Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Software DescriptionInter Satellite Linksthan one error has occurred and if at a given point of time m (m > 4 for FD and m > 5 for FDI)range type measurements are available, then linearization yields the linear modely = Gx + εEq. 5.6-1But what, if no measurement is faulty but the ephemeris or clock state? To allow the isolationof the satellites own faulty clock or ephemeris, these parameters are introduced as pseudoobservations and the above equation replaced bywithy = G * ⋅x+ ε ∗* Eq. 5.6-2and⎛ 0 ⎞⎜ ⎟⎜ 0 ⎟⎜ ⎟y * =⎜ ⎟⎜0 ,⎟⎜ ⎟⎜ 0 ⎟⎜ ⎟⎝yM ⎠T Te , R ATTCT⎛T⎜e R⎜⎜e⎜G*=T⎜e⎜T⎜ 0⎜⎝ GTATCT0⎞⎟⎟0⎟⎟0⎟⎟1⎟⎟g⎠and ε∗ =⎛ ε⎜⎜ε⎜⎜⎜ε⎜⎜ ε⎜⎝ εe , e unit vector in radial, along track and cross track directionRATCTCM⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠Eq. 5.6-3The residuals are given as zero, i.e. "no ephemeris fault" and "no clock fault". The RAIMalgorithm is now capable of removing the bad assumption of "no radial error" for example, ifthe removal of this row in the system of observation equations minimises the sample varianceof residuals.A major draw back of that kind of snapshot algorithm based on the sample variance is theneed for a sophisticated pre-processing of the raw data. The sample variance taken from theraw measurements is still too noisy, thus leading to lots of false alarms.Another possible way of monitoring the integrity of a satellites position and clock is byseparating satellite dynamics / errors / and observation noise by their dynamic behaviour.This can be achieved using the Kalman filter with the following state vector⎡ ∆x⎤⎢ ⎥⎢∆y⎥⎢ ∆z⎥⎢ ⎥⎢∆Tx = ⎥⎢ ∆x⎥⎢ ⎥⎢ ∆y⎥⎢ ∆z⎥⎢ ⎥⎢⎣∆T⎥⎦Eq. 5.6-4which is kept very adaptive by adding high process noise. The Kalman filter is then inert withrespect to noise, but reacts immediately on real errors. The dynamic model which has beenPage 90R. Wolf