S Shivshankar, Indian Institute of Science; Debasish Ghose, Indian Institute of Science
Keywords: Space Situational Awareness, Non-Cooperative Satellites, Maneuver Time Estimation, Time-to-Event Data Analysis, Regression Analysis, Machine Learning for SSA Applications
Abstract:
Estimation of Maneuver Occurrence time of Non-Cooperative Satellites using Time-to-Event Data Analysis and other Machine Learning Techniques
Shivshankar. S and Debasish Ghose
Modelling pattern-of-life of non-cooperative space objects is an essential requirement of Space Situational Awareness (SSA). Maneuvers of non-cooperative satellites is an important event of interest in the pattern-of-life of the satellite. Estimating the occurrence time of maneuver of a non-cooperative satellite, based on the available historical data collected from ground-based sensors is one of the important objectives of SSA.
However, the active satellites to be monitored is huge in number and the available ground surveillance sensors are limited as well as costly. Due to this limitation, a non-cooperative satellite may go unobserved by ground sensors. Therefore, there exists a problem of gaps in the available orbital data of non-cooperative satellites.
The authors wish to propose a solution methodology to tackle the problem using Time-to-Event data analysis which has been an active research topic due to its impactful applications in a variety of disciplines as found in literature survey. To the best knowledge of the authors, Time-to-Event data analysis techniques have not yet been explored for SSA applications. Time-to-Event analysis is a branch of statistics concerned with analyzing temporal data and predicting the probability of occurrence of an event.
In the research problem at hand, the event of interest may be considered as the maneuver of a non-cooperative satellite. Time-to-Event estimation model not only helps to assess whether or not a satellite maneuver (event of interest) occurred, but also when that event occurred.
The most interesting feature of the Time-to-Event estimation problem is the presence of censored examples in the data. A censored example is an example whose event occurrence time is unobserved due to observation window limits or losing track during the observation window. Time-to-Event data analysis is also called survival analysis, reliability analysis, duration modelling and event history analysis. Many popular ideas of machine learning such as gradient boosting, random forests and support vector machines have been adapted from Time-to-Event analysis.
The benefit of Time-to-Event analysis techniques is that it can incorporate data from multiple time points across various satellites. The data of satellites which have not maneuvered till a time instant or data of satellites unavailable during a time window can still contribute to the Time-to-Event analysis. Therefore, the behaviour modelling of non-cooperative satellites can also be done using historical orbital data of cooperative satellites operating in similar orbital characteristics and operating for similar mission objectives. The advantage is that the ground based SSA sensors need not be burdened to acquire orbital data of cooperative satellites since it is available through other means.
The expected behaviour of a benign active satellite can be modelled based on orbital regime in space in which the satellite is operating (that is LEO, GEO, etc.,) and the mission objectives for which the satellite is operating. For example, the housekeeping maneuvers of a GEO satellite carrying a payload for supporting terrestrial communications is performed in a certain manner. Even a non-cooperative GEO satellite which claims to operate for a similar mission objective should behave in a similar way.
Conventional machine learning methods of logistic and linear regression are not suited to be able to include both the event and time aspects as the outcome in the Time-to-Event estimation model. Traditional regression methods also are not equipped to handle censored examples in the data.
A variety of parametric, semi-parametric and non-parametric approaches are available in literature for Time-to-Event data analysis used in the field of medical research. Since the conventional regression methods cannot be adopted, our work attempts to explore special techniques for Time-to-Event data analysis such as penalized Cox model, Random Survival Forest and Survival Support Vector Machine to solve the research problem at hand. This would aid in utilizing even the partial information on each satellite with censored data (unobservable data) and provide unbiased Tim-to-Event estimates.
A spin-off is being attempted by the authors to apply the Time-to-Event data analysis and estimation modelling to space debris wherein the event of interest would be the rentry of the debris into Earth’s atmosphere and the statistical survival analysis would give insights into the space debris modelling. Detailed experimental results based on real life satellite orbital datasets and discussions on the results would be presented in the full paper.
Date of Conference: September 19-22, 2023
Track: Machine Learning for SDA Applications