ObjectiveHigh-precision prediction of space debris positions is critical for the successful implementation of laser ranging to space debris. Currently, the prediction using TLE (Two-Line Element) data for space debris is subject to significant errors. When tracking a target, these errors mainly manifest as positional bias within the telescope's field of view and distance bias between the ground station and the target. Excessive positional bias can prevent laser pulses from hitting the target, while large bias in the predicted distance between the station and the target can cause a mismatch between the expected and actual echo arrival times. This mismatch can result in the failure of the single-photon detector to detect echo photons during the distance gate opening period. To improve the success rate of laser ranging to space debris, this paper proposes an optimization method for predicting space debris positions based on time bias correction. This method aims to improve the accuracy of position and distance predictions for the target, thereby enhancing the probability of laser pulse hits and the detection capability of echo signals.
MethodsTo theoretically verify the effectiveness of time bias correction for optimizing orbit prediction, three low Earth orbit satellites with SP3 precise orbit data were selected. The SP3 data is used for high-precision orbital analysis and serves as the nominal orbit for comparison with TLE data. The specific calculation process is as follows: based on the Kunming observation station, visible observation arcs predicted by TLE are selected, and SP3 data for the same time period is matched. Subsequently, both the TLE and SP3 data are converted into azimuth and elevation angle observations for the observation station. These observations are then compared to identify the closest azimuth and elevation angles between TLE and SP3, determining the time bias of the TLE prediction. After correcting the time bias, the remaining azimuth and elevation bias are calculated.Based on theoretical calculations, this study uses the 1.2-meter telescope space debris laser ranging system of the Yunnan Astronomical Observatory, Chinese Academy of Sciences, for experimental verification, investigating the impact of time bias on space debris position prediction. Prior to the experiment, to achieve high-precision pointing, a new pointing model for the 1.2-meter telescope was established, and system errors were recalibrated. During the experiment, the 1.2-meter telescope tracks space debris based on TLE orbit data. Once the target is captured in the CMOS camera, the time bias is first corrected to adjust the target's position in the camera. When the azimuth or elevation deviation approaches zero, further corrections to azimuth and elevation bias are made. After the target enters the center of the telescope’s ranging system field of view, the corrected time bias, azimuth deviation, and elevation deviation data are recorded.Upon completing the data collection, the data is analyzed to determine the azimuth and elevation angles of the space debris when it first enters the field of view, when it is at the center of the field of view, and after time bias correction. The azimuth and elevation bias of the space debris relative to the center of the field of view are first calculated, followed by the reduction in bias after time bias correction. This evaluation assesses the improvement in prediction accuracy for space debris positions due to time bias correction, thereby validating the effectiveness of this method.
Results and DiscussionsTo verify the effectiveness of time bias correction for optimizing orbit prediction, theoretical calculations were first conducted for three low Earth orbit satellites with SP3 precise orbit data: Starlette, Larets, and Lares. The azimuth and elevation angle data from TLE and SP3 were compared. Since both azimuth and elevation bias need to be minimized during theoretical calculations and actual ranging processes, the sum of azimuth deviation and elevation deviation was used as the evaluation criterion in the theoretical analysis. The theoretical results showed that after time bias correction, the average correction percentages of the sum of the absolute values of azimuth and elevation bias for Starlette, Larets, and Lares were 51.7%, 76.0%, and 95.0%, respectively, proving that time bias correction has a significant effect on optimizing the orbital prediction of space debris. Meanwhile, this paper proposes a method for calculating time deviations by treating the forecast azimuth and elevation angle time series as a whole, and achieves the simulation calculation of time deviations for three satellites. Based on the theoretical calculations, this study conducted optical tracking experiments on space debris. Analyzing tracking data for 179 orbits, it was found that after time bias correction, the average correction percentage of azimuth deviation was 83.5%, and that of elevation deviation was 79.8%. This indicates that the time bias correction method can effectively reduce most of the positional prediction errors. From April 23, 2024, to May 18, 2024, tracking experiments of 37 different pieces of space debris were conducted at the Kunming station. It was found that 15 pieces of space debris exhibited a significant positive and negative pattern in their time bias, with 14 showing a clear positive pattern and 1 (ID 00694) having negative pattern.It was also observed that using time bias correction to adjust the predicted positions of space debris resulted in more stable tracking compared to correcting only the telescope's azimuth and elevation. After time bias correction, the telescope was able to maintain the space debris more stably at the center of the camera's field of view, requiring smaller adjustments in azimuth and elevation. For space debris with small time biases, azimuth, and elevation bias, an analysis of their orbits revealed that the difference between the perigee and apogee was within 15 km. Selecting near-circular orbit space debris with a difference between the perigee and apogee of less than 50 km from the tracking experiment data, it was found that the mean absolute value of time bias correction for near-circular orbit space debris was 59.5 ms, while for elliptical orbit space debris it was 80.9 ms. This indicates that near-circular orbit space debris generally has a lower time bias correction, and that the shape of the orbit has a significant impact on the time bias.
ConclusionsThis study proposes a space debris position prediction optimization method based on time bias correction. Theoretical calculations and experimental validation demonstrated that this method can significantly improve the accuracy of space debris position prediction, reduce positional bias within the telescope's field of view, and decrease the distance deviation between the observation station and the target. This provides methodological support for stable tracking of space debris and enhances the success rate of laser ranging to space debris. Analysis of observational data also revealed that the shape of the orbit is a key factor influencing the time bias of space debris, and that some space debris exhibits a pattern of positive and negative time bias. The time bias correction method not only improves the tracking stability of space targets during twilight periods but can also be extended to daytime observations. In particular, for specific space debris in Earth's shadow regions, the regularity of the time bias can be used to optimize search strategies, improve search efficiency, and avoid blind searches.