An Efficient Approach for Two-Dimensional Parameter Estimation of a Single-Tone

Abstract

Abstract-In this paper, parameter estimation of a two-dimensional (2-D) single damped real/complex tone in the presence of additive white Gaussian noise is addressed. By utilizing the rank-one property of the 2-D noise-free data matrix, the damping factor and frequency for each dimension are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure. The remaining parameters are then obtained straightforwardly using standard least squares. The biases as well as variances of the damping factor and frequency estimates are also derived, which show that they are approximately unbiased and their performance achieves Cramér-Rao lower bound (CRLB) at sufficiently large signal-to-noise ratio (SNR) and/or data size conditions. We refer the proposed approach to as principal-singular-vector utilization for modal analysis (PUMA) which performs estimation in a fast and accurate manner. The development and analysis can easily be adapted for a tone which is undamped in at least one dimension. Furthermore, comparative simulation results with several conventional 2-D estimators and CRLB are included to corroborate the theoretical development of the PUMA approach as well as to demonstrate its superiority.

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

“…Note that {γ f } can be easily estimated by applying a least squares (LS) fit [14] on (1) after the frequencies and damping factors have been determined.…”

“…At sufficiently high SNR conditions such thatâ R is located at a reasonable proximity of a R and assuming that J ′′ (ã R ) is smooth enough around a R , we expand J ′ (â R ) using Taylor series to yield [14]:…”

“…By exploiting the subspace methodology of principal-singular-vector utilization for modal analysis (PUMA) and tensor algebra, the proposed estimation algorithm is developed in Section III. Note that we have already applied PUMA for a single 2-D tone in [14] where the key ideas are to exploit the rank-one property of the corresponding 2-D noise-free data matrix and to find the damping factor as well as frequency parameters for each dimension from the left and right principal singular vectors in a separable manner. With the use of tensor algebra, the parameters of interest at one dimension will first be accurately estimated according to an iterative procedure which utilizes the sinusoidal linear prediction (LP) property and weighted least squares (WLS).…”

High-Resolution Subspace-Based Methods: Eigenvalue- or Eigenvector-Based Estimation?

“…To deal with this problem, several methods have been proposed. They include linear prediction-based methods such as 2-D TLS-Prony [10], and subspace approaches such as matrix enhancement and matrix pencil (MEMP) [3], 2-D ESPRIT [8], improved multidimensional folding (IMDF) [7,6], Tensor-ESPRIT [2], principal-singular-vector utilization for modal analysis (PUMA) [14,13]. Among the most promising are N-D ESPRIT [8,12] and IMDF [7,6].…”

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

“…We refer our approach to as principal-singularvector utilization for modal analysis (PUMA), meaning that the principal singular vectors of the data matrix are effectively exploited in the estimation process. This work is a follow-up of [14] where the PUMA algorithm for a single damped/undamped real/complex tone or K = 1 is devised and analyzed.…”