Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Autonomous Onboard ProcessingInter Satellite Linkszz1312==[ h h ]11⎡x1⎤⋅ ⎢ ⎥⎣x3 ⎦x⎢ ⎥⎣x2 ⎦⎡p11= ⎢⎣ 0p⎢⎣ 00 ⎤p⎥33 ⎦0⎡ 1 ⎤⎡ 11 ⎤[ h h ] ⋅ , P = ⎥ ⎦211322,Pfilter1filter2p22Eq. 7.2-8Both filters contain the state of sat1, because sat1 is involved in both measurements . TheKalman gain for the sat2 state is now obtained byK22=h211p11h+p13 332h13p33+ r13Eq. 7.2-9It can also be shown that both filters yield Kalman gain factors also for sat1, which will not beequal.All measurements, covariances and satellite states should be available at the same time in thesame place to perform an optimal estimation. The easiest way to achieve this would be todownload the measurements and process inter satellite links on ground and in post processing.Unfortunately this removes one of the greatest benefits of the inter satellite links with respectto autonomy.The second approach, to process two satellites pair-wise leads to sub-optimal but maybe alsosatisfactory results.A third approach consists in the processing of inter satellite links without estimating thesending satellites state. This would require the smallest amount of communication betweenthe satellites. The partner satellites simply transmit their state vector (or corrections to thestate vector) which are frequently updated. In fact, this seems to be the only feasible way.7.3 Application Example: Availability during Orbit ManoeuvresPerturbations acting on the satellites orbit make it necessary to correct the space crafttrajectory from time to time in order to maintain the desired orbit. These orbit corrections,achieved by activating the spaces craft's propulsion system, lead to a discontinuity in theacceleration acting on the satellite. Although it is no problem to account for thrust forces inthe numerical integration during a propulsive flight phase, the accuracy of the broadcastmessage, which has to be fit over a certain period of validity, will be degraded if engine startor cut off falls within that time span. The amount of degradation depends strongly on thethrust level.Unintentional thrusters firing on the other hand issues an integrity problem, because thebroadcast ephemeris do not apply anymore. This means, the user computes his positionrelative to a satellite based a wrong S/V position information. However, this topic shall beaddressed in the next section.The conventional approach (GPS for example) is to set the space craft status to unhealthy,short before an orbit manoeuvre and up to the time when the orbit determination providesPage 158R. Wolf