Weize Sun

Subspace Approach for Fast and Accurate Single-Tone Frequency Estimation

A new signal subspace approach for estimating the frequency of a single complex tone in additive white noise is proposed in this correspondence. Our main ideas are to use a matrix without repeated elements to represent the observed signal and exploit the principal singular vectors of this matrix for frequency estimation. It is proved that for small error conditions, the frequency estimate is approximately unbiased and its variance is equal to Cramér-Rao lower bound. Computer simulations are included to compare the proposed approach with the generalized weighted linear predictor, periodogram, and phase-based maximum likelihood estimators in terms of estimation accuracy, computational complexity, and threshold performance.

Accurate and Computationally Efficient Tensor-Based Subspace Approach for Multidimensional Harmonic Retrieval

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.

Subspace approach for two-dimensional parameter estimation of multiple damped sinusoids

In this paper, we tackle the two-dimensional (2-D) parameter estimation problem for a sum of K>=2 real/complex damped sinusoids in additive white Gaussian noise. According to the rank-property of the 2-D noise-free data matrix, the damping factor and frequency information is contained in the dominant left and right singular vectors. Using the sinusoidal linear prediction property of these vectors, the frequencies and damping factors of the first dimension are first estimated. The parameters of the second dimension are then computed such that frequency pairing is automatically achieved. Computer simulations are included to compare the proposed approach with several conventional 2-D estimators in terms of mean square error performance and computational complexity.

Tensor Approach for Eigenvector-Based Multi-Dimensional Harmonic Retrieval

In this paper, we propose an eigenvector-based frequency estimator for R-dimensional (R-D) sinusoids with R ≥ 2 in additive white Gaussian noise. Our underlying idea is to utilize the tensorial structure of the received data and then apply higher-order singular value decomposition (HOSVD) and structure least squares (SLS) to perform estimation. After obtaining the tensor-based signal subspace from HOSVD, we decompose it into a set of single-tone tensors from which single-tone vectors can be constructed by another HOSVD. In doing so, the R-D multiple sinusoids are converted to a set of single-tone sequences whose frequencies are individually estimated according to SLS. The mean and variance of the frequency estimator are also derived. 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 particularly in the presence of identical frequencies.

Efficient frequency estimation of a single real tone based on principal singular value decomposition

The problem of single-tone frequency estimation for a discrete-time real sinusoid in white Gaussian noise is addressed. We first show that the frequency information is embedded in the principal singular vectors of a matrix which stores the observed data with no repeated entry. The technique of weighted least squares is then utilized for finding the frequency from the singular vectors. It is proved that the variance of the frequency estimate approaches Cramer-Rao lower bound when the data observation length tends to infinity. The computational efficiency and estimation accuracy are demonstrated via computer simulations.

Efficient parameter estimation of multiple damped sinusoids by combining subspace and weighted least squares techniques

A new signal subspace approach for sinusoidal parameter estimation of multiple tones is proposed in this paper. Our main ideas are to arrange the observed data into a matrix without reuse of elements and exploit the principal singular vectors of this matrix for parameter estimation. Comparing with the conventional subspace methods which employ Hankel-style matrices with redundant entries, the proposed approach is more computationally efficient. Computer simulations are also included to compare the proposed methodology with the weighted least squares and ESPRIT approaches in terms of estimation accuracy and computational complexity.

Correlation-based algorithm for multi-dimensional single-tone frequency estimation

In this paper, parameter estimation for a R-dimensional (R-D) single cisoid with R>=2 in additive white Gaussian noise is addressed. By exploiting the correlation of the data samples, we construct R single-tone sequences which contain the R-D frequency parameters. Based on linear prediction and weighted linear squares techniques, two proposals are developed for fast and accurate frequency estimation from each constructed sequence. The two devised estimators are proved to be asymptotically unbiased while their variances achieve Cramer-Rao lower bound when the signal-to-noise ratio and/or data length tend to infinity. 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.

Accurate estimation of common sinusoidal parameters in multiple channels

Parameter estimation for exponentially damped complex sinusoids in the presence of white noise using multiple channel measurements is addressed. More precisely, we are interested in the damping factor and frequency parameters which are common among all channels. By exploiting linear prediction and weighted least squares technique, an iterative algorithm is devised to extract the common dynamics of the cisoids. Statistical analysis of the proposed method is studied and confirmed by computer simulations. Moreover, it is shown that the developed estimator attains optimum estimation accuracy and is superior to a conventional subspace-based algorithm when the signal-to-noise ratio is sufficiently high.

Improvement to esprit-type frequency estimators via reducing data redundancy

In this paper, the problem of estimating the damping factor and frequency parameters from multiple cisoids in noise is addressed. We first propose a data matrix which generalizes the commonly used Hankel-style matrices so that the number of repeated entries can be reduced. A new computationally efficient ESPRIT estimator that makes use of the right singular vectors is then devised. Algorithm modification for undamped sinusoids and complexity are also discussed. Computer simulations are included to compare the proposed approach with the conventional ESPRIT methods and Cramér-Rao lower bound.

Approximate Subspace-Based Iterative Adaptive Approach for Fast Two-Dimensional Spectral Estimation

In this paper, we devise a new approach for fast implementation of two-dimensional (2-D) iterative adaptive approach (IAA) using single or multiple snapshots. Our underlying idea is to apply the subspace methodology in this nonparametric technique by performing the IAA on the dominant singular vectors extracted from the singular value decomposition (SVD) or higher-order SVD of the multidimensional observations. In doing so, 2-D IAA is approximately realized by multiple steps of 1-D IAA, implying that computational attractiveness is achieved particularly for large data size, number of grid points and/or snapshot number. Algorithms based on matrix and tensor operations are developed, and their implementation complexities are analyzed. Computer simulations are also included to compare the proposed approach with the state-of-the-art techniques in terms of resolution probability, spectral estimation performance and computational requirement.