Zhang Xiu-zhong

Orbit determination for Chang'E-2 lunar probe and evaluation of lunar gravity models

The Unified S-Band (USB) ranging/Doppler system and the Very Long Baseline Interferometry (VLBI) system as the ground tracking system jointly supported the lunar orbit capture of both Chang’E-2 (CE-2) and Chang’E-1 (CE-1) missions. The tracking system is also responsible for providing precise orbits for scientific data processing. New VLBI equipment and data processing strategies have been proposed based on CE-1 experiences and implemented for CE-2. In this work the role VLBI tracking data played was reassessed through precision orbit determination (POD) experiments for CE-2. Significant improvement in terms of both VLBI delay and delay rate data accuracy was achieved with the noise level of X-band band-width synthesis delay data reaching 0.2–0.3 ns. Short-arc orbit determination experiments showed that the combination of only 15 min’s range and VLBI data was able to improve the accuracy of 3 h’s orbit using range data only by a 1–1.5 order of magnitude, confirming a similar conclusion for CE-1. Moreover, because of the accuracy improvement, VLBI data was able to contribute to CE-2’s long-arc POD especially in the along-track and orbital normal directions. Orbital accuracy was assessed through the orbital overlapping analysis (2 h arc overlapping for 18 h POD arc). Compared with about 100 m position error of CE-1’s 200 km×200 km lunar orbit, for CE-2’s 100 km×100 km lunar orbit, the position errors were better than 31 and 6 m in the radial direction, and for CE-2’s 15 km×100 km orbit, the position errors were better than 45 and 12 m in the radial direction. In addition, in trying to analyze the Delta Differential One-Way Ranging (ΔDOR) experiments data we concluded that the accuracy of ΔDOR delay was dramatically improved with the noise level better than 0.1 ns and systematic errors better calibrated, and the Short-arc POD tests with ΔDOR data showed excellent results. Although unable to support the development of an independent lunar gravity model, the tracking data of CE-2 provided evaluations of different lunar gravity models through POD. It is found that for the 100 km×100 km lunar orbit, with a degree and order expansion up to 165, JPL’s gravity model LP165P did not show noticeable improvement over Japan’s SGM series models (100×100), but for the 15 km×100 km lunar orbit, a higher degree-order model can significantly improve the orbit accuracy.

VLBI phase delay and its application in orbit determination of spacecraft

As one of the key technologies for orbit determination, very long baseline interferometry (VLBI) will play an important role in deep space explorations. The traditional group delay of VLBI is affected by the signal to noise ratio (SNR). As the spacecraft going to outer space, the random error of group delay increases quickly because of the SNR getting worse and worse. In this paper, we introduce the phase delay whose random error is much smaller than that of group delay at the same SNR. We deduce the conditions and method to determine the phase ambiguity, and then give the formula of calculating phase delay. The phase delay is used to determine the orbit of Change 2 (CE2) satellite with Doppler/ranging data when it flies to the Sun-Earth Lagrangian point L2 which is 1 500 000 km away from the Earth. It proves that the phase delay is useful for orbit determination.

High-accuracy VLBI technique using ΔDOR signals

During the Chinese Lunar Project ChangE-2 mission, a series of experiments on ΔDOR (delta differential one-way ranging) technology was carried out over a two week period starting on April 2, 2011. ΔDOR technology was first adopted in China deep space navigation, and the ΔDOR delay observables were obtained and used for orbit determination. In this paper, we introduce the ΔDOR observing technology, including the ΔDOR measurement principles. We also discuss the experiment design, the rules for selecting the calibration quasars, the switching time choice, the signal recording setup for the channels, the ΔDOR data processing method implemented in the software, and our analysis of the error sources of the ΔDOR delay and its contribution to orbit determination based on the characteristics of the Chinese VLBI network. Through these analyses and verification studies on the orbit determination from the satellite orbits in the CE-1 and CE-2 missions, we conclude that the accuracy of the ΔDOR delay is about 0.5 ns, an improvement of about one order of magnitude compared with that from S-band telemetry signals of less than 1 MHz. This study presents an important technique for high precision orbit determination of lunar and deep space explorations.