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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.

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Gravity field reconstruction via the analysis of kinematic orbit positions has been proven to provide essential information for Earth system research purposes. For this aim, various approaches have been developed and applied to exploit kinematic orbits. In addition to those existing methods, in this paper we present a new technique. By means of a series of simulation studies we demonstrate that the novel method is comparable with the hitherto proposed techniques. As the main difference with existing methods, our approach is based on the so-called Lagrange coefficients, i.e., a semi-analytical description of the satellite motion. For this reason, we denote the technique to as the Lagrange formalism. The low sensitivity to the priori information about the gravity field, and less influence of the polar gap are of its characteristics. The investigations demonstrate that the idea of the Lagrange method in determining the Earth's gravity field could represent comparable results in term of quality with other approaches.