State-space-varied moving horizon estimation for real-time PPP in the challenging low-cost antenna and chipset

The moving horizon estimation (MHE) always plays an important estimation role in low-cost devices. We introduced the MHE into the precise point positioning (PPP). However, the dimension of the state-space vector is constant in the conventional MHE, it limits applications of the MHE algorithm in PPP where the number of estimated parameters is varied, such as the number of integer ambiguity and ionosphere varying with satellites. We presented a state-space-varied moving horizon estimation (SSV-MHE) algorithm for PPP. Meanwhile, the Cramer-Rao Lower Bound (CRLB) is derived to analyze the convergence of SSV-MHE. Finally, the real-time PPP field experiments are conducted to verify the performance of SSV-MHE in different environments by using the devices with low-cost antenna and chipset, such as the receiver Ublox C099 and smartphone Huawei Nova 8 pro. The results show that the mean convergence time of the SSV-MHE algorithm is approximate to that of the Extended Kalman Filter (EKF) algorithm. As to the mean accuracy, there is a 9.8% increase, while to the mean precision, the increase, which is relatively larger, is 28.7%. Although the field test results show a similar convergence time of the two algorithms, the positioning performance, in terms of accuracy and precision, almost always has a commendable improvement for the SSV-MHE algorithm, especially in a poor environment. This indicates that the SSV-MHE algorithm can make positioning results of PPP accurate and stable when a low-cost receiver encounters a harsh environment.