Joint SVD of Two Cross-Correlation Matrices to Achieve Automatic Pairing in 2-D Angle Estimation Problems

Recently, Kikuchi
et al
. proposed a pair-matching method for two-dimensional (2-D) angle estimation using a cross-correlation matrix. Unlike some classical pair matching methods which require a complex process, Kikuchi's method utilizes the corresponding combinations of the elevation and azimuth angles emerging in the cross-correlation matrix of two uniform linear arrays (ULAs) to achieve automatic pairing. However, Kikuchi's method has some drawbacks such as the pair matching and failure problems when the difference of the corresponding combinations of the 2-D angles {cos
thetas_k
- cos
Phi_k
}
<sub>k

=1</sub>

^K
is small and the signal-to-noise ratio (SNR) is low. Furthermore, this method does not make good use of the cross correlation, where the effect of additive noise is eliminated, to improve the estimation performance. We propose a novel automatic pairing scheme for estimating 2-D angle by simultaneous singular value decomposition (SVD) of two cross-correlation matrices. Computer simulation results are presented to show that the proposed technique can overcome these problems and offer better estimation performance.