Rational invariant subspace approximations with applications

M.A. Hasan, M.R. Azimi-Sadjadi, A.A. Hasan
2000 IEEE Transactions on Signal Processing  
Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct
more » ... or the sample covariance matrix. Several ESPRIT-as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained comparing with those associated with the eigendecomposition-based methods. These methods are demonstrated to have performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace matrix. Index Terms-DOA, ESPRIT, frequency estimation, minimum norm, MUSIC, power methods, rational subspace approximation. I. INTRODUCTION T HE SIGNAL subspace approach has found applications in several fields such as harmonic retrieval [1 ], [2], spectral estimation and autoregressive moving average (ARMA) modeling [3], [4], sensor array processing [5], [6], system identification [7], and even in filter design applications [8]. Signal subspace algorithms can usually provide much better performance than traditional least squares methods; however, associated computational load make them less attractive for real-time implementation. Among the most attractive ones are MUSIC [5], MIN-NORM linear prediction [9], [10] and ESPRIT [11]-[14] . In subspace methods, the data matrix or a matrix of some statistics of the data is normally decomposed into two orthogonal subspaces. Then, the direction of arrival (DOA) is estimated using the orthogonality of the noise subspace and the array manifold (MUSIC and MIN-NORM) or the rotation invariance over the signal subspace (ESPRIT). This decomposition is usually carried out using the singular value or eigenvalue decomposition. Several exact methods have been presented in [15] and [16]. However, the computation of these exact decompositions is often very intensive, which may make the subspace algorithms prohibitive. . His research interests include adaptive systems, signal/image processing, estimation theory, control theory, numerical analysis, optimization, numerical linear algebra, and computational and applied mathematics. His current research includes high-resolution methods, fast algorithms, parallelizable inverse-free algorithms, subspace decompositions and their applications in signal processing, and sinusoidal frequency estimation. One of his educational interests is the use of microprocessor DSP chips in teaching signal processing and signals and systems courses. Mahmood R. Azimi-Sadjadi (SM'89) received the M.Sc. and Ph.D. degrees from the
doi:10.1109/78.875461 fatcat:rkeokyfghfaaxlymptm6u563kq