Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Software DescriptionInter Satellite Links5.5.2 Ephemeris Contribution to UREIn a satellite navigation application, an important quantity is the range error, which the userwill experience. While the user range error (URE) is composed of many contributors, hereonly the ephemeris contribution will be addressed. The contribution of the (broadcast)ephemeris it self can be divided into three sub-contributors:• orbit determination error• orbit propagation error• broadcast model fit errorThe RMS error of the broadcast ephemeris is component-wise computed using the followingequations.withe radiale alonge crossσσσradialalongcross===∑n∑n∑n(( x − x ) ⋅ e )Broadcastn( x − x ) ⋅ e )Broadcastn(( x − x ) ⋅ e )BroadcastnTrueTrueTrueradialalongcrossUnit vector in radial directionUnit vector in along track directionUnit vector in cross track direction222Eq. 5.5-1Using these error components, the URE can be computed under the (justified) assumption thatthe worst URE is obtained from a satellite at nearly zero elevation.2 2( σ + σ ) ⋅ α2URE = σ ⋅ cosα +sinradialalongcrossEq. 5.5-2whereα Angle between the satellites radius vector and the local horizontal plane of an observer,which is not the elevation.Page 88R. Wolf