A closed-form formula to calculate geometric dilution of precision (GDOP) for multi-GNSS constellations

With the future global navigation satellite system (GNSS), the multi-GNSS constellations, which are composed of various single systems, will be the main navigation method in future. For the multi-GNSS constellations, the geometric dilution of precision (GDOP) is an important parameter used for satellite selection and the evaluation of positioning accuracy. However, the calculation of GDOP is a time-consuming and power-consuming task. Using Schur complement, we present a closed-form formula to calculate GDOP for multi-GNSS constellations. The formula can be applied to multi-GNSS constellations that include two, three or four different single systems. Furthermore, a closed-form formula for the case of exactly five satellites is also derived. Compared with the conventional numerical methods, the formula can reduce the amounts of multiplication and addition effectively. Numerical experiments validate the effectiveness and feasibility of the closed-form formula.

[1]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[2]  Xiaochun Lu,et al.  Impact of the GNSS Time Offsets on Positioning Reliability , 2011 .

[3]  Peter Teunissen,et al.  A proof of Nielsen's conjecture on the GPS dilution of precision , 1998 .

[4]  Diane Valérie Ouellette.  Schur complements and statistics , 1981 .

[5]  Dah-Jing Jwo,et al.  NEURAL NETWORK-BASED GEOMETRY CLASSIFICATION FOR NAVIGATION SATELLITE SELECTION. , 2003 .

[6]  G. Lachapelle,et al.  Assessment of GPS/GLONASS RTK Under Various Operational Conditions , 2009 .

[7]  Yunlong Teng,et al.  New Characteristics of Geometric Dilution of Precision (GDOP) for Multi-GNSS Constellations , 2014, Journal of Navigation.

[8]  A. Leick.  GPS satellite surveying , 1990 .

[9]  Jinling Wang,et al.  GNSS receiver autonomous integrity monitoring (RAIM) performance analysis , 2006 .

[10]  Dan Simon,et al.  Navigation satellite selection using neural networks , 1995, Neurocomputing.

[11]  Dah-Jing Jwo,et al.  Neural network-based GPS GDOP approximation and classification , 2006 .

[12]  Dah-Jing Jwo,et al.  Applying Back-propagation Neural Networks to GDOP Approximation , 2002, Journal of Navigation.

[13]  Washington Y. Ochieng,et al.  An Assessment of the RAIM Performance of a Combined Galileo/GPS Navigation System Using the Marginally Detectable Errors (MDE) Algorithm , 2002, GPS Solutions.

[14]  Markus Rippl,et al.  Advanced RAIM Architecture Design and User Algorithm Performance in a Real GPS, GLONASS and Galileo Scenario , 2013 .

[15]  Jun Zhang,et al.  A Fast Satellite Selection Algorithm: Beyond Four Satellites , 2009, IEEE Journal of Selected Topics in Signal Processing.

[16]  Jijie Zhu,et al.  Calculation of geometric dilution of precision , 1992 .

[17]  Jinling Wang,et al.  On the Availability of Fault Detection and Exclusion in GNSS Receiver Autonomous Integrity Monitoring , 2009, Journal of Navigation.

[18]  E. Haynsworth.  Determination of the inertia of a partitioned Hermitian matrix , 1968 .

[19]  S. Doong,et al.  A closed-form formula for GPS GDOP computation , 2009 .

[20]  Yuanxi Yang,et al.  Contribution of the Compass satellite navigation system to global PNT users , 2011 .

[21]  Chih-Hung Wu,et al.  A Study on GPS GDOP Approximation Using Support-Vector Machines , 2011, IEEE Transactions on Instrumentation and Measurement.