Multi-dimensional particle filter-based estimation of inter-system phase biases for multi-GNSS real-time integer ambiguity resolution

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm.

[1]  Peter Teunissen,et al.  Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution , 2013, GPS Solutions.

[2]  M. Meindl,et al.  GNSS processing at CODE: status report , 2009 .

[3]  Y. Bock,et al.  Global Positioning System Network analysis with phase ambiguity resolution applied to crustal deformation studies in California , 1989 .

[4]  Fredrik Gustafsson,et al.  Particle filters for positioning, navigation, and tracking , 2002, IEEE Trans. Signal Process..

[5]  James V. Candy,et al.  Bayesian Signal Processing , 2009 .

[6]  Anton J. Haug.  Bayesian Estimation and Tracking: A Practical Guide , 2012 .

[7]  D. A. Force,et al.  Combined Global Navigation Satellite Systems in the Space Service Volume , 2015 .

[8]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[9]  Maorong Ge,et al.  Determining inter-system bias of GNSS signals with narrowly spaced frequencies for GNSS positioning , 2018, Journal of Geodesy.

[10]  Xingxing Li,et al.  Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo , 2015, Journal of Geodesy.

[11]  Robert Odolinski,et al.  Combined BDS, Galileo, QZSS and GPS single-frequency RTK , 2014, GPS Solutions.

[12]  G. Gendt,et al.  Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations , 2008 .

[13]  H.-J. Euler,et al.  On a Measure for the Discernibility between Different Ambiguity Solutions in the Static-Kinematic GPS-Mode , 1991 .

[14]  Dmitry Kozlov,et al.  Instant RTK cm with Low Cost GPS+GLONASS C/A Receivers , 1997 .

[15]  Chris Rizos,et al.  GPS and GLONASS Integration: Modeling and Ambiguity Resolution Issues , 2001, GPS Solutions.

[16]  Maorong Ge,et al.  Particle filter-based estimation of inter-frequency phase bias for real-time GLONASS integer ambiguity resolution , 2015, Journal of Geodesy.

[17]  P. Teunissen,et al.  The ratio test for future GNSS ambiguity resolution , 2013, GPS Solutions.

[18]  I D.,et al.  Processing Combined GPS / GLONASS Data at swisstopo ' s Local Analysis Center , 2008 .

[19]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[20]  Peter Teunissen,et al.  GPS Carrier Phase Ambiguity Fixing Concepts , 1998 .

[21]  G. Blewitt.  Carrier Phase Ambiguity Resolution for the Global Positioning System Applied to Geodetic Baselines up to 2000 km , 1989 .

[22]  Nobuaki Kubo,et al.  Mixed GPS–BeiDou RTK with inter-systems bias estimation aided by CSAC , 2017, GPS Solutions.

[23]  K. Jong,et al.  Interchangeable Integration of GPS and GLONASS by Using a Common System Clock in PPP , 2013 .

[24]  Maorong Ge,et al.  Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution , 2017, GPS Solutions.

[25]  Dennis Odijk,et al.  ESTIMATION OF DIFFERENTIAL INTER-SYSTEM BIASES BETWEEN THE OVERLAPPING FREQUENCIES OF GPS , GALILEO , BEIDOU AND QZSS , 2013 .

[26]  Pawel Wielgosz,et al.  Accounting for Galileo–GPS inter-system biases in precise satellite positioning , 2014, Journal of Geodesy.

[27]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[28]  James V. Candy,et al.  Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods , 2009 .

[29]  Peter Teunissen,et al.  PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK , 2016, Journal of Geodesy.