Virtual multidimensional structure‐based subspace estimation to improve parameter estimation accuracy in harmonic retrieval problems

Abstract

For R-dimensional (R-D) harmonic retrieval problems with R ≥ 2, it has been demonstrated that higher-order singular value decomposition (HOSVD) of the measurement data can be used to improve the signal subspace estimation, leading to high parameter estimation accuracy. This, however, usually cannot be applied to the one-dimensional harmonic retrieval problem due to the absence of the multidimensional structure in the measurement data. To overcome this difficulty, the authors propose to construct a virtual multidimensional structure in the measurement data, upon which the HOSVD can be used to estimate the signal subspace. Moreover, the idea of constructing a virtual multidimensional structure is also introduced to the R-D harmonic retrieval problems. In conjunction with its inherent multidimensional structure, the virtual multidimensional structure is exploited to further enhance the signal subspace estimation. As examples, estimation of signal parameters via rotational invariance technique algorithms are employed to estimate the signal parameters. Finally, theoretical analysis and simulation results demonstrate the effectiveness and efficiency of the authors’ proposal.