Covariance Eigenanalysis for Direction Finding with Analytic Ray-Traced Steering Vectors

Abstract

Greg Passmore

In our setup of multiple phased array antennas, the goal was to replicate current techniques for object location. For this, we incorporated Multiple Signal Classification (MUSIC), a subspace DOA estimator for multiple narrowband sources impinging on our phased arrays. This is based on the eigendecomposition of the sample spatial covariance R^{^} and the resulting partition C^M of into orthogonal signal and noise subspaces. Candidate directions are evaluated by the noise-subspace projection energy d(theta) = â?£â?£Un^Ha(theta)â?£â?£²₂ and DOA hypotheses are taken from peaks of the reciprocal pseudospectrum P_MUSIC(θ) = d(θ) ⁻¹.

Here a(θ) is generated by our analytic ray tracer rather than a typical ideal plane-wave model. For each scan direction, the ray tracer returns the per-element complex field after integrating refractive optical path length and attenuation along the propagation path to each sensor, with optional instrument phase and gain terms. MUSIC is then applied, but steering-vector mismatch from refraction and loss is moved from an unmodeled error term into the forward model used inside d(θ).

This combination provides several operational advantages. MUSIC preserves super-resolution angular discrimination by exploiting covariance eigenstructure rather than relying on beamwidth- limited steering. Ray tracing reduces deterministic bias by ensuring the steering vector includes atmospheric refraction and absorption, preventing these effects from being absorbed into noise- subspace leakage. The result is a DOA estimator that remains mathematically identical to standard MUSIC, but produces bearings that are physically consistent under non-ideal propagation conditions, improving downstream fusion stability and track repeatability.

The development proceeds from the narrowband array model through finite-snapshot covariance estimation and Hermitian eigenanalysis to an explicit summation-form master equation that maps directly to loop-based implementations. The same algebra is retained when the steering vector is replaced by ray-integrated propagation, enabling a propagation-aware pseudospectrum evaluation under refracting and lossy atmospheres. Keywords: Direction-Of-Arrival Estimation, MUSIC Algorithm, Covariance Eigenanalysis, Ray- Traced Steering Vectors, Atmospheric Propagation Modeling

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