A Comparison between Numerical Differentiation and Kalman Filtering for a Leo Satellite Velocity Determination

The kinematic orbit is a time series of position vectors generally obtained from GPS observations. Velocity vector is required for satellite gravimetry application. It cannot directly be observed and should be numerically determined from position vectors. Numerical differentiation is usually employed for a satellite’s velocity, and acceleration determination. However, noise amplification is the single obstacle to the numerical differentiation. As an alternative, velocity vector is considered as a part of the state vector and is determined using the Kalman filter method. In this study, velocity vector is computed using the numerical differentiation (e.g., 9-point Newton interpolation scheme) and Kalman filtering for the GRACE twin satellites. The numerical results show that Kalman filtering yields more accurate results than numerical differentiation when they are compared with the intersatellite range-rate measurements.