Table.1: Calculation of Statistical, Spatial decorrelation, and Gradient errors of GIVE
| IGP location in Latitude Longitude |
Surrounding IPPS |
Statistical error of GIVE in m. |
Spatial Decorrelation and Gradient errors of GIVE in m. |
Combined GIVE in m. |
| Latitude in deg. |
Longitude in deg. |
Distance form IGP to IPP in nmi |
| 15,75 |
17.2254 |
74.99734 |
151.35 |
7.8840 |
0.3393
1.5963 |
8.0511 |
| 14.8973 |
77.9728 |
172.39 |
| 14.55362 |
77.8489 |
127.51 |
| 19.41429 |
77.90869 |
313.7 |
| 20,75 |
14.5536 |
72.8489 |
348.56 |
6.9000 |
0.6859
3.2277 |
7.6484 |
| 19.4142 |
77.9086 |
167.28 |
| 20.6898 |
79.9896 |
284.34 |
| 23.3134 |
73.1131 |
225.47 |
| 20,70 |
14.5536 |
72.8489 |
364.12 |
9.4251 |
0.7166
3.3718 |
10.0357 |
| 23.3134 |
73.1133 |
265.19 |
| 15.7613 |
66.2421 |
331.31 |
| 15,70 |
14.55362 |
72.8489 |
171.08 |
7.3110 |
0.6430
3.0259 |
7.9385 |
| 15.76133 |
66.24219 |
222.53 |
| 17.52254 |
74.99734 |
326.77 |
| 10,75 |
14.8973 |
77.9728 |
342.33 |
6.6177 |
0.6244
3.17 |
7.3643 |
| 14.55362 |
72.8489 |
301.33 |
| 9.960221 |
79.97086 |
293.72 |
| 10,80 |
9.960221 |
79.97086 |
2.9546 |
12.6782 |
0.6244
2.9383 |
13.0292 |
| 12.31622 |
82.23859 |
191.84 |
| 14.8973 |
77.9728 |
317.31 |
Fit
i is the delay at the corresponding measurement pierce point computed by user. The factor 3.3 and si are introduced as the GIVE is designed to bound 99.9% of errors.
Spatial Decorrelation Error
Since WRS measured IPPs and user IPPs are widely separated, the spatial variability, or decorrelation, of the ionosphere becomes important. Therefore, an additional interpolation-based on GIVE term that depends on the distance between the user IPP and the WRS measured IPP is necessary. Since the locations of user IPPs are unknown during GIVE generation, a “worst case” distance D
MAX for a user in the region surrounding an IGP is to be calculated.
Spatial Decorrelation Error term is GIVE
DEC = bV
MAX D
MAX
Where
V
MAX = largest vertical ionosperic delay in the four quadrants
surrounding the IGP
b = Scaling factor based on estimates of decorrelation derived from previous experiences of Jet Propulsion Laboratories (JPL, USA).
Gradient
WRS measurements are mapped to vertical, and IGP calibration delays to slant paths, using the obliquity function, which is based on the thin shell ionosphere model. Obliquity factor depends on elevation of a slant line of sight, but independent of azimuth. Therefore, calibration errors for users will arise that depend, on the local horizontal electron density gradients found in the real ionosphere that cause azimuthal delay variation. Such effects are accounted for by a mapping-based
GIVE term GIVE
GRAD = gÑ
MAX
Where
Ñ
MAX = Estimate of the maximum delay gradient surrounding the IGP
b = Scaling factor based on studies of obliquity function errors made at JPL. a, b and g values are taken from the JPL studies which are applicable for mid latitude region. Due to lack of relevant Indian values the same values are used.
Results and Discussion
The GPS data required for calculation of IPPs is collected from a dual frequency receiver located at NGRI, Hyderabad, India. The data corresponds to 18 th April, 1998. Latitude and longitude of some of the IPPs monitored in the four surrounding square grids (10° -20° latitude and 70° -80° longitude band) cover some of the IGPs. The IPP latitude, longitude, vertical ionospheric delay, slant factor, elevation angles and IGP delays are calculated using standard formulas (Conker, 1995) and also IRI-90 model is used in the prediction delays at various IPPs for comparison. The distances between IGP and the monitored IPPs are calculated using an algorithm known as Radar Operation Analysis Tool (ROAT, Westing House Corporation, USA). The GIVE
SE, GIVE
GRAD and GIVE
DEC terms and GIVE
TOT value are presented in Table1.
GIVE increases by 0.5m when gradient is 0.5cm/km and g is 1.6 x 10
6 meters . GIVE increases by 5% at 500km when b = 1.6 x 10
-7 meters. The combined GIVE is mainly dependent on the statistical error. For example, at 10° latitude and 75° longitude the GIVES
E and GIVE
TOT are 6.6177 and 7.3643 m respectively. The values of the a, b and g may not be applicable to Indian subcontinent. These results give only broad view of the influence of these parameters on GIVE.
Conclusions
To define the ionosphere above the Indian subcontinent, delays at 60 IGPs are to be deined. As India comes under equatorial region where ionospheric behavior is dominated by intense irregularities and large horizontal gradients associated with F-region equatorial anomaly, more care is to be taken in the calculation of GIVE. In the calculation of GIVE, the a, b and g are taken from the literature. Using Indian ionospheric data, better values for these parameters are to be found. These values may not be appropriate for Indian conditions. However, the GIVE calculations presented here give an insight on the influence of these parameters on GIVE.
Acknowledgements
The above work has been carried out under the project entitled “WAAS for India–A Test-Bed Approach” sponsored by the Ministry of Information Technology, Govt. of India, New Delhi, vide sanction order letter No. DE/SED/TDP–152 dated 31-03-1999.
References
- Sarma, A. D., G. Sasi Bhushana Rao and V. Venkata Rao, “Ionospheric Reference Station Placement for INWAAS – A Preliminary Study” J. of Ind. Geophys. Union, Vol. 4, No. 1, pp. 41-49, 2000.
- Minimum Operational Performance Standards for GPS/ WAAS Airborne Equipment”, RTCA/DO-229B, October6, 1999.
- Harris Ian, Manucci A, Iijima B, Lindqwister U, Muna D, Pi X and Wilson B C. and Dennis, L. Shaver, “Ionospheric Effects Symposium”,. Pp 221-229,1999.
- Conker R., El-Arini, B., Albertson, T. and Klobuchar, J., “Development of Real-time algorithms to estimate the ionospheric error bounds for WAAS” ION GPS, 1995.
- “Radar Operation and Analysis Tool”, Westing House Corporation, USA, 1995.