Branch-Aware Phase-to-Bearing Diagnostics in an Idealized Helical DAS Phase Array

Abstract

Circular phase error is invariant to integer multiples of 2π and can therefore conceal a wrong phase branch. This study evaluates a branch-preserving phase-to-bearing protocol in a locked, idealized 60-channel helical phase array with normalized multiple-signal-classification azimuth estimation. The protocol separates local phase error, samplewise branch-label mismatch, target-frequency spatial consistency, and signed recovery, nominal-manifold, and total bearing errors. One counterexample combines a circular RMSE of 0.0224 rad with an absolute RMSE of 3.77 rad and a branch-mismatch density of 0.36. Under a fixed compound-geometry stress, accurate recovery leaves an approximately 13° nominal-manifold bias while the actual-manifold oracle remains near zero. Another checkpoint yields a small total error through cancellation of two large opposite-signed components. The first-order diagnostic also fails under the reported compound stress. Phase- and task-failure labels disagree in both directions across locked design cells. The results apply to the tested point-channel simulator; transfer to measured DAS has not been established.