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Spherical subspace tracking for efficient, high performance adaptive signal processing applications
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DOI：10.1016/0165-1684(96)00004-7.png)
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In this paper we develop and analyze multilevel spherical subspace updating algorithms. These algorithms track eigenvectors and/or eigensubspaces associated with time-varying data that arises in adaptive signal processing, direction of arrival (DOA) or frequency tracking problems. Spherical subspaces can be created by setting groups of eigenvalues to their average value. Because of the sphericity, the subspace basis vectors can be reoriented to deflate the update problem and reduce computation. In this paper, we focus on a four-level update that efficiently tracks the signal subspace and generates just enough eigenlevel information to make strongly consistent signal subspace rank estimates. The four-level method is O(nr) per update when n is the data dimension and r is the signal subspace rank. In order to analyze the multilevel algorithms, we use Ljung's method to derive ordinary differential equations (ODEs) that characterize the asymptotic eigenlevel and subspace projection operator trajectories. Under certain weak assumptions, we prove that the multilevel algorithms asymptotically converge with probability one to the true subspace and eigenlevel values. We also present a four-level MDL-based rank detection scheme and show it to be strongly consistent. Simulation studies support the theoretical results and demonstrate the performance of our methods with frequency tracking data.
Keyword:
array signal processing
subspace methods
recursive estimation
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3.6
论文数:
10.0K
被引数:
1.7W
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