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

Wong, Kon Max ; Jian-Kang Zhang ; Jiaping Liang ; Huiying Jiang

IEEE Transactions on Signal Processing, 15 December 2017, Vol.65(24), pp.6536-6550 [Periódico revisado por pares]

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  • Título:
    Mean and Median of PSD Matrices on a Riemannian Manifold: Application to Detection of Narrow-Band Sonar Signals
  • Autor: Wong, Kon Max ; Jian-Kang Zhang ; Jiaping Liang ; Huiying Jiang
  • Assuntos: Manifolds ; Covariance Matrices ; Signal Processing ; Symmetric Matrices ; Frequency Measurement ; Sonar ; Covariance and Psd Matrices ; Matrix Processing on a Riemannian Manifold ; Sonar Signal Detection ; Engineering
  • É parte de: IEEE Transactions on Signal Processing, 15 December 2017, Vol.65(24), pp.6536-6550
  • Descrição: The rich information in the power spectral density (PSD) matrix of a received signal can be extracted in different ways for various purposes in signal processing. Care, however, must be taken when distances between PSD matrices are considered because these matrices form a Riemannian manifold in the signal space. In this paper, two Riemannian distances (RD) are introduced for the measurement of distances between PSD matrices on the manifold. The principle by which the geodesics on the manifold can be lifted to a Euclidean subspace isometric with the tangent space of the manifold is also explained and emphasized. This leads to the concept that any optimization involving the RD on the manifold can be equivalently performed in this Euclidean subspace. The application of this principle is illustrated by the development of iterative algorithms to find the Riemannian means and Riemannian medians according to the two RD. These distance measures are then applied to the detection of narrow-band sonar signals. Exploration of the translation of measure reference as well as the application of optimum weighting show substantial improvement in detection performance over classical detection method.
  • Idioma: Inglês

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