Trajectory and atmospheric structure from entry probes: Feasibility study of a real-time reconstruction technique using a radio link

Many recent planetary entry vehicles have maintained radio links to receivers on either Earth or a nearby spacecraft during their risky atmospheric entries. The trajectory and the associated atmospheric structure of a descending entry vehicle are traditionally reconstructed from onboard accelerometer data, but they can in principle be reconstructed from the Doppler shift in a radio link instead. However, such methods have only been explored at the proof-of-concept level. Here we develop an improved radio-based reconstruction method and use it to simulate reconstruction of the trajectories and atmospheric structures of Pathfinder, Spirit, Opportunity, Phoenix, and Curiosity, validating the simulated results against those obtained by traditional means. Due to a singularity in the underlying equations, the radio-based reconstruction method may fail badly if the velocity vector of the transmitting entry vehicle with respect to the atmosphere is perpendicular to the line of sight between the transmitter and the receiver. A simple plot of the rate of change of the received frequency is also helpful for indicating the likely applicability of this method. Agreement between simulated and actual trajectories and atmospheric structures is very good for Spirit and Opportunity and for receivers on Earth and an orbiter, which establishes the validity and potential value of this method. The root-mean-square temperature error is no greater than 5 K at radial distances between 3410 km and 3470 km, a range of six scale heights. Agreement is less good for Pathfinder due to limitations in the available data and for Phoenix due to geometrical reasons. The method assumes a lift-free trajectory, which is a valid assumption for the first four landers, but not for Curiosity. Nevertheless, the results of this method are reasonable for Curiosity before its period of horizontal flight, which was not reconstructed adequately by this method at all. Sensitivity studies found that results are satisfactory for thermal noise of less than 1 part in 108 and frequency drift of less than 1 part in 109 per second. A frequency offset has no impact on the results. The radio-based reconstruction method is ready to be applied to the upcoming atmospheric entries of several Mars landers.