Satellite Orbit and Ephemeris Determination using Inter Satellite Links

ISL Observation ModelInter Satellite Links2 ISL OBSERVATION MODELThe majority of the observation used in the orbit determination of satellites orbiting the earth,are radio frequency (pseudo-) range and Doppler measurements. Angle measurements, i.e.azimuth and elevation provide insufficient accuracy for precise orbit determination. Laserranging measurements, which are the most precise measurements available today, are stronglysubjected to weather conditions. Thus, they are used mainly for calibration purposes. Theobservations considered in this text, are therefore only one and two-way range and range rate(Doppler) measurement.2.1 Derivation of the Range EquationThe pseudo range between two points is the difference between two clock readings, the clockat the sender and the clock at the receiver. If the clocks are coarsely synchronized, the largestpart of the measured clock difference will be due to the signal travelling at the speed of light,thus representing the geometric distance.( TSat− TGroundSat 2) ⋅ c =+ c ⋅ ( δTSat− δTGround/ Sat 2) + δiono+ δTropo+ δMultipathεnoiseL =/Eq. 2.1-1= ρ +GeometricwithLandPseudo rangec Speed of lightδT Sat Deviation of satellite clock from system timeδT Groundδ IonoDeviation of ground receiver clock from system timeIonospheric delayδ Tropo Troposheric delayδ MultipathMultipath errorε noise Thermal noiseρGeometric=22( x − x ) + ( y − y ) + ( z − ) 21 2 1 2 1z2being the geometric distance between the two points.Eq. 2.1-2To obtain a linear measurement equation, the partials with respect to the unknown parametershave to be formed. Assuming that all other error contributions except the satellite clock can bemeasured or modelled, and therefore removed, we can write the linearized observationequation as a function of the three position errors and the satellite clock error. Remainingerrors e.g. due to mismodelling are added to the measurement noise.Page 4R. Wolf