Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Inter Satellite LinksAutonomous Onboard Processingor the same value for one ground linkzj= R − REq. 7.4-10SVGS j ,measuredThe observation matrix H is⎛ h1⎞⎜ ⎟⎜ h2 ⎟H = ⎜ ... ⎟⎜ ⎟⎝hn ⎠SVGSj,ComputedEq. 7.4-11with each row containing the partial derivative for the measurement with respect to theKalman filter stateshijjj⎛ x⎞i,LOSyi,LOSzi,LOS= ⎜1 0 0 0 0⎟jjj⎝ RiRiRi⎠Eq. 7.4-12Before the Kalman filter routines are executed, the covariance matrix of the a priori residualswithE = e T ⋅ eEq. 7.4-13~e = z − H ⋅ xEq. 7.4-14is tested to exclude faulty measurements. The i th measurement, and therefore the i th row of theobservation matrix H would be excluded if the following relationship holdswithT i,iT , ii> 9 ⇒ Measurement i excluded Eq. 7.4-15diagonal element of matrix TT = E ⋅( ~ T−H ⋅ P ⋅ H + R) 1Eq. 7.4-16which is the covariance matrix of the a-priori residuals times the inverse of the statecovariance matrix P mapped into the residual domain inflated by observation noise. Thisformulation is close to the equation for the Kalman gain and is therefore proportional to theweight this particular measurement will have. The test is formulated in way that ameasurement must not exceed 3 σ, which translates to a 99 % probability if a Gaussiandistribution is assumed.After testing all residuals, it has to be decided if only the measurements where faulty or if themeasurements have been excluded due to a satellites own integrity problem. If the more than50 % of the valid observation had to be removed, the onboard integrity monitor flags thesatellite unhealthy.R. Wolf Page 165