Off-grid Sparse Bayesian Learning Research Articles

Off-Grid Underwater Acoustic Source Direction-of-Arrival Estimation Method Based on Iterative Empirical Mode Decomposition Interval Threshold.

To solve the problem that the hydrophone arrays are disturbed by ocean noise when collecting signals in shallow seas, resulting in reduced accuracy and resolution of target orientation estimation, a direction-of-arrival (DOA) estimation algorithm based on iterative EMD interval thresholding (EMD-IIT) and off-grid sparse Bayesian learning is proposed. Firstly, the noisy signal acquired by the hydrophone array is denoised by the EMD-IIT algorithm. Secondly, the singular value decomposition is performed on the denoised signal, and then an off-grid sparse reconstruction model is established. Finally, the maximum a posteriori probability of the target signal is obtained by the Bayesian learning algorithm, and the DOA estimate of the target is derived to achieve the orientation estimation of the target. Simulation analysis and sea trial data results show that the algorithm achieves a resolution probability of 100% at an azimuthal separation of 8° between adjacent signal sources. At a low signal-to-noise ratio of -9 dB, the resolution probability reaches 100%. Compared with the conventional MUSIC-like and OGSBI-SVD algorithms, this algorithm can effectively eliminate noise interference and provides better performance in terms of localization accuracy, algorithm runtime, and algorithm robustness.

Co-Prime Sampling-Based Time-Delay Estimation for Roadway Survey by Ground Penetrating Radar via Off-Grid Sparse Bayesian Learning

Co-Prime Sampling-Based Time-Delay Estimation for Roadway Survey by Ground Penetrating Radar via Off-Grid Sparse Bayesian Learning

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

Passive localization of wideband near-field sources using Sparse Bayesian learning and envelope alignment

Most studies about passive localization of near-field signals are limited to narrowband sources. In this paper, a novel efficient algorithm is developed for direction of arrival (DOA) and range estimation of wideband near-field sources. Using the specific structure of symmetric linear array, the direction information is extracted and the off-grid Sparse Bayesian learning (SBL) framework is established for DOA estimation. The generalized approximate message passing (GAMP) strategy is applied for fast implementation. Then the envelope aligned approach is proposed for the range estimation in time domain and the linear searching concept is applied to accelerate the computation. Compared with the existing wideband near-field localization methods, the proposed algorithm has better performance of accuracy and resolution probability. Simulation results validate the feasibility and effectiveness of the proposed algorithm.

Off-Grid DOA Estimation Using Sparse Bayesian Learning for MIMO Radar under Impulsive Noise.

Direction of arrival (DOA) estimation is an essential and fundamental part of array signal processing, which has been widely used in radio monitoring, autonomous driving of vehicles, intelligent navigation, etc. However, it remains a challenge to accurately estimate DOA for multiple-input multiple-output (MIMO) radar in impulsive noise environments. To address this problem, an off-grid DOA estimation method for monostatic MIMO radar is proposed to deal with non-circular signals under impulsive noise. In the proposed method, firstly, based on the property of non-circular signal and array structure, a virtual array output was built and a real-valued sparse representation for the signal model was constructed. Then, an off-grid sparse Bayesian learning (SBL) framework is proposed and further applied to the virtual array to construct novel off-grid sparse model. Finally, off-grid DOA estimation was realized through the solution of the sparse reconstruction with high accuracy even in impulsive noise. Numerous simulations were performed to compare the algorithm with existing methods. Simulation results verify that the proposed off-grid DOA method enables evident performance improvement in terms of accuracy and robustness compared with other works on impulsive noise.

Airborne Passive Bistatic Radar Clutter Suppression Algorithm Based on Root Off-Grid Sparse Bayesian Learning

When the transmitter is in motion, the airborne passive bistatic radar (PBR) has a complex clutter geometry and lacks independent and identically distributed training samples in clutter estimation and suppression. In order to solve these problems, this paper proposes a space–time adaptive processing (STAP) algorithm based on root off-grid sparse Bayesian learning. The proposed algorithm first models the space–time base of the dictionary as an adjustable state. Then, the positions of those dynamic bases are optimized by iterating a maximum expectation algorithm. In this way, the off-grid error in clutter estimation can be eliminated even when the modeling grid is wide. To further improve the accuracy of clutter estimation, the proposed algorithm eliminates the error caused by samples with singular values in the root off-grid sparse Bayes learning by artificially adding pseudorandom noise and using hypothesis testing. The simulation results show that the proposed algorithm achieves better performance than the existing algorithms.

DOA and Range Estimation for FDA-MIMO Radar with Sparse Bayesian Learning

Due to grid division, the existing target localization algorithms based on sparse signal recovery for the frequency diverse array multiple-input multiple-output (FDA-MIMO) radar not only suffer from high computational complexity but also encounter significant estimation performance degradation caused by off-grid gaps. To tackle the aforementioned problems, an effective off-grid Sparse Bayesian Learning (SBL) method is proposed in this paper, which enables the calculation the direction of arrival (DOA) and range estimates. First of all, the angle-dependent component is split by reconstructing the received data and contributes to immediately extract rough DOA estimates with the root SBL algorithm, which, subsequently, are utilized to obtain the paired rough range estimates. Furthermore, a discrete grid is constructed by the rough DOA and range estimates, and the 2D-SBL model is proposed to optimize the rough DOA and range estimates. Moreover, the expectation-maximization (EM) algorithm is utilized to update the grid points iteratively to further eliminate the errors caused by the off-grid model. Finally, theoretical analyses and numerical simulations illustrate the effectiveness and superiority of the proposed method.

Phase Difference Compensation Method for Range Estimation in an MFCW–CW Radar

Multifrequency continuous-wave-continuous-wave (MFCW-CW) radars simultaneously transmit multifrequency continuous-wave (MFCW) signals sequentially at a constant time step and a continuous-wave (CW) signal constantly. As MFCW signals are transmitted sequentially, only one phase difference exists at each time. All phase differences between the MFCW and CW signals should be exploited to resolve ambiguous ranges. In this article, we propose a method to compensate the phase difference between the sequential MFCW signals and CW signal using the Doppler frequency of the CW signal. To verify the phase difference compensation result, we estimated the range of multiple targets. The simulation results showed that the proposed phase difference compensation method performed well regardless of compensation direction and target motion. Moreover, we proposed applying the maximum likelihood estimation (MLE) and reduced-complexity off-grid sparse Bayesian learning (RC-OGSBL) to estimate ranges and analyzed their performance. The range accuracy of the MLE using a 0.1- m grid search showed superior performance and the running time of the MLE using the simple method is the fastest among the simulated methods. The RC-OGSBL using a 5- m grid showed good results in terms of range accuracy and running time.

Angle-Domain Aided UL/DL Channel Estimation for Wideband mmWave Massive MIMO Systems With Beam Squint

In this paper, we design an uplink/downlink channel estimation method for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems and investigate the impact of beam squint effect that accompanies large array configuration. Specifically, we adopt the off-grid sparse Bayesian learning (SBL) that directly works on the continuous angle-delay parameter domain and avoids the grid mismatch problem. Hence, the proposed method achieves good channel estimation accuracy and handles the wideband direction of arrival (DOA) estimation problem for mmWave massive MIMO communications, where beam squint effect was previously ignored by many existing literatures. The Cramér-Rao bound for unknown parameters is derived to make the proposed study complete. More importantly, a much simplified downlink channel estimation scheme is designed with the aid of angle-delay reciprocity, which significantly reduces training and feedback overhead. The simulation results are provided to demonstrate the superior performance of the proposed method over existing ones.

Off-Grid DOA Estimation for Colocated MIMO Radar via Reduced-Complexity Sparse Bayesian Learning

Recent advance on signal processing has witnessed increasing interest in machine learning. In this paper, we revisit the problem of direction-of-arrival (DOA) estimation for colocated multiple-input multiple-output (MIMO) radar from the perspective of machine learning. The reduced-complexity transformation is first applied on the array data from matched filters, thus eliminating the redundancy of the array data for the relief of calculational burden. Furthermore, the pre-whitening is followed to obtain a simplified noise model. Finally, the DOA estimation is linked to off-grid sparse Bayesian learning (OGSBL), which does not require to update the noise hyper-parameter, and a block hyper-parameter is utilized to accelerate the convergence of the OGSBL algorithm. The proposed estimator provides better DOA estimation accuracy than the existing peak searching algorithm. The effectiveness of the proposed algorithm is verified via numerical simulation.

Sparse Bayesian learning for off-grid DOA estimation with nested arrays

The existing off-grid sparse Bayesian learning (SBL) DOA estimation method for nested arrays suffers from two major drawbacks: reduced array aperture and high modeling error. To solve these issues, a new data model formulation is first presented in this paper, in which we take the noise variance as a part of the unknown signal of interest, so as to learn its value by the Bayesian inference inherently. Then, we provide a novel grid refining procedure to eliminate the modeling error caused by off-grid gap, where we consider the locations of grid points as adjustable parameters and proceed to refine the grid point iteratively. Simulation results demonstrate that our method significantly improves the DOA estimation performance especially using a coarse grid.

Theoretical and Experimental Comparison of Off-Grid Sparse Bayesian Direction-of-Arrival Estimation Algorithms

Off-grid sparse Bayesian learning algorithms for estimating the directions-of-arrival (DOAs) of multiple signals using an array of sensors are attractive in practice due to three primary reasons. First, these algorithms are fully automatic Bayesian algorithms and hence tuning of regularization parameters (hyperparameters) is not necessary. Second, since these algorithms are based on sparsity, they can produce high accuracy DOA estimates by exploiting the spatial sparsity of acoustic signals even when the signals are coherent. Third, they can also estimate the offset in the DOAs for signals, whose DOAs are not exactly aligned with the steering vectors. Two previously proposed off-grid sparse Bayesian DOA estimation algorithms are considered. The first off-grid model is based on the Taylor series expansion method (OGSBL-T algorithm) and the second is based on the linear interpolation method (OGSBL-I algorithm). The Cramer–Rao lower bound (CRLB) of the off-grid bias parameters for both the algorithms is derived for multiple snapshots. It is shown that the CRLB of the off-grid bias parameters for the OGSBL-T algorithm is significantly less than that for the OGSBL-I algorithm. It is also shown that the CRLBs of the off-grid bias parameters for both the algorithms get worse when we move from the broadside to the endfire directions. A simulation study is also carried out to characterize the performances of both the algorithms in terms of the root-mean-squared error in the DOA estimates. It is shown that the OGSBL-T algorithm performs comparably to the OGSBL-I algorithm when the signals are relatively broadside and better than the OGSBL-I algorithm when the signals are relatively endfire. Finally, the application of the OGSBL-T algorithm for high resolution DOA estimation in an underwater communication system is demonstrated by analyzing passive sonar data from the SWellEx-96 ocean acoustic experiment.