the propagation delay depends on the total electron content (TEC) along the signals path and on the frequency of the signal itself as well as on the geographic location and time(ionosphere is most active at noon, quiet at night; 1l-year Sun spot cycle the ionospheric terms for range and phase are as follows. range, and integration of the refractive index renders the measured measured distance s=nds (mo=403 TEC and Aono =-40 TEC where total electron content TEC TEC=.dso[10 6 electrons per m where so is the geometric range at zenith differencing technique and ion-free combination of observations on both frequencies eliminate first-order terms, secondary effects can be neglected for the short baselines differential effect on the long baselines: 1-3 cm wv Principles of the Global Positioning System 20054-1(1 year Sun Spo t Cvcle SUNSPOT NUMBER 100 Cyole 23 Sunspot Number Prediction 13801986199019952000200 Gv Principles of the Global Positioning System 200541(12
6 Principles of the Global Positioning System 2005-4-1 11 Propagation media cont. • the propagation delay depends on the total electron content (TEC) along the signal’s path and on the frequency of the signal itself as well as on the geographic location and time (ionosphere is most active at noon, quiet at night; 11-year Sun spot cycle) • integration of the refractive index renders the measured range, and the ionospheric terms for range and phase are as follows: • differencing technique and ion-free combination of observations on both frequencies eliminate first-order terms, secondary effects can be neglected for the short baselines • differential effect on the long baselines: 1-3 cm TEC [10 electrons per m ] where is the geometric range at zenith where total electron content TEC 40.3 and 40.3 measured distance 0 16 2 0 2 2 N ds s TEC f TEC f s n ds e iono ph iono gr ∫ ∫ = ∆ = ∆ = − = Principles of the Global Positioning System 2005-4-1 12 11-year Sun Spot Cycle
Estimated ionospheric Group Delay for GPS Signal Residual range Error First order 16.2m 26.7m 0.0 Second Order: 1/f 3 ~1.6cm ~3.3cm ~-1.1cm Third Order: 1/f4 0.86mm 2.4 mm Calibrated llf term Based on a Thin Layer ~1-2mm ionospheric Model The phase advance can be obtained from the above table by multiplying each number by, -0.5 and -1/3 for the 1/f2,1/f and l/fterm, respectively wy Principles of the Global Positioning System 13 ionospheric Effect Removal by Using Dual Frequency Receivers ionosphere-free phase measurement Φ12=a1Φ1+a2 =p+T+a1N+a12N2+aE+a2E22=-2 f2-f2 similarly, ionosphere-free pseudorange can be obtained R2=R-2R2 The conditions applied are that sum of ionospheric effects on both frequencies multiplied by constants to be determined must be zero second condition is for example that sum of the constants is 1,or one constant is set to 1(verify!) Principles of the Global Positioning System 20054-1(14
7 Principles of the Global Positioning System 2005-4-1 13 L1 L2 Residual Range Error First Order: 1/f 2 16.2 m 26.7 m 0.0 Second Order: 1/f 3 ~ 1.6 cm ~ 3.3 cm ~ -1.1 cm Third Order: 1/f 4 ~ 0.86 mm ~ 2.4 mm ~ -0.66 mm Calibrated 1/f 3 Term Based on a Thin Layer Ionospheric Model ~ 1-2 mm The phase advance can be obtained from the above table by multiplying each number by -1, -0.5 and -1/3 for the 1/f 2, 1/f 3 and 1/f 4 term, respectively Estimated Ionospheric Group Delay for GPS Signal Principles of the Global Positioning System 2005-4-1 14 • ionosphere-free phase measurement Φ ΦΦ 12 1 1 2 2 1 1 1 2 2 2 11 2 2 , = + =++ + + + α α ρ αλ αλ αε αε TN N α α 1 1 2 1 2 2 2 2 2 2 1 2 2 2 = − = − − f f f f f f • similarly, ionosphere-free pseudorange can be obtained • The conditions applied are that sum of ionospheric effects on both frequencies multiplied by constants to be determined must be zero; second condition is for example that sum of the constants is 1, or one constant is set to 1 (verify!). 2 2 2 2 1 1,2 1 R f f R = R − Ionospheric Ionospheric Effect Removal by Effect Removal by Using Dual Frequency Receivers Using Dual Frequency Receivers