A Progressive dPDOA Localization Method with Quality Control

To address unreliable positioning caused by phase ambiguity and noise in phase difference of arrival (PDOA) systems, this paper proposes a progressive differential phase difference of arrival (dPDOA) localization algorithm with multi-height consistency-based quality control. The algorithm uses dPDOA as the observation model. First, TDOA direction finding obtains a target azimuth prior, reducing the 3D search to a ray. Then, a coarse range search under multiple height hypotheses gives a rough position. The LAMBDA method then fixes integer ambiguities, and a nonlinear least-squares iteration yields the final high-precision result. For reliability, a quality-control step based on the standard deviation of range across multiple heights (stdR) is applied after coarse positioning. By exploiting the closeness of range estimates under different height hypotheses, stdR rejects spurious samples caused by cost-function multimodality. Its computation is simple, using only intermediate coarse-search results, and enables efficient screening of reliable samples before the complex ambiguity-fixing stage. A localization is considered successful when the 3D positioning error is below 8% of the true range. Compared with the same progressive chain without quality control, under 30° RMS single-difference phase noise, the stdR quality control increases the positioning success rate from 48.10% to 68.11%, reduces the median localization error from 38.06 km to 13.02 km, and retains 60.03% of the successful samples.