Autonomous coordinate establishment of local reference frames for ground-based positioning systems without known points

Ground-based positioning systems (GBPSs) can serve as a supplement and backup to global navigation satellite systems. GBPSs are known for their low cost and high flexibility, but most of them have difficulty in achieving rapid deployment and operation, since the coordinates of transmitters rely on external precise measurements. Several existing self-calibration methods based on carrier phase measurements require known points of GBPS transmitters or receivers, which implies dependence on external measurements. This paper proposes an autonomous coordinate establishment (ACE) method without using known reference points for GBPSs. ACE utilizes a kinematic receiver to collect carrier phase measurements and employs a three-step procedure to establish a regional coordinate system. In the first step, ACE uses the properties of matrix structures to decouple generalized ambiguities and coordinates. Then, ACE obtains the rough estimation of the transmitter coordinates via multi-dimensional scaling in the second step. In the third step, ACE refines the estimate by solving a least squares problem which would be difficult to solve without the previous two steps. Numerical simulations and a real-world experiment show that the coordinate estimation of ACE can achieve decimeter to centimeter-level accuracy. The proposed method enables rapid deployment and operation for GBPSs.