Application of higher order finite differencing techniques in velocity and acceleration determination of satellite navigation systems

Abstract

The work in the current manuscript encompasses the use of a higher order finite differencing method in the determination of velocity and acceleration of navigational satellites. The Earth Centred Earth Fixed (ECEF) positions of the satellites are first obtained from the broadcast ephemeris which is followed by the application of a fourth-order differencing technique to calculate the satellites ECEF velocity from these ECEF positions. In a similar manner, the satellites ECEF acceleration are then derived from the ECEF velocities. The methodology have been implemented on navigation systems like BeiDou and NavIC (IRNSS). As the described technique is much simple and pretty candid than the traditional approaches, it may be a great alternative to the traditional methodologies. The presented results exemplify that the ECEF velocities of the satellites can be derived with accuracies of 0.5 mm/s and the ECEF accelerations of the satellites can be derived with a substantial accuracy of 0.05 mm/s. Subject Classification: 00A72, 65Y99, 68N01, 68U20.