Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Software DescriptionInter Satellite LinksK R Link technology factor for ranging noise, can be obtained fromKR= Dd2BLARxATxkABoltzSysGNRxGTxPT14πfcEq. 5.3-15The exact quantification of the link technology factor K R is subject to link budget design, butin the frame of an inter satellite study conducted for ESA, it has been shown thatK R ~ 1 x 10 –9 m/mcan easily be achieved and has been found to be a reasonable value for the simulations in thisthesis. This leads to a ranging precision of approximately 2.5 cm due to thermal noise for a25000 km range. This can be regarded as a realistic value for a carrier smoothed code range.To derive the precision of a range rate measurement, we start with the formulation of theDoppler shift and difference the range rate with respect to the Doppler shift.fRx∆f== fR= θ⋅∂R=∂θTx( f − f )RxcfcfTxTx⎛ R ⎞ ⋅ ⎜1⎟+c⎝ ⎠Tx Eq. 5.3-16= fTxR⋅ = θcWe can therefore rewrite 5.3-11 toσRR Eq. 5.3-17∂R= ⋅θ∂θDopplerc=fTxωLωLNo2 2ξCThe precision of a Doppler measurement is strongly related to the phase measurement. Thuswe assume also a linear relationship between distance and range rate accuracy.σ ≈ ⋅ dEq. 5.3-18RRK RRFrom the DORIS system specification we obtain a value of 0.3 mm/s for low earth orbits.Thus we can find a scale factor of approximatelyK RR = 2 x 10 -10 m/sto be a representative. Figure 5-5 shows the range rate precision up to a distance of 42 000km.Page 80R. Wolf