Airborne-Pseudolite (A-PL) systems have been proposed to augment Global Navigation Satellite Systems (GNSSs) in difficult areas where GNSS-only navigation cannot be guaranteed due to signal blockages, signal jamming, etc. One of the challenges in realising such a system is to determine the coordinates of the A-PLs to a high accuracy. The GNSS Precise Point Positioning (PPP) technique is a possible alternative to differential GNSS techniques such as those that generate Real-Time Kinematic (RTK) solutions. To enhance the A-PL positioning performance in GNSS challenged areas, it is assumed that inter-PL range measurements are also used in addition to GNSS measurements. When processing these new measurements, cross-correlations among A-PL estimated states introduced during measurement updates need to be accounted for so as to obtain consistent estimated states. In this paper, a distributed algorithm based on a Split Covariance Intersection Filter (SCIF) is proposed. Three commonly used means of implementing the SCIF algorithm are analysed. Another challenge is that real-time GNSS PPP relies on the use of precise satellite orbit and clock information. One problem is that these real-time orbit and satellite clock error corrections may not be always available, especially for moving A-PLs in challenging environments when signal outages occur. To maintain A-PL positioning accuracy using GNSS PPP, it is necessary to predict these error corrections during outages. Different prediction models for orbit and clock error corrections are discussed. A test was conducted to evaluate the A-PL positioning based on GNSS PPP and inter-PL ranges, as well as the performance of error prediction modelling. It was found that GNSS PPP combined with inter-PL ranges could achieve better converged positioning accuracy and a reduction in convergence time of GNSS PPP. However, the performance of GNSS PPP with inter-PL ranges was degraded by observing A-PLs with limited positioning accuracy. Although the performance improvement achieved by the SCIF-based distributed algorithms was smaller than that by the centralised algorithm, greater robustness in dealing with deteriorated observed A-PLs' trajectory data was demonstrated by the distributed algorithms. In addition, short-term prediction models were analysed, and their performance was shown to reduce the effect of error correction outages on A-PL positioning accuracy.
Reconciling fault-tolerant distributed algorithms and real-time computing
