Reduced-Observation Approximation of Near-Field Gaussian Covariance Matrices

Abstract

Near-field covariance matrices are central to local- ization, covariance-aware estimation, and linear MMSE filtering in large-aperture arrays, but Gaussian position uncertainty requires costly numerical averaging of nonlinear spherical-wave steering vectors. This letter proposes a low-complexity framework for two-dimensional near-field Gaussian covariance approxima- tion. By writing the quadrature covariance as RQ = HHH , the dominant covariance spectrum is obtained from a reduced observation representation, avoiding full MxM eigendecom- position. A self-calibrated non-reference spectral-error estimator is further introduced using only grid-to-grid dominant-spectrum differences. Numerical results show accurate convergence track- ing and substantial complexity reduction.