Satellite Orbit and Ephemeris Determination using Inter Satellite Links
Satellite Orbit and Ephemeris Determination using Inter Satellite Links Satellite Orbit and Ephemeris Determination using Inter Satellite Links
Software DescriptionInter Satellite LinksElectron Density Distribution1.00E+131.00E+121.00E+11n e [m -3 ]1.00E+101.00E+091.00E+081.00E+0750165032504850645080509650112501285014450160501765019250208502245024050256502725028850304503205033650352503685038450Altitude [km]Figure 5-6 Chapman Profile of the IonosphereIt shows that the ionospheric density has a large maximum at approximately 350 – 400 km.Additional to this nominal shape, the ionosphere is subject to the local time (i.e. the sunangle), disturbances, ionospheric storms and the solar cycle. For the simulations in this thesis,a simple model for the ionosphere had to be sufficient. To account for the nominal shape ofthe ionosphere, the Chapman profile has been approximated by three ionospheric "layers",with linear electron density distribution.TEC = a ⋅ r + bEq. 5.3-19iiiwithi = 0 from 50 - 380 km altitudei = 1 for altitudes between 380 and 1000 kmi = 2 for altitudes between 1000 and 30000 kmThis linear approximation has the advantage that the electron content can be integratedpiecewise analytically, only as a function of the known starting and end points of the signalpath, thus increasing computation speed compared to a numerical integration of the curvedprofile.The ionospheric delay is then obtained fromPage 82R. Wolf
Inter Satellite LinksSoftware Description∆IO40.3= ⋅ TEC2fEq. 5.3-20whithTEC Total Electron Content along the signal pathf FrequencyThe error of the model has been assumed to be 50%. This value is added to the observationvariance.5.3.3 Tropospheric ModelA radio signal is also subject to tropospheric refraction, causing a delay in the signal receptiontime, similar to the ionospheric delay, but much less in magnitude. There are severaltropospheric models in use. The one utilised in the simulations is the Saastamionentropospheric model [HWL-94].with∆pTeTr0.002277= ⋅ (p +πcos( - δ)21255π( + 0.05) ⋅ e - tan( - δ))T2atmospheric pressureTemperaturePartial pressure of water vapourEq. 5.3-21δ ElevationIt can be assumed as sufficient to take average values for p and T and e. The residual error hasbeen assumed as 20 % of the result from above equation.5.3.4 Multipath SimulationMultipath is not easy to model, but can be assumed as being a more or less slowly varyingbias. It was simulated using the functionyA⋅sinωt= eEq. 5.3-22which resembles a multipath figure with a slowly varying geometry. All delays and errorshave been added to the measurements as biases.R. Wolf Page 83
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Software Description<strong>Inter</strong> <strong>Satellite</strong> <strong>Links</strong>Electron Density Distribution1.00E+131.00E+121.00E+11n e [m -3 ]1.00E+101.00E+091.00E+081.00E+0750165032504850645080509650112501285014450160501765019250208502245024050256502725028850304503205033650352503685038450Altitude [km]Figure 5-6 Chapman Profile of the IonosphereIt shows that the ionospheric density has a large maximum at approximately 350 – 400 km.Additional to this nominal shape, the ionosphere is subject to the local time (i.e. the sunangle), disturbances, ionospheric storms <strong>and</strong> the solar cycle. For the simulations in this thesis,a simple model for the ionosphere had to be sufficient. To account for the nominal shape ofthe ionosphere, the Chapman profile has been approximated by three ionospheric "layers",with linear electron density distribution.TEC = a ⋅ r + bEq. 5.3-19iiiwithi = 0 from 50 - 380 km altitudei = 1 for altitudes between 380 <strong>and</strong> 1000 kmi = 2 for altitudes between 1000 <strong>and</strong> 30000 kmThis linear approximation has the advantage that the electron content can be integratedpiecewise analytically, only as a function of the known starting <strong>and</strong> end points of the signalpath, thus increasing computation speed compared to a numerical integration of the curvedprofile.The ionospheric delay is then obtained fromPage 82R. Wolf
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