R-D Frequency estimation of multidimensional sinusoids based on eigenvalues and eigenvectors

In this paper, a new subspace-based algorithm is proposed for the R-D signal parameter estimations of multidimensional sinusoids. The perspective idea of the algorithm is to rearrange the R-D sampling arrays into a series of two dimensional matrix columns distributed in the first dimension and the $$r\,\hbox {th}$$rth dimension, and then use the obtained matrix columns to construct a set of new matrices. As a result, the two-dimensional parameters in the first dimension as well as the $$r\,\hbox {th}$$rth dimension, can be estimated from the eigenvalues and eigenvectors of the constructed matrix, respectively. As the matrix’s eigenvalues and eigenvectors are related, the estimated signal parameters in each dimension are automatically paired.