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

Abstract

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 Cramér-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.

Multidimensional Single-Tone Frequency Estimation Based on QR Decomposition

“…The MSE in comparison is computed using E{(ω r −ω r ) 2 }, with the CRLB to measure the performance of the proposed method. The correlation-based methods C-1 and C-2 in [20], and IMDF algorithm in [10] TPUMA method [17], N-D ESPRIT algorithm [18], and N-D Sparse algorithm [19] are included for comparison. Note that a Fast N-D ESPRIT algorithm is also developed in [18], but its performance is similar with the N-D ESPRIT algorithm, so we only compare the computation time of the Fast N-D ESPRIT algorithm in the computation comparison experiment.…”

“…Most of the proposed methods can handle both multi-tone and single-tone frequency estimation problems. While [20] proposes a correlation-based method for single-tone frequency estimation of multidimensional data.…”

“…In Section III, the performance analysis of proposed algorithm in term of theoretical mean square error (MSE) is formulated. And in Section IV, numerical simulations are included to evaluate the performance of the proposed algorithm by comparing with the correlation-based methods C-1 and C-2 [20], IMDF method [10], TPUMA method [17], N-D ESPRIT algorithm [18], and N-D Sparse algorithm [19] as well as the Cramér-Rao lower bound (CRLB) [21]. Finally, conclusions are drawn in Section V.…”