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Subspace tracking with adaptive threshold rank estimation

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Abstract

In frequency and direction of arrival (DOA) tracking problems, singular value decomposition (SVD) can be used to track the signal subspace. Typically, for a problem sizen, only a few, sayr dominant eigencomponents need to be tracked, wherer⋘n. In this paper we show how to modify the Jacobi-type SVD to track only ther-dimensional signal subspace by forcing the (n-r)-dimensional noise subspace to be spherical. Therby, the computational complexity is brought down fromO(n2) toO(nr) per update. In addition to tracking the subspace itself, we demonstrate how to exploit the structure of the Jacobi-type SVD to estimate the signal subspace dimension via a simple adptive threshold comparison technique. Most available computationally efficient subspace tracking algorithms rely on off-line estimation of the signal subspace dimension, which acts as a bottleneck in real-time parallel implementations. The noise averaged Jacobi-type SVD updating algorithm presented in this paper is capable of simultaneously tracking the signal subspace and its dimension, while preserving both the low computational cost ofO(nr) and the parallel structure of the method, as demonstrated in a systolic implementation. Furthermore, the algorithm tracks all signal singular values. Their squares are estimates of the powers in the orthogonal modes of the signal. Thus, applications of the algorithm are not limited to only DOA and frequency tracking where information about the powers of signal components is not exploited.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Carnegie Mellon University, 15213, Pittsburgh, PA

    Aleksandar Kavčić

  2. Department of Electrical Engineering, Ruhr University Bochum, 44780, Bochum, Germany

    Bin Yang

Authors
  1. Aleksandar Kavčić
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  2. Bin Yang
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Kavčić, A., Yang, B. Subspace tracking with adaptive threshold rank estimation. J VLSI Sign Process Syst Sign Image Video Technol 14, 75–91 (1996). https://doi.org/10.1007/BF00925270

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  • DOI: https://doi.org/10.1007/BF00925270

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