A practical method to improve the accuracy of orbit prediction and covariance prediction of position errors

With the continuous developments in the space industry, the near-Earth space is occupied by a variety of spacecraft whose number is increasing exponentially every year. To avoid collision, huge computational power is necessary to determine the probability of a collision between two space objects. However, there are many uncertainties in the collision prediction process, which exacerbate the burdens on space safety management.

Since collision probability is usually applied to evaluate a critically close encounter, improving the accuracy of orbit prediction and heterojunction prediction is key.

In a research paper recently published in Space: Science and TechnologyZhaokui Wang, of Tsinghua University, proposed an effective method with a back propagation (BP) neural network to improve the accuracy of orbit prediction and predict the variance in position errors of space targets.

Wang’s team also applied the proposed collision probability estimation method for Q-Sat and space debris with a NORAD ID of 49863. Q-Sat refers to the Tsinghua Gravity and Atmospheric Science Satellite, which is a spherical spherical satellite developed and dedicated by the Distributed and Intelligent Space System Lab (DSSL) To recover the Earth’s gravitational field and reveal the density of the atmosphere.

First, the author introduces the collision analysis model. In collision analysis, orbit prediction and covariance were performed according to the initial states and initial covariance of two space objects. By using a suitable algorithm, the instance of the time where the distance between the two objects was the smallest can be obtained.

Thus, the collision probability can be derived by combining the predicted state vectors and the predicted covariances of the two objects at that time. Next, the author developed an optimal atmospheric model. The first step was to choose an atmospheric density model and its correction parameters.

In an experimental model of atmospheric density, parameters such as solar activity and geomagnetic activity were used to describe the state of the atmosphere. In order to optimize the selection of the atmospheric density model, it was necessary to consider the sensitivity of the parameters in the model and the performance of the model in terms of orbit prediction. At present, the commonly used empirical atmospheric density models are the Jacchia family of models and the MSISE models.

For orbits less than 500 km, the JB2008 and Jacchia models performed better on atmospheric density and orbit prediction tasks. Therefore, the Jacchia-Roberts model was chosen as the atmospheric density model to be improved. The atmospheric temperature as well as the sensitivity matrix in terms of atmospheric resistance were mainly taken into account in the optimization process.

The second step was to apply the dynamic inversion method to optimize the parameters in the selected experimental atmospheric density models. In order to test the performance of the atmospheric density model correction method, a five-day total Q-sat orbital data from January 11 to January 15, 2022, was chosen.

Among them, each 24-hour period is used as a correction unit. To examine the accuracy of the improved Jacchia-Roberts model, the NRLMSISE-00 model was used for comparison. The position error of the 24-h prediction using the modified Jacchia-Roberts model is about 65 μm lower than the prediction using the NRLMSISE-00 model. Compared to the original Jacchia-Roberts model, the average forecast accuracy over a 24-hour period over a 14-day period is about 170 metres.

Next, the author used the back-propagation (BP) neural network to predict the covariance of the location error between the Q-Sat and the space debris. The learning rule for the BP neural network was to use the regression method to adjust the weights and thresholds of the network through backpropagation.

The same method was used to reduce the sum of squares of network errors. It is proved that the three-layer neural network can approximate a nonlinear continuous function with arbitrary accuracy, and the approximation accuracy is higher than that of the polynomial method.

However, the accuracy of the BP neural network is highly dependent on the quality of the sample data. In this investigation, a large number of covariance datasets were used to train the BP neural network. Fifty sets of high-resolution Q-Sat orbit data from November 2021 to January 2022 were used.

The orbit prediction model was used to predict the orbit of the satellite. The deviation between the expected ephemeris and the exact ephemeris was obtained. It can be seen that the Q-Sat prediction errors increased over time. The longer the prediction time, the greater the prediction errors. Errors in the T directions were the largest among the errors in the three directions. Location prediction errors were used to train the BP neural network.

After propagating the errors from the output layer towards the input layer, an accurate nonlinear relationship can be established between the input and the output. When it comes to a BP neural network to predict location errors for space debris, two-line element (TLE) data is usually the only representation of its orbital behaviour.

However, the TLE data did not include errors for the entire orbital period. Thus, the orbit from half an orbital period before and after a time period was taken as a reference. The SGP4 model was used for orbit prediction based on the TLE data.

Space debris TLE data with a NORAD ID of 49,863,249 from November 2021 to January 2022 were selected for 250 BP neural network training data. According to the actual prediction errors, the designed BP neural network was reliable to predict the space debris location prediction error with covariance with the TLE data.

Finally, the author introduces and discusses his own simulation results and reported results of the dangerous encounter between Q-Sat and Space Debris. It was reported that the Q-Sat will collide with space debris on January 18, 2022, and the probability of collision is about 3.71 x 10-4. According to the author’s investigation, the closest distance between Q-Sat and Space Debris was 2.71 282 km and the collision probability was 1.16×10– 11. It was determined that the confrontation warning was in fact a false alarm.

The results also showed that the proposed method can improve the prediction accuracy of space object collisions. The improvement in collision warning accuracy relied on higher quality long-term tracking data. By equipping precision orbit finders on satellites, the accuracy of space debris collision prediction will be greatly improved, and the number of unnecessary avoidance maneuvers will be reduced.