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⩾2R⩾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.

► R single-tone sequences that contain the R-D frequency parameters are constructed.
► Two proposals are developed for fast and accurate frequency estimation.
► The WLS technique is employed in the estimation of the parameters.
► The performance of the two estimators is also analyzed.