Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Autonomous Onboard ProcessingInter Satellite LinksFrom experiences made during this project regarding execution times of different softwaremodules, and under the assumption that the CPU is approximately 20 times slower than a 350MHz Pentium II, a very rough estimate can be derived for the required computational poweronboard a satellite:~ 100 ms for orbit determination (including non-linear state prediction) per measurementepoch (realtime)~ 30 ms for orbit propagation per epoch, i.e. 1 s to generate 50 trajectory points ahead,separated 144 s. (offline)~ 10 s for fitting a 2-hour-valid broadcast ephemeris over approximately 50 trajectory points.(offline)~ 2 ms for orbit propagation per epoch using broadcast ephemeris force model (for othersatellites in constellation); for 20 ISL’s requiring 40 ms. (realtime)~ 50 ms to perform a RAIM-like algorithm using 20 ISL’s (realtime)This results in approximately 200 ms for the tasks which have to be performed in realtime, i.e.once per second, in order to achieve integrity requirements. The remaining 800 ms per onesecond-duty-cyclecan be used to perform sequentially the (slightly more than) 10 s offlinetask. The 2-hour-valid broadcast ephemeris could updated, say every 30 minutes and wouldrequire less than 6 ms of computing time per one-second-duty-cycle, i.e. 0.6% of the availablecomputing power.Note that this is a very rough preliminary estimate, but it seems to be feasible to perform allthese tasks, required for full autonomous onboard processing with 20% – 25% of the availablecomputing power.7.2.2 Onboard Processing using ISLsInter satellite links are per definition measurements which are taken onboard and thereforeseem to perfectly match the requirements for an onboard processor. But ISL’s bear someproblems for a constellation consisting of autonomous processing satellites.The optimal approach to process ISL's would be, to process all measurements and all satellitesstates in one large filter. This is hard to achieve, if each satellite has its own state estimatoronboard. The following example shall highlight how satellite state estimates get correlated bythe inter satellite links.Let us assume 3 satellites , represented by their state X 1,2,3 . The measurements are processedtogether in on Kalman filter some other least squares estimator. The state transition of allthree satellites can be written as⎡x1⎤ ⎡Φ10 0 ⎤ ⎡x1⎤Eq. 7.2-1⎢x⎥ ⎢2020⎥ ⎢x⎥⎢ ⎥=⎢Φ⎥⋅⎢2⎥⎢⎣x ⎥ ⎢3 ⎦ ⎣ 0 0 Φ ⎥ ⎢3 ⎦ ⎣x⎥3 ⎦kkk−1Page 156R. Wolf