Detection of narrow-band sonar signal on a Riemannian manifold

Abstract

We consider the problem of narrow-band signal detection in a passive sonar environment. The classical method employs a fast Fourier Transform (FFT) delay-sum beamformer in which the feature used in detection is the output of the FFT spectrum analyser in each frequency bin. This is compared to a locally estimated mean noise power to establish a likelihood ratio test (LRT). In this paper, we suggest to use the power spectral density (PSD) matrix of the spectrum analyser output as the feature for detection due to the additional cross-correlation information contained in such matrices. However, PSD matrices have structural constraints and describe a manifold in the signal space. Thus, instead of the widely used Euclidean distance (ED), we must use the Riemannian distance (RD) on the manifold for measuring the similarity between such features. Here, we develop methods for measuring the Fréchet mean of noise PSD matrices and optimum weighting matrices for measuring similarity of noise and signal PSD matrices. These are then used to develop a decision rule for the detection of narrow-band sonar signals using PSD matrices. The results yielded by the new detection method are very encouraging.

The Efficacy and Utility of Lower-Dimensional Riemannian Geometry for EEG-Based Emotion Classification

“…On the other hand, tangent space mapping creates a higher dimensional space that allows the acquisition of more spatial information [12]. However, this comes at a high computational cost, limiting the implementation of some algorithms that could lead to bias or overfitting [10,13,14]. Such spatial filtering techniques used on EEG signals rely heavily on sophisticated computations based on covariance matrices estimated from EEG signals, which can be employed directly as the features of interest in the Riemannian framework.…”

Mean and Median of PSD Matrices on a Riemannian Manifold: Application to Detection of Narrow-Band Sonar Signals

“…In this section, we will set up the detection procedure for the narrow-band sonar signals using the PSD matrix as the detection feature [25]. As we mentioned earlier, since PSD matrices possess additional correlation information between different segments of measured signals, we expect more accurate detection results.…”

“…On the other hand, d R 1 and d R 2 are newly developed [8] and have not been widely used yet. However, since it is much easier to manipulate in mathmatics, d R 2 has been employed in robust beamforming and signal detection recently with very encouraging results [23], [24], [25].…”

“…To find the mean of PSD matrices for d R 1 , the algorithm given in [11] may not be able to obtain the optimum weighting matrix, based on which we develop a new algorithm. For finding the mean for d R 2 , the algorithm given in [11] is applied. In many situations, it is desirable to weight the PSD matrices in order to enhance their similarities/dissimilarities.…”