Comparison of sparse Bayesian learning and atomic norm minimization in detecting passive tonal signals

The frequency estimation of tonal signals in passive sonar systems is crucial to the identification of the marine object. In this study, we introduce the frequency estimation of tonal signals using the multiple measurement vector atomic norm minimization(MMV-ANM) technique based on compressive sensing (CS) and sparse Bayesian learning (SBL) technique based on Bayesian Inference. CS techniques have been employed in identifying the tonal frequency components. It is now well-known from the theory of CS that a high-dimensional signal can be recovered from a relatively small number of measurements as long as the desired signal is sparsely represented. MMV-ANM, an extended version of CS technique for solving the basis mismatch problem, has been proposed and shown better performance in terms of resolution and stability. On the other hand, tonal signals at passive sonar systems are also estimated with sparse Bayesian learning (SBL) using MMV. The prior source amplitudes are assumed independent zero-mean complex Gaussian distribution with the unknown variances (hyperparameters). The hyperparameters are derived by maximizing the probability of given passive data, which leads to sparse tonal signal frequencies. We compare performance of SBL and MMV-ANM in estimation of passive tonal signals with synthetic and in situ data. [*corresponding author Youngmin Choo]The frequency estimation of tonal signals in passive sonar systems is crucial to the identification of the marine object. In this study, we introduce the frequency estimation of tonal signals using the multiple measurement vector atomic norm minimization(MMV-ANM) technique based on compressive sensing (CS) and sparse Bayesian learning (SBL) technique based on Bayesian Inference. CS techniques have been employed in identifying the tonal frequency components. It is now well-known from the theory of CS that a high-dimensional signal can be recovered from a relatively small number of measurements as long as the desired signal is sparsely represented. MMV-ANM, an extended version of CS technique for solving the basis mismatch problem, has been proposed and shown better performance in terms of resolution and stability. On the other hand, tonal signals at passive sonar systems are also estimated with sparse Bayesian learning (SBL) using MMV. The prior source amplitudes are assumed independent zero-mean complex G...