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

Abstract

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-K property of the 2-D noise-free data matrix, the damping factor and frequency information is contained in the K 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. For each frequency of the first dimension, the corresponding parameter in the second dimension is then obtained to achieve autopairing. 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.

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

“…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.…”

“…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.…”

Mismatched Estimation of Polynomially Damped Signals

“…The estimation of such signal models have been approached in a variety of ways (see [1] for a more general review), e.g., by exploiting subspace decompositions [6], [7], linear system descriptions [8], as well as compressed sensing methods [9]- [11]. However, for some responses, the first-order polynomial is insufficient for accurately modeling the observed data, and one instead requires the use of Voigt line shapes to more accurately capture the structure of the signal.…”

Computationally efficient estimation of multi-dimensional spectral lines

“…Typically, for such problems, the highresolution evaluation of the signal characteristics can require both notable computational efforts as well as vast memory requirements, and several efforts have been made to propose various forms of parametric and semi-parametric estimators (see, e.g., [1,2]). In particular, the two-dimensional (2-D) case has been investigated in several works, such as [3][4][5], wherein the authors examine algorithms based on the problem's eigenvector structure, exploit a sparsity framework, as well as a subspace framework, respectively. Further works include [6], which examined the 3-D case, [7,8], wherein different compressed sensing methods are compared for high dimensional NMR signals, and [8,9], which examined high-dimensional subspace based estimators.…”