Article
Polar Region Integrated Navigation Method Based on
Covariance Transformation
Yongjian Zhang, Lin Wang *, Guo Wei and Chunfeng Gao
Citation: Zhang, Y.; Wang, L.; Wei,
G.; Gao, C. Polar Region Integrated
Navigation Method Based on
Covariance Transformation. Appl. Sci.
2021, 11, 9572. https://doi.org/
10.3390/app11209572
Academic Editors: Kamil Krasuski
and Damian Wierzbicki
Received: 8 June 2021
Accepted: 12 October 2021
Published: 14 October 2021
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Attribution (CC BY) license (https://
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4.0/).
College of Advanced Interdisciplinary Studies, National University of Defense Technology,
Changsha 410073, China; zhang_yongjian15@163.com (Y.Z.); nudtweiguo@163.com (G.W.);
neil1989@126.com (C.G.)
* Correspondence: wanglin11@nudt.edu.cn
Abstract:
Aircraft flying the trans-arctic routes usually apply inertial navigation mechanization in
two different navigation frames, e.g., the local geographic frame and the grid frame. However,
this change of navigation frame will cause filter overshoot and error discontinuity. To solve this
problem, taking the inertial navigation system/global navigation satellite system (INS/GNSS) in-
tegrated navigation system as an example, an integrated navigation method based on covariance
transformation is proposed. The relationship of the system error state between different navigation
frames is deduced as a means to accurately convert the Kalman filter’s covariance matrix. The
experiment and semi-physical simulation results show that the presented covariance transformation
algorithm can effectively solve the filter overshoot and error discontinuity caused by the change of
navigation frame. Compared with non-covariance transformation, the system state error is thereby
reduced significantly.
Keywords: covariance transformation; integrated navigation; polar region
1. Introduction
Considering that the distance of a great circle flight route is shorter, using trans-arctic
routes can accomplish great savings in flying time when aircraft make transcontinental
flights. Due to the demands of flight safety, each aircraft usually uses an INS/GNSS inte-
grated navigation system to provide high-precision navigation information. The INS/GNSS
integrated navigation system has broad development prospects. Previous literature [
1
]
proposed an integrated navigation scheme based on INS and GNSS single-frequency pre-
cision point positioning, which is expected to be an advantage for low-cost precise land
vehicle navigation applications. Several researchers [
2
,
3
] have discussed the application of
GNSS/INS on railways. Traditional INS/GNSS-integrated navigation algorithms are based
on a north-oriented geographic frame. However, as the latitude increases, the traditional
algorithms lose their efficacy in the polar region because of the meridian convergence.
To solve this problem, when the aircraft is in the polar region, pilots usually plan their
route based on polar-adaptable coordinate frames, such as the Earth-centered Earth-fixed
frame (e-frame) [
4
], transversal Earth frame (t-frame) [
5
,
6
], pseudo-Earth frame [
7
], wander
frame [8] and grid frame (G-frame) [9,10].
Although these coordinate frames are adaptable to polar regions, they cannot ac-
complish successful global navigation individually because some of them have specific
mathematical singularities, such as the t-frame, pseudo-Earth frame, wander frame, and
G-frame. These coordinate frames are usually adopted only in the polar region, and the
local geographic frame (n-frame) is used as the reference navigation frame in non-polar
regions. The e-frame can be used for continuous worldwide navigation. However, because
the e-frame adopts Cartesian coordinates, the height channel is coupled with three rectan-
gular coordinates but this causes position errors to diverge rapidly and brings difficulties
to damping filtering. In addition, the e-frame does not have an explicit azimuth, which is
Appl. Sci. 2021, 11, 9572. https://doi.org/10.3390/app11209572 https://www.mdpi.com/journal/applsci
