Elliptic positioning system offers a precise alternative to global navigation satellite system (GNSS). However, ranging measurements upon a single UAV only delineate the location estimates to a spherical region. Data infusion from inertial measurement units (IMUs) may refine these estimates, while its fidelity is undermined by IMUs’ lack of self-alignment to a specified reference frame. In this paper, we explore the minimal number of assisted UAVs or anchors for absolute positioning, i.e., location and alignment in a fixed frame, during complete GNSS outages. We first prove that the observability establishes under a UAV in a 3-D trajectory or a pair of static anchors. The two numbers are new theoretical limit, significantly lower than the three anchors in 2-D or four in 3-D scenarios required by traditional theorems. We propose a sequential scheme for the multi-parameter estimation problem ensuring rapid convergence. An iterative solution is derived, flexible to UAV and anchor-based configurations, that provides instant location updates free of computational overhead. Thereafter, we also circumvent NLOS effects by employing inverse estimation of range. Accordingly, we devise a tiered positioning framework that commences with a location-unknown UAV to first cooperate with LOS anchors, and then extend the service to UE via a single NLOS link outside anchors’ coverage. In the experiments, the proposed scheme reaches (10⁻²)° orientation alignment and centimeter-level accuracy in NLOS scenarios, which attains the Cramer-Rao lower bound (CRLB) accuracy. Moreover, the accuracy notably exceeds the noise level of ranging measurements at high sampling rate, and also shows robustness against local clock drifting.