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Space-time Dynamics Estimation from Space Mission Tracking Data

Many physical parameters that can be estimated from space mission tracking data influence both the translational dynamics and proper time rates of observers. These different proper time rates cause a variability of the time transfer observable beyond that caused by their translational (and rotational) dynamics. With the near-future implementation of (interplanetary) transponder laser ranging, these effects will become increasingly important, requiring a re-evaluation of the common data analysis practice of using a priori time ephemerides, which is the goal of this paper. We develop a framework for the simultaneous estimation of the initial translational state and the initial proper time of an observer, with the goal of facilitating robust tracking data analysis from next-generation space missions carrying highly accurate clocks and tracking equipment. Using our approach, the influence of physical parameters on both translational and time dynamics are considered at the same level in the analysis, and mutual correlations between the signatures of the two are automatically identified. We perform a covariance analysis using our proposed method with simulated laser data from Earth-based stations to both a Mars and Mercury lander. Using four years of tracking data for the Mars lander simulations, we find a difference between our results using the simultaneous space-time dynamics estimation and the classical analysis technique (with an ta priori time ephemeris) of around 0.1 % in formal errors and correlation coefficients. For a Mercury lander this rises to around 1% for a 1-month mission and 10 % for a 4-year mission. By means of Monte Carlo simulation, we find that using an a priori time ephemeris of representative accuracy will result in estimation errors that are orders of magnitude above the formal error when processing highly accurate laser time transfer data.