Simultaneous subspace tracking and rank estimation

Aleksandar Kavcic; Bin Yang

doi:10.1117/12.211398

7 June 1995 Simultaneous subspace tracking and rank estimation

Aleksandar Kavcic, Bin Yang

Proceedings Volume 2563, Advanced Signal Processing Algorithms; (1995) https://doi.org/10.1117/12.211398
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Jacobi-type singular value decomposition (SVD) is an exceptionally suitable method for recursive SVD updating. It has a low computational complexity per update, O(n²), where n is the problem size. Due to its parallel structure, it is very attractive for real-time applications on systolic arrays. In frequency and angle of arrival tracking problems, SVD can be used to track the signal subspace. Typically, only a few, r, dominant eigencomponents need to be tracked, where r is less than n. In this paper we show how to modify the Jacobi-type SVD to track only the r-dimensional signal subspace by forcing the (n - r)-dimensional noise subspace to be spherical. Thereby, the computational complexity is brought down from O(n²) to O(nr). Furthermore, we show how to exploit the structure of the Jacobi-type SVD to estimate the signal subspace dimension, r, in addition to tracking the subspace itself. Most available computationally efficient subspace tracking algorithms rely on off-line estimation of the singal subspace dimension. This acts as a bottleneck in real-time parallel implementations. The Jacobi-type spherical subspace tracking algorithm presented in this paper is thus a subspace tracking method of computational complexity O(nr), capable of tracking both the signal subspace and its dimension simultaneously. Thereby, the parallelism of the algorithm is not destroyed, as demonstrated in a systolic array implementation. Simulation results are presented to show the applicability of the algorithm in adaptive frequency tracking problems.

Citation Download Citation

Aleksandar Kavcic and Bin Yang "Simultaneous subspace tracking and rank estimation", Proc. SPIE 2563, Advanced Signal Processing Algorithms, (7 June 1995); https://doi.org/10.1117/12.211398

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