Subspace-based methods suffer from the rank loss of the noise free data covariance matrix in the context of direction of arrival (DOA) estimation of coherent sources. The well-known spatial smoothing techniques are then widely employed to create a rank restored data covariance matrix. However, conventional spatial smoothing techniques, such as the spatial smoothing pre-processing (SSP), modified spatial smoothing pre-processing (MSSP), and improved spatial smoothing (ISS), do not make full use of the available information in the data covariance matrix. In this paper, an enhanced spatial smoothing (ESS) technique is proposed to exploit both the covariance matrices of individual subarrays and the cross-covariance matrices of different subarrays. Besides, the proposed method can work directly on the signal subspace (ESS-SS), since the signal subspace contains all the information of the DOAs of incoming signals. After de-correlation, the subspace method ESPRIT is adopted to estimate the DOAs. Compared with conventional approaches, the proposed method is more powerful to de-correlate the correlation between signals, and also more robust to the noise impact. The proposed method is tested on numerical data in coherent scenarios, and compared with conventional approaches. Simulation results show that the proposed method has an enhanced resolving capability and a lower signal-to-noise ratio threshold.

For the target tracking problem where the number of targets fluctuates with time and the measurement is a point measurement, the random finite set (RFS) class filtering is an available solution. However, in direction of arrival (DOA) tracking, the array observation is a super-positional value, and the tracking performance can be severely impaired if the RFS-based filter approach is applied. As a result, a novel measurement association mapping (NMAP) approach has been presented to cope with the mapping problem between the array observations and sources. Nevertheless, the tracking performance is poor when the number of particles is small. In this paper, a modified delta-Generalized Labeled Multi-Bernoulli (δ-GLMB) DOA tracking particle filter is proposed in combination with the NMAP strategy, which can achieve the same tracking performance with a smaller number of particles by modifying the particles in the δ-GLMB prediction step. Furthermore, the approach is extended to a coprime array and can achieve better DOA tracking performance than a uniform linear array. Simulation experiments validate the effectiveness of the proposed algorithm.

Direction of arrival (DOA) estimation with co-prime array is a hot issue in array signal processing. By using co-prime array structure, the degrees of freedom has been greatly improved, which can estimate much more sources than that of the conventional array structure. In the scenario of impulsive noise, the high-order (2-order or 4-order) moments of received signal do not exist, fractional low-order moments (FLOM) can be applied. In this paper, the concept of the co-prime array is extended to be applied on FLOM of received signal in presence of impulsive noise. And then MUSIC algorithm is used for DOA estimation. The proposed method is tested on the numerical data. The simulation results prove the effectiveness of the proposed method in impulsive noise scheme.

In coherent direction of arrival (DOA) estimation, subspace-based methods suffer from performance deterioration because of the rank loss of the signal covariance matrix. A variety of spatial smoothing preprocessing techniques have been proposed for decorrelation, among which the enhanced spatial smoothing preprocessing (ESS) technique shows outstanding performance by exploiting the signal subspace. However, ESS is applied by squaring the matrix whose columns span the signal subspace (called signal matrix), which involves unnecessary computational loads. Besides, the smoothed covariance matrix after ESS is a linear combination of the sub-matrices of signal matrix, where the coefficients of the combination may undermine the decorrelation performance. In this context, a simplified spatial smoothing (SSS) technique is proposed for decorrelation by averaging the sub-matrices of the signal matrix directly, and avoids redundant operations in squared signal matrix. The proposed method is tested numerically in terms of the signalto-noise ratio (SNR), the number of snapshots, angle separation, and the execution time. Simulation results show the improvement of the decorrelation performance, efficiency, and robustness with the proposed method in coherent scenarios, compared with the other spatial smoothing preprocessing based methods.

Co-prime array configuration is popular in the recent development of array signal processing by exploiting the sparse arrangement of arrays and the co-prime feature of the number of subarray elements. However, the assumption of Gaussian noise in most co-prime array processing research might lead to model mismatch in practical scenarios of impulsive noise, and therefore have an adverse impact on the estimation of direction of arrival (DOA). Moreover, co-prime array builds an enlarged virtual array by vectorizing the covariance matrix of the received signals, where the equivalent received signals of the virtual array have only a single snapshot. In this paper, we propose an enhanced fractional low-order method (EFLOM) for co-prime array configuration in scenarios of impulsive noise, from the perspective of pseudo snapshot increment. Since impulsive noise does not have finite second-order statistics or high-order cumulant, we construct a series of equivalent covariance matrices by using phased fractional low-order moments with different orders of the received signals. Then, the vectorization of multiple equivalent covariance matrices can be formed as the equivalent received signals of the virtual array with multiple snapshots. Since the reformed observations of the equivalent received signals are from the same sources, additional spatial smoothing preprocessing operations are still needed for decorrelation. While in this paper, we propose an improved spatial smoothing (ISS) technique by applying the information of both autocorrelation and cross subarray correlation of the covariance matrix. Afterwards, the classical multiple signal classification (MUSIC) is applied for the estimation of DOAs. The performance of the proposed method is theoretically verified and simulations are also provided to show its effectiveness in terms of the generalized signal to noise ratio (GSNR), parameter of impulsive noise, and angle separation.

Sparse array is popular in the field of array signal processing. However, in direction of arrival (DOA) estimation, most research on sparse array assumes Gaussian noise, resulting in model mismatch in the practical scenarios of impulsive noise. We investigate the estimation performance of the bounded non-linear covariance (BNC) matrix based methods, which can be used to replace the original data covariance matrix of the received signal and achieve good robustness to the impulsive interference. We propose an enhanced BNC (EBNC) matrix with non-circular signal for nested array in the scenario of impulsive noise. The proposed EBNC matrix can fight against the impulsive noise outliers and its boundedness and convergence are shown. The proposed method's performance is assessed with simulations. Simulation results indicate that the proposed method provides better performance in DOA estimation than the classical BNC, correntropy-based covariance matrix and Gaussian covariance based methods, especially in highly impulsive noise scenario.