Title :
Accurate and Computationally Efficient Tensor-Based Subspace Approach for Multidimensional Harmonic Retrieval
Author :
Sun, Weize ; So, H.C.
Author_Institution :
Dept. of Electron. Eng., City Univ. of Hong Kong, Hong Kong, China
Abstract :
In this paper, parameter estimation for R-dimensional (R -D) sinusoids with R >; 2 in additive white Gaussian noise is addressed. With the use of tensor algebra and principal-singular-vector utilization for modal analysis, the sinusoidal parameters at one dimension are first accurately estimated according to an iterative procedure which utilizes the linear prediction property and weighted least squares. The damping factors and frequencies in the remaining dimensions are then solved such that pairing of the R-D parameters is automatically achieved. Algorithm modification for a single R -D tone is made and it is proved that the frequency estimates are asymptotically unbiased while their variances approach Cramér-Rao lower bound at sufficiently high signal-to-noise ratio conditions. Computer simulations are also included to compare the proposed approach with conventional R -D harmonic retrieval schemes in terms of mean square error performance and computational complexity.
Keywords :
AWGN; computational complexity; iterative methods; least squares approximations; mean square error methods; parameter estimation; signal processing; tensors; Cramér-Rao lower bound; R -D harmonic retrieval schemes; R -D tone; R-D parameters; additive white Gaussian noise; computational complexity; computationally efficient tensor-based subspace approach; computer simulations; damping factors; damping frequencies; iterative procedure; linear prediction property; mean square error performance; modal analysis; multidimensional harmonic retrieval; parameter estimation; principal-singular-vector utilization; signal-to-noise ratio conditions; tensor algebra; weighted least squares; Covariance matrix; Damping; Estimation; Frequency estimation; Tensile stress; Vectors; Multidimensional spectral analysis; harmonic retrieval (HR); parameter estimation; subspace method; tensor algebra;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2012.2205571