGSBI; (b) it enjoys the best angle estimation accuracy for closely spaced correlated signals without requiring the decorrelation procedure among the methods tested and (c) it jointly detects the number of signals and estimates their DOAs without additional prior information on the number of signals.

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A sparse noise reduction method applied to Loran-C skywave delay estimation is presented, which is both simple and practicable. Signal sparsity is utilised to reduce the noise inside the Loran frequency band and significant improvement in the performance of estimation is achieved. The proposed method shows increased estimation accuracy with reduced computational complexity owing to no matrix inversion in the computation process.