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Analysis of a variational Bayesian adaptive cubature Kalman filter tracking loop for high dynamic conditions

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Abstract and Figures

Under high dynamic conditions, a robust tracking loop is essential for accuracy positioning with the global position system. In previous studies, the extended Kalman filter (EKF)-based tracking loop technology has been proven better than the traditional tracking loop technology under high dynamic conditions. However, the performance of EKF may degrade because under high dynamic conditions, the statistics of measurement noise may change with time. In order to improve the robustness of the tracking loop under high dynamic conditions, the variational Bayesian adaptive cubature Kalman filter (VBACKF) algorithm with different types of measurement noise variances is proposed and used to track the carrier and code in this study. In the proposed algorithm, the measurement noise is considered as random variables and dynamically estimated by variational Bayesian theory. We take into consideration the two-measurement model with measurements in-phase and quadra-phase prompt (IP and QP), and the six-measurement model with measurements in-phase and quadra-phase prompt, early and late (IP, QP, IE, QE, IL and QL), and compare the proposed method with the EKF- and CKF-based tracking loops. The analytical and simulation results show that the VBACKF-based tracking loop performs better than both the EKF- and CKF-based tracking loops. Furthermore, the influence on the tracking loop of the different numbers of measurements used in the measurement model is also investigated. The results show that the phase, code and frequency tracking performances of EKF-, CKF- and VBACKF-based six measurements outperform those of the corresponding filter-based two measurements under dynamic conditions.
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ORIGINAL ARTICLE
Analysis of a variational Bayesian adaptive cubature Kalman
filter tracking loop for high dynamic conditions
Zhi-yong Miao
1
Yun-long Lv
1
Ding-jie Xu
2
Feng Shen
1
Shun-wan Pang
1
Received: 14 June 2015 / Accepted: 17 December 2015 / Published online: 2 January 2016
ÓSpringer-Verlag Berlin Heidelberg 2016
Abstract Under high dynamic conditions, a robust
tracking loop is essential for accuracy positioning with the
global position system. In previous studies, the extended
Kalman filter (EKF)-based tracking loop technology has
been proven better than the traditional tracking loop tech-
nology under high dynamic conditions. However, the per-
formance of EKF may degrade because under high
dynamic conditions, the statistics of measurement noise
may change with time. In order to improve the robustness
of the tracking loop under high dynamic conditions, the
variational Bayesian adaptive cubature Kalman filter
(VBACKF) algorithm with different types of measurement
noise variances is proposed and used to track the carrier
and code in this study. In the proposed algorithm, the
measurement noise is considered as random variables and
dynamically estimated by variational Bayesian theory. We
take into consideration the two-measurement model with
measurements in-phase and quadra-phase prompt (IP and
QP), and the six-measurement model with measurements
in-phase and quadra-phase prompt, early and late (IP, QP,
IE, QE, IL and QL), and compare the proposed method
with the EKF- and CKF-based tracking loops. The ana-
lytical and simulation results show that the VBACKF-
based tracking loop performs better than both the EKF- and
CKF-based tracking loops. Furthermore, the influence on
the tracking loop of the different numbers of measurements
used in the measurement model is also investigated. The
results show that the phase, code and frequency tracking
performances of EKF-, CKF- and VBACKF-based six
measurements outperform those of the corresponding filter-
based two measurements under dynamic conditions.
Keywords High dynamic conditions Global position
system Tracking loop Extended Kalman filter
Variational Bayesian adaptive cubature Kalman filter
Cubature Kalman filter
Introduction
In general, the Kalman filter (KF)-based tracking loop
technology includes linear KF- and extended Kalman filter
(EKF)-based tracking loops. The main difference between
these two tracking loops is the type of measurements. The
KF-based tracking loop uses the output of the discriminator
as measurements, where only the loop filter is replaced by
the KF. However, the EKF-based tracking loop directly
uses the outputs of correlator in their in-phase (I) and
quadrature (Q) signals as measurements, where both the
code and carrier discriminators and loop filters are replaced
by EKF (Woessner et al. 2006; Won et al. 2009). Although
the linear KF-based tracking loop outperforms the tradi-
tional tracking loop, the tracking errors increase because
the linearity of discriminator cannot be maintained when
&Zhi-yong Miao
mzy407@126.com
Yun-long Lv
lyl407@126.com
Ding-jie Xu
xdj407@126.com
Feng Shen
shenfeng@hrbeu.edu.cn
Shun-wan Pang
psw407@126.com
1
College of Automation, Harbin Engineering University,
Harbin 150000, Heilongjiang Province, China
2
School of Electrical Engineering and Automation, Harbin
Institute of Technology, Harbin 150000, Heilongjiang
Province, China
123
GPS Solut (2017) 21:111–122
DOI 10.1007/s10291-015-0510-0
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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BIOGRAPHY Sung-Hyuck Im is a Ph.D student in Navigation and Control System lab, the Department of Electronics Engineering, Konkuk University, Korea. He received B.Sc degree and M.Sc degree from Konkuk University in 2003 and 2005 respectively. He is interested in (Real-time) Software GNSS receiver, Generation and processing of navigation signals, Vector-based signal processing, Anti-jamming, Indoor location using repeater, Navigation sensor integration, etc. Jong-Hwa Song is a Ph.D. student in GPS system lab, the Department of Electronics Engineering, Konkuk University, Korea. He received his B.S. and M.S. degrees in Electronic Engineering from the Ajou University in 2005 and 2007, respectively. His current research interests are in Software GPS receiver, GNSS navigation algorithm, GNSS precise positioning algorithm and GPS signal processing algorithm. Gyu-In Jee is a professor in the department of Electronics Engineering at Konkuk University in Seoul, Korea. He received his Ph.D. in Systems Engineering from Case Western Reserve University. His research has been focused on GPS and navigation system. He has worked on several research and development projects: WLAN based wireless positioning system, Indoor GPS positioning using GPS repeaters, Software GNSS receiver, IEEE 802.16e based wireless location system, etc.
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