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

Abstract

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 Cramér-Rao lower bound when the data observation length tends to infinity. The computational efficiency and estimation accuracy are demonstrated via computer simulations.

Subspace Approach for Frequency Estimation of Superimposed Exponential signals in Multiplicative and Additive Noise

“…In this paper, we considered the estimation of frequencies of a superimposed exponential signal model. We generalized the PUMA method [13][14][15][16] from sinusoids with additive noise to multiple signals with multiplicative and additive noise. The techniques SVD and WLS are used to obtain the frequency estimation.…”

“…It can be observed that the frequency information is contained in G and H but the frequency estimation is not directly available from { ( )} y t . In this paper, we use the PUMA method [13][14][15][16] for frequency estimation as follows.…”

“…In each table the first row in each of the cell represents the true frequency values, the corresponding ME and MSEs are reported in the second and last rows, respectively. Tables 1-2 show the performance of the proposed method L M = , (32,8) and (16,16) are best choices. It is also observed that the biases increase as the additive noise deviation increases, which indicates that the proposed method for larger v σ it is more difficult to estimate the unknown frequencies.…”

“…Recently, [13][14][15][16] introduced a principal singular-value-vector utilization for model analysis (PUMA) method based iterative procedure for parameter estimation of sinusoidal signals in additive noise. It is observed that such a method works satisfactorily for estimation of the signal parameters in terms of computational complexity and accuracy.…”

“…The greatest advantage of the method lies in that they make full use of the inner relationship between the weighting matrix for iteration and the parameters to raise the accuracy of the estimators iteratively. Inspired by the works [13][14][15][16], in this paper, we generalize the PUMA method to the case of the superimposed exponential signals in the presence of multiplicative and additive noise. It is observed from computer simulations that the proposed method provides fast and accurate frequency estimates at small noise deviation.…”