Lagrange Interpolation in Satellite Positioning for Inter-Vehicle Distance Estimation: A Case Study

Cooperative Inter-vehicle Distance (IVD) estimation algorithms such as Absolute Position Differencing (APD), Single-Differencing (SD), and Double-Differencing (DD) are promising and cost-effective solutions thanks to Global Navigation Satellite System (GNSS) observables. These algorithms directly utilize pseudorange measurements, i.e., the estimated distance between the antennas of satellites orbiting the Earth and the GNSS receiver installed on the vehicle. However, an accurate IVD estimate using these techniques is dependent on exact satellite coordinates, as any GNSS pseudorange requires precise satellite positions. To compute satellite positions, the satellite’s distributed navigation message or interpolation methods can be employed. This paper examines the performance of the Lagrange interpolation approach for estimating satellite locations epoch-by-epoch in a real-world experiment in the IVD estimation problem. The experimental results demonstrate that the Lagrange interpolation ...