An optimal linear combination model to accelerate PPP convergence using multi-frequency multi-GNSS measurements

We propose an optimal ionospheric-free linear combination (LC) model for dual- and triple-frequency PPP which can accelerate carrier phase ambiguity and decrease the position solution convergence time. To reduce computational complexity, a near-optimal LC model for triple-frequency PPP is also proposed. The uncombined observation (UC) model estimating ionospheric delay gives the best performance, because all information contained within the observations are kept. The proposed optimal and near-optimal LC models are compared with the UC model, using both simulated and real data from five GNSS stations in Australia over 30 consecutive days in 2017. We determine a necessary and sufficient condition for a combination operator matrix which can eliminate the first-order ionospheric component to obtain the optimal LC model for dual- and triple-frequency PPP. Numerical results show that the proposed LC model is identical to the UC model. In addition, the proposed near-optimal LC model even outperforms the current LC models. Ambiguity resolution (AR) is faster and positioning accuracy is improved using the optimal triple-frequency LC model compared to using the optimal dual-frequency LC model. An average time-to-first-fix of 10min with a fixing success rate of 95% can be achieved with triple-frequency AR.