Variational Bayesian Inference-Based Method for Antenna Array Diagnosis

Sparse diagnosis techniques for antenna arrays provide an efficient approach to fault diagnosis by leveraging the sparse nature of faulty elements. In practical scenarios, an unknown measurement scale factor exists between measured signals and fault-free reference signals. Existing works often implicitly assume perfect data normalization, yet even slight scale mismatches can destroy the sparsity of differential signals and induce an estimation error floor. A sparse diagnosis method based on variational Bayesian inference (VBI) is proposed to jointly model and estimate the scale factor and sparse fault parameters. First, a complex measurement scale factor is introduced to quantitatively characterize the scale mismatch between measured signals and the reference signals. Second, within the VBI framework, we design a coordinate ascent variational inference (CAVI) algorithm that delivers stable convergence by alternately updating the variational distributions of the sparse fault parameters and the scale factor. Simulation results demonstrate that the proposed method can accurately localize faulty elements and estimate their parameters. Additionally, it achieves high-precision estimation of the scale factor, overcoming the limitations of traditional methods that either overlook the scale factor or fail to estimate it with sufficient precision.