Citation: Xu, S.; Long, J.; Wang, J.;
Zhang, W. An Efficient Method to
Compensate Receiver Clock Jumps in
Real-Time Precise Point Positioning.
Remote Sens. 2022, 14, 5222. https://
doi.org/10.3390/rs14205222
Academic Editors: Damian
Wierzbicki and Kamil Krasuski
Received: 3 September 2022
Accepted: 14 October 2022
Published: 19 October 2022
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Article
An Efficient Method to Compensate Receiver Clock Jumps in
Real-Time Precise Point Positioning
Shaoguang Xu
1,
* , Jialu Long
2
, Jinling Wang
3
and Wenhao Zhang
3
1
Faculty of Geoscience and Environmental Engineering, Southwest Jiaotong University,
Chengdu 611756, China
2
School of Natural Resources and Surveying, Nanning Normal University, Nanning 530001, China
3
School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia
* Correspondence: shaoguangxu@swjtu.edu.cn; Tel.: +86-158-8225-6854
Abstract:
In global navigation satellite systems (GNSSs)-based positioning, user receiver clock jump
is a common phenomenon on the low-cost receiver clocks and can break the continuity of observation
time tag, carrier phase and pseudo range. The discontinuity may affect precise point positioning-
related parameter estimation, including receiver clock error, position, troposphere and ionosphere
parameters. It is important to note that these parameters can be used for timing, positioning,
atmospheric inversion and so on. In response to this problem, the receiver clock jumps are divided
into two types. The first one can be expressed by the carrier phase and pseudo range having the
same scale jump, and the second one is that they are having different scale jumps. For the first type, if
a small priori variance of receiver clock error is provided, it can affect the accuracy of ionospheric
delay estimation both in static and kinematic mode, while in the latter mode, it also affects position
estimation. However, if large process noise is provided, numerical problems may arise since other
parameters’ process noises are usually small, it is proposed to use the single point positioning with
pseudo ranges to provide a priori value of receiver clock error, and an empiric value is assigned
to its prior variance, this handle can avoid the above problems. For the second type, instead of
compensating so many raw observations in the traditional methods, it is proposed to compensate the
ambiguities at the clock jump epochs only in a new method. The new method corrects the Melbourne–
Wubbena (MW) combination firstly in order to avoid the misjudging of cycle slips for current epoch,
and the second step is to compensate the corresponding ambiguities, then, after Kalman filtering,
the MW and its mean should be corrected back in order to avoid the misjudging of cycle slips at
the next epoch. This approach has the advantage of handling the clock jump epoch-wise and can
avoid correcting the rest of the observations as the traditional methods used to. With the numerical
validation examples both in static and kinematic modes, it shows the new method is simple but
efficient for real time precise point positioning (PPP).
Keywords:
receiver clock jump; precise point positioning; receiver clock error; ambiguity; Melbourne–
Wubbena combination
1. Introduction
The clock is important for global navigation satellite systems (GNSSs) positioning,
since the GNSS observation is measured with satellite and receiver clocks’ difference
multiplied by the light speed [
1
,
2
]. In order to archive the highest positioning accuracy, the
satellites in space are installed with atomic clocks which are very stable. At the user end,
most of the receivers on the ground are usually equipped with low-cost clocks except some
special sites for time datum or other special use. Currently, in order to keep consistent with
global positioning system (GPS) time, there are satellite clock error and receiver clock error
for satellite and receiver during the positioning [
1
,
2
]. The clock’s character is shown on
either satellite clock error or receiver clock error. For double difference positioning, the clock
Remote Sens. 2022, 14, 5222. https://doi.org/10.3390/rs14205222 https://www.mdpi.com/journal/remotesensing
