2 research outputs found
Super-Resolution DOA Estimation for Arbitrary Array Geometries Using a Single Noisy Snapshot
We address the problem of search-free DOA estimation from a single noisy
snapshot for sensor arrays of arbitrary geometry, by extending a method of
gridless super-resolution beamforming to arbitrary arrays with noisy
measurements. The primal atomic norm minimization problem is converted to a
dual problem in which the periodic dual function is represented with a
trigonometric polynomial using truncated Fourier series. The number of terms
required for accurate representation depends linearly on the distance of the
farthest sensor from a reference. The dual problem is then expressed as a
semidefinite program and solved in polynomial time. DOA estimates are obtained
via polynomial rooting followed by a LASSO based approach to remove extraneous
roots arising in root finding from noisy data, and then source amplitudes are
recovered by least squares. Simulations using circular and random planar arrays
show high resolution DOA estimation in white and colored noise scenarios.Comment: To appear in Proc. ICASSP 2019, May 12-17, 2019, Brighton, UK. arXiv
admin note: substantial text overlap with arXiv:1810.0001
Gridless DOA Estimation and Root-MUSIC for Non-Uniform Arrays
The problem of gridless direction of arrival (DOA) estimation is addressed in
the non-uniform array (NUA) case. Traditionally, gridless DOA estimation and
root-MUSIC are only applicable for measurements from a uniform linear array
(ULA). This is because the sample covariance matrix of ULA measurements has
Toeplitz structure, and both algorithms are based on the Vandermonde
decomposition of a Toeplitz matrix. The Vandermonde decomposition breaks a
Toeplitz matrix into its harmonic components, from which the DOAs are
estimated. First, we present the `irregular' Toeplitz matrix and irregular
Vandermonde decomposition (IVD), which generalizes the Vandermonde
decomposition to apply to a more general set of matrices. It is shown that the
IVD is related to the MUSIC and root-MUSIC algorithms. Next, gridless DOA is
generalized to the NUA case using IVD. The resulting non-convex optimization
problem is solved using alternating projections (AP). A numerical analysis is
performed on the AP based solution which shows that the generalization to NUAs
has similar performance to traditional gridless DOA