Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Autonomous Onboard ProcessingInter Satellite Links⎛1 0 0 0 ∆t0 0 0 ⎞Eq. 7.4-2⎜⎟⎜01 0 0 0 ∆t0 0 ⎟⎜00 1 0 0 0 ∆t0 ⎟⎜⎟⎜00 0 1 0 0 0 ∆t⎟Φ = ⎜⎟⎜0 0 0 0 1 0 0 0⎟⎜00 0 0 0 1 0 0 ⎟⎜⎟⎜00 0 0 0 0 1 0 ⎟⎝00 0 0 0 0 0 1 ⎠At each epoch, the error state is propagated by~x K= Φ ⋅ xˆEq. 7.4-3k−1And the covariance matrix byP ~T= Φ ⋅ Pˆ−⋅ Φ QEq. 7.4-4K k 1+The noise matrix Q is a diagonal matrix, adding a small amount of noise on the each state.To obtain the observations, the nominal ranges to the ground stations and satellites have to becomputed.rLOS= r − rEq. 7.4-5SVGSrLOS,ISL= r − rEq. 7.4-6SVSV,ISLThe positions of the satellites are derived from the broadcast ephemeris and are thereforereferenced in the earth-centred-earth-fixed frame. The range is derived from the magnitude ofthe line of sight vectorR = rEq. 7.4-7SVGSLOSThe measurement vector z is derived from⎛ z⎜⎜ zz = ⎜⎜⎝z12n⎞⎟⎟⎟R⎟⎠SVSV,ISL,measured− RSVSV,ISLEq. 7.4-8where the i th row consists of the measured range minus the computed range for oneintersatellite linkz = R − REq. 7.4-9iSVSV i ,ISL,measuredSVSV i ,ISL,ComputedPage 164R. Wolf