Statistical Comparison of Various Interpolation Algorithms for Grid-Based Single Shell Ionospheric Model over Indian Region

Ashish K Shukla, Neha Nagori, Saurabh Das, Nishkam Jain, M R Sivaraman, K Bandyopadhyay

SATCOM & IT Applications Area, Space Applications Centre, Indian Space Research Organisation, Ahmedabad, 380015, INDIA.

DOI:                 

Abstract

Future Satellite Based Navigation Systems based on GPS, like US Wide Area Augmentation Sysytem (WAAS), are of global interest to the scientific community. Precise estimation of ionospheric delay is most crucial for successful implementation of the systems. Due to the complex ionospheric structure and large variation of Total Electron Content (TEC) in low latitudes, it is necessary to compare and validate the efficiency of the existing algorithms in this region. In this study, performances of the various interpolation algorithms for TEC calculation at ionospheric grid point (IGP) and user position for grid-based Single Shell Model have been tested for 72 test days of 2005. Based on the results obtained from this analysis, it has been found that, for the Indian region, it would be more suitable to use Ordinary Kriging in place of Planar Fit to estimate delay at an IGP (as used by US WAAS). It has also been found that Ordinary Kriging performs better than the Bilinear Interpolation technique at the user end.

Keywords

GAGAN, Ionosphere, Interpolation algorithm, Single Shell Model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Acharya R., Nagori N., Jain N., Sunda S., Sivaraman M. R., Bandyopadhyay K. (2006) Ionospheric Correlation Analysis for GAGAN, Proceedings of CODEC-2006,Kolkata,India.
[2]	Acharya R., Nagori N., Jain N., Sunda S., Sivaraman M. R., Bandyopadhyay K. (2007) Ionospheric studies for the implementation of GAGAN, Indian Journal of Radio and Space Physics.
[3]	Blanch J (September 2002). An Ionospheric Estimation Algorithm for WAAS based on Kriging, ION's GPS Meeting, Portland
[4]	Blanch J. (2003) Using Kriging bound satellite ranging errors due to the ionosphere, PhD. Thesis, Stanford University.
[5]	Blanch J., Walter T., Enge P.(January 2003), Adapting Kriging to the WAAS MOPS Ionospheric Grid, ION's National Technical Meeting, Anaheim, CA
[6]	CODE website, http://www.aiub.unibe.ch/ionosphere.html.
[7]	Cressie N.A.C, (1993) Statistics for spatial data. Revised edition. John Wiley and Sons, New York.
[8]	Davis J. C.(1986), Statistics and data analysis in geology, 2nd edition, John Wiley and sons, NewYork
[9]	Gao Y. and Liu Z.(2002): Precise Ionosphere Modeling Using Regional GPS Network Data, Journal of Global Positioning Systems vol 1( 1): 18-24
[10]	Klobuchar J A (1987), Ionospheric Time Delay Algorithm for Single Frequency GPS Users, IEEE Transactions on Aerospace and Electronics Systems,Vol. AES-23 (3): 325-31.
[11]	Mannucci A.J, Wilson B.D, Yuan D.N, Ho C.H, Lindqwister U.J, Runge T.F. (1998), A Global mapping technique for GPS-derived ionospheric total electron content measurements, Radio Science, 33(3): 565-582.
[12]	Misra P. and Enge P. (2001), Global Positioning System Signals, Measurements and Performance, G-J Press, Massachusetts.
[13]	Parkinson B. W., Spilker J. J., Axelrad P., and Enge P., Ed (1996), Global Positioning System: Theory and Applications (Progress in Astronautics, vols. 62 and 63) Washington, DC: AIAA, vol. 1, Chap. 12: 492.
[14]	Rama Rao P.V.S, Niranjan K., Prasad D.S.V.V.D, Gopi Krishna S, Uma G (2006), On the validity of the ionospheric pierce point (IPP) altitude of 350 km in the Indian equatorial and low-latitude sector. Annales Geophysics, Vol 24: 2159-2168.
[15]	RTCA special committee 159 (November 2001), Minimum Operational Performance Standards for Airborne equipment using Global Positioning System/Wide Area Augmented System, RTCA/DO – 229 C
[16]	Sardon E., Rus A. and Zarroa N. (1994) Estimation of the transmitter and receiver differential biases and the ionospheric Total Electron Content from GPS observations, Radio Science, vol. 29: 577.
[17]	Sardon E., and Zarrao N. (1997), Estimation of total electron content using GPS data: How stable are the differential satellite and receiver instrumental biases?, Radio Science, vol. 32(5):1899-1910.
[18]	Walter T, Hansen A, Blanch J, and Enge P (September 2000) Robust detection of ionospheric irregularities, in proceedings of ION GPS, Salt Lake City, UT.
[19]	Walter T(2002), Introduction to the Wide Area Augmentation System, Journal of Global Positioning Systems, vol 1(2): 151-153
[20]	WAAS (2008) Wide area augmentation system, http://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/waas/.
[21]	Wielgosz P, Brzezinska D and Kashani I(2003), Regional Ionosphere Mapping with Kriging and Multiquadric Methods, Journal of Global Positioning Systems, vol 2(1):48-55
[22]	Wilson, B. D. and Mannucci A. J., Instrumental Biases in Ionospheric Measurements derived from GPS data, Proceedings of ION GPS’93, Salt Lake City, 1993.