Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Inter Satellite LinksSoftware Description5.3 Measurement SimulationMeasurements are computed from the geometric range or range rate using the true satelliteorbits and adding delays from the signal path, clock offsets and random errors. The computedrange is also used to derive the free distance attenuation of the signals. The followingmeasurement equation indicates the considered components of a pseudo range measurement.PR0 ρGeometric+ c⋅T( δTSat− δ Ground / Sat2 + δiono+ δ Tropo + δ Multipath ) + ε noise= Eq. 5.3-1The largest part is represented by the true geometric range. The delays, which are scaled withthe speed of light to obtain a distance, are• Satellite clock offset• Ground station clock offset or 2 nd satellite clock offset• Ionospheric delay• Tropospheric delay• MultipathThe two clock offsets are generated by initialising the clock offset variable of each satelliteand ground station using a random number with• 3 milliseconds standard deviation for the satellite clocks.• 100 nanoseconds standard deviation for the ground station clocksThe errors introduced by the signal propagation path are considered by computingtropospheric and ionospheric delays from models. The last error contributor is the thermalnoise, which has been computed using the range dependent free distance attenuation.Under the assumption, that tropospheric and ionospheric delays can be removed to a certaindegree using models, only the residual errors of these contributor are considered in themeasurement noise, as indicated in the following equation.σ222( 0.2⋅ δ ) + ( 0. ⋅ ∆ ) + δ2 2Range = σThermal+ Tropo 5IonoMultipathEq. 5.3-2The simulated range measurements is then obtained byPR= PR 0 + RANDOM⋅σRangeEq. 5.3-3The error of a range rate measurement has been assumed to depend only on the thermal noise.σ2RangeRate= σ2ThermalEq. 5.3-4The measurement errors had been obtained bywherePRD = PR D 0 + RANDOM⋅σEq. 5.3-5RangeRateR. Wolf Page 75