Citation: Xue, B.; Yuan, Y.; Wang, H.;
Wang, H. Evaluation of the Integrity
Risk for Precise Point Positioning.
Remote Sens. 2022, 14, 128. https://
doi.org/10.3390/rs14010128
Academic Editors: Kamil Krasuski
and Damian Wierzbicki
Received: 4 December 2021
Accepted: 27 December 2021
Published: 29 December 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Evaluation of the Integrity Risk for Precise Point Positioning
Bing Xue
1,2
, Yunbin Yuan
1
, Han Wang
1,2
and Haitao Wang
1,
*
1
State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy for Precision Measurement
Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China;
xuebing@asch.whigg.ac.cn (B.X.); yybgps@asch.whigg.ac.cn (Y.Y.); wanghan@apm.ac.cn (H.W.)
2
College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
* Correspondence: whigg_wang@whigg.ac.cn
Abstract:
Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) is an attractive
positioning technology due to its high precision and flexibility. However, the vulnerability of PPP
brings a safety risk to its application in the field of life safety, which must be evaluated quantitatively
to provide integrity for PPP users. Generally, PPP solutions are processed recursively based on
the extended Kalman filter (EKF) estimator, utilizing both the previous and current measurements.
Therefore, the integrity risk should be qualified considering the effects of all the potential observation
faults in history. However, this will cause the calculation load to explode over time, which is
impractical for long-time missions. This study used the innovations in a time window to detect
the faults in the measurements, quantifying the integrity risk by traversing the fault modes in the
window to maintain a stable computation cost. A non-zero bias was conservatively introduced
to encapsulate the effect of the faults before the window. Coping with the multiple simultaneous
faults, the worst-case integrity risk was calculated to overbound the real risk in the multiple fault
modes. In order to verify the proposed method, simulation and experimental tests were carried out
in this study. The results showed that the fixed and hold mode adopted for ambiguity resolution is
critical to an integrity risk evaluation, which can improve the observation redundancy and remove
the influence of the biased predicted ambiguities on the integrity risk. Increasing the length of the
window can weaken the impact of the conservative assumption on the integrity risk due to the
smoothing effect of the EKF estimator. In addition, improving the accuracy of observations can also
reduce the integrity risk, which indicates that establishing a refined PPP random model can improve
the integrity performance.
Keywords:
precise point positioning; integrity risk; extend Kalman filter; probability distributions;
fault modes
1. Introduction
Precise single positioning (PPP) technology can provide high-precision positioning
for Global Navigation Satellite System (GNSS) users with the help of precise correction
information, and by utilizing the code and carrier phase observations [
1
–
3
]. Generally, the
positioning accuracy of the kinematic PPP solution with float-ambiguity after convergence
can reach the decimeter to centimeter level. An even better solution and shorter convergence
time can be obtained with the integer carrier-phase ambiguities resolved correctly
[4–8]
.
Unlike traditional differential positioning, such as real time kinematic (RTK) and network
RTK, PPP is an absolute positioning technology that requires no reference stations and
can be applied anywhere in the world. Moreover, PPP can also be augmented by a
regional reference station network or integrated with satellite based augmentation system
services
[9–14]
. Benefiting from the high precision and flexibility, the application range
of PPP is gradually expanding, even moving toward the life-critical field, such as in
automotive, maritime and air navigation applications [
15
–
18
]. For users in the field relating
to life safety, the accuracy is no longer the most concerning requirement but the safety,
Remote Sens. 2022, 14, 128. https://doi.org/10.3390/rs14010128 https://www.mdpi.com/journal/remotesensing
