Abstract
We present a new algorithm for tracking the signal subspace recursively. It is based on an interpretation of the signal subspace as the solution of a constrained minimization task. This algorithm, referred to as the constrained projection approximation subspace tracking (CPAST) algorithm, guarantees the orthonormality of the estimated signal subspace basis at each iteration. Thus, the proposed algorithm avoids orthonormalization process after each update for postprocessing algorithms which need an orthonormal basis for the signal subspace. To reduce the computational complexity, the fast CPAST algorithm is introduced which has complexity. In addition, for tracking the signal sources with abrupt change in their parameters, an alternative implementation of the algorithm with truncated window is proposed. Furthermore, a signal subspace rank estimator is employed to track the number of sources. Various simulation results show good performance of the proposed algorithms.
Highlights
Subspace-based signal analysis methods play a major role in contemporary signal processing area
Subspace-based highresolution methods have been developed in numerous signal processing domains such as the MUSIC, the minimumnorm, the ESPRIT, and the weighted subspace fitting (WSF) methods for estimating frequencies of sinusoids or directions of arrival (DOA) of plane waves impinging on a sensor array
We investigate the performance of fast constrained projection approximation subspace tracking (CPAST) in estimating the signal subspace and compare it with other subspace tracking algorithms
Summary
Subspace-based signal analysis methods play a major role in contemporary signal processing area. Variations and extensions of Bunch’s rankone updating algorithm [9], such as subspace averaging [10], have been proposed Another class of algorithms considers the EVD/SVD as a constrained or unconstrained optimization problem, for which the introduction of a projection approximation leads to fast subspace tracking methods such as PAST [11] and NIC [12] algorithms. We present a recursive algorithm for tracking the signal subspace spanned by the eigenvectors corresponding to the r largest eigenvalues This algorithm relies on an interpretation of the signal subspace as the solution of a constrained optimization problem based on an approximated projection.
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