An Eigenvector-Based Approach for Multidimensional Frequency Estimation With Improved Identifiability

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

“…for m = n in (16), which is in fact the weighted linear predictor estimate [21] (iii) Construct W M 2 −1 (ω 2 ) according to (16) with ω 2 =ω 2 (iv) Compute an updatedω 2 using (15) (v) Repeat Steps (iii)-(iv) until a stopping criterion is reached.…”

“…According to Table 1, the major computations in the rth dimension has a complexity of O(τ M r ), implying that the orders of complexity for the C-1 and C-2 algorithms are O( R r=1 τ M r ) and O( R r=1 τ (M r − 1)), respectively. As a comparison, the complexity order of the AIQML [15] method is O( R r=1 τ M r ) while the IMDF [16] and UE [8] …”

“…Section 3 generalizes the proposed solutions to higher dimensional signals with the use of tensor algebra [19]. Simulation results are included in Section 4 to corroborate the theoretical development and to compare the correlation-based approach with the approximate iterative quadratic ML (AIQML) [15], IMDF [16] and UE [8] algorithms as well as Cramér-Rao lower bound (CRLB) [20].…”

“…For 2-D frequency estimation, maximum-likelihood (ML) [14]- [15] and subspace [8]- [13], [16]- [17] approaches are commonly used choices.…”

“…State-of-the-art subspace methods include MUSIC [9], decoupled root-MUSIC [17], unitary ESPRIT (UE) [8], rank reduction estimator (RARE) [12], multi-dimensional folding (MDF) [11] and improved MDF (IMDF) [16], and they usually need eigenvalue decomposition (EVD) or singular value decomposition (SVD) in the algorithm implementation. By effectively utilizing the correlation of the observed data, we contribute to devising an accurate frequency estimator for a R-D single-tone with less computational load in this work.…”