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Multi-dimensional harmonic retrieval (HR) in white noise is required in numerous applications such as channel estimation in wireless communications and imaging in multiple-input multiple-output radar. In this paper, we propose two R-dimensional (R-D) extensions of the subspace-based MUSIC model order selection scheme, for R2, to detect the number of multi-dimensional cisoids. The key idea in the algorithm development is to utilize the principle angles between multilinear signal subspaces via the truncated higher-order singular value decomposition. The first method is designed for multiple-snapshot scenarios. It considerably outperforms existing algorithms in terms of both detection accuracy and identifiability particularly when a large number of snapshots are available. However, its computational cost is relatively quite high. The second method is computationally much simpler and performs almost as well as the first one when the number of snapshots is small. Simulation results are conducted to demonstrate the performance of the proposed estimators.

Detecting the number of components of the CANDECOMP/PARAFAC (CP) model, also known as CP model order selection, is an essential task in signal processing and data mining applications. Existing multilinear detection algorithms for handling N-dimensional data, where N ? 3 , e.g., the CORe CONsistency DIAgnostic, rely on the CP decomposition which is computationally very expensive. An alternative solution is to rearrange the tensor as a matrix using the unfolding operation and then utilize the eigenvalues of the resultant matrices for CP model order selection. We propose to employ the eigenvalues associated with the unfolding along merged dimensions, namely, the multi-mode eigenvalues, as well as the n-mode eigenvalues for accurate rank detection. These multiple sets of eigenvalues are combined via the information theoretic criterion. By designing a sequential detection scheme starting from the most squared unfolded matrix, the identifiable rank is increased to the square root of the product of all dimension lengths, which renders the detection algorithm to estimate the rank that can exceed any individual dimension length. The conditions under which the proposed multilinear detection algorithm correctly detects the tensor rank are theoretically investigated and its computational efficiency and detection performance are verified. The problem of CANDECOMP/PARAFAC (CP) model order selection is addressed.Computational efficiency is achieved via matricization of a tensor.Eigenvalues associated with the block or multi-mode matricization are exploited.Able to detect rank up to the square root of the product of all dimension lengths.Accuracy comparable to CP-decomposition based tensor rank detectors.

The order estimation algorithm relies on multidimensional folding combined with ESTimation ERror criterion.Multidimensional folding and unfolding construct two matrix slices that satisfy the shift invariance equality.The ESTER criterion estimates number of harmonics based on shift invariance equality.The algorithm is able to identify significantly more harmonics.The algorithm is robust against colored noise. Estimation of the number of harmonics in multidimensional sinusoids is studied in this paper. The ESTimation ERror (ESTER) is a subspace based detection approach that is robust against colored noise. However, the number of signals it can detect is very limited. To improve the identifiability, we propose to combine the multidimensional folding (MDF) techniques with ESTER for multidimensional sinusoidal order selection. Our algorithm development is inspired by the shift invariance properties of the two matrix slices resulting from multidimensional folding and unfolding, which have been exploited to extract the spatial frequencies in the literature. The maximum identifiable number of signals of the MDF-ESTER is of the order of magnitude of product of the lengths of all spatial dimensions with uniform spacing, which is significantly larger than that of the conventional multidimensional ESTER methods. Meanwhile, it inherits the robustness of the ESTER against colored noise, and performs comparably to state-of-the-art schemes when the number of signals is small.

Accurate estimation of the attitude of unmanned aerial vehicles (UAVs) is crucial for their control and displacement. Errors in the attitude estimate may misuse the limited battery energy of UAVs or even cause an accident. For attitude estimation, proprioceptive sensors such as inertial measurement units (IMUs) are widely applied, but they are susceptible to inertial guidance error. With antenna arrays currently being installed in UAVs for communication with ground base stations, we can take advantage of the array structure in order to improve the estimates of IMUs via data fusion. In this paper, we therefore propose an attitude estimation system based on a hexagon-shaped 7-element electronically steerable parasitic antenna radiator (ESPAR) array. The ESPAR array is well-suited for installment in the UAVs with broad wings and short bodies. Our proposed solution returns an estimation for the pitch and roll based on the inter-element phase delay estimates of the line-of-sight path of the impinging signal over the antenna array. By exploiting the parallel and centrosymmetric structure in the hexagon-shaped ESPAR array, the 3-dimensional Unitary ESPRIT algorithm is applied for phase delay estimation to achieve high accuracy as well as computational efficiency. We devise an attitude estimation algorithm by exploiting the geometrical relationship between the UAV attitude and the estimated phase delays. An analytical closed-form expression of the attitude estimates is obtained by solving the established simultaneous nonlinear equations. Simulations results show the feasibility of our proposed solution for different signal-to-noise ratio levels as well as multipath scenarios.