Integrated Model for Prediction of Reentry Time of Risk Objects

Abstract

S PACE object reentry prediction studies have been considered as one of the important topics in space research. Accurate prediction of reentry time and impact location is necessary tomitigate the Earth impact risks. There were many large objects, including the Upper Atmosphere Research Satellite, Roentgen Satellite (ROSAT), Phobos Grunt, and Gravity Field and Steady-State Ocean Circulation Satellite, which reentered Earth’s atmosphere in the recent past. It is essential to have suitablemathematicalmodels to predict the reentry time and the impact locationof riskobjects fordesigningandexecutingproper mitigation and remediation processes. Prediction of reentry time is a challenging problem because of the uncertainties in the orbital propagation models, atmospheric density models, solar flux, and geomagnetic activity indices. There are observational uncertainties in the orbital parameters as well [1]. Atmospheric drag is the major perturbing force on the spacecraft during its reentry [2]. The ballistic parameter B m∕ A × Cd (where m and A are mass and effective surface area of the object, respectively, and Cd is coefficient of drag) is a direct measure of the drag force experienced by the object. Hence, the orbital decay of the space object depends significantly on B. Orbital data of the catalogued space objects are provided by Space-Track in the form of two-line elements (TLEs). The concept of using TLE data to estimate the ballistic parameter of a reentering object has been investigated by many researchers. Chao and Platt [3] developed a lifetime prediction tool based on simplified averaged equations of motion expressed in classical orbital elements. Strizzi [4] improved Chao’s lifetime tool by using the Runge–Kutta integration technique for propagating the final orbits to reduce the uncertainty in the prediction. This improved lifetime tool was tested for its accuracy considering North American Aerospace Defense Command decayed objects [5]. Anilkumar et al. [6] used a Kalman filter approach with constant gains to estimate the ballistic parameter from TLEs. The states considered in this study were the semimajor axis, eccentricity, and ballistic parameter. The measurements were apogee and perigee altitudes computed from the TLEs. In this model, the mean U.S. standard atmosphere and a simple propagator considering atmospheric drag effects were used. Later, Sharma and Anilkumar [7] improved this method by incorporating a more accurate propagation model based on Kustaanheimo–Stiefel element equations. The constant Kalman gains were estimated byminimizing an objective function through a genetic algorithm. There are many other methodologies to compute the reentry time of a satellite using TLEs during its last orbital phase [8,9]. When the perigee altitude becomes less than a certain altitude, where the drag effect dominates the decay of the orbit, it can be termed as the last phase of orbital decay. Typically, this altitude can be taken to be 150 km. Pardini and Anselmo [10] analyzed the effect of time span (TLE data span) required to estimate the ballistic parameter of a space object by considering seven interagency space debris reentry test campaign objects. The study indicates that 10–15 TLEs provide reasonably good predictions during the final phase of reentry. An integrated model consisting of a highly accurate numerical propagation model and a multi-objective function optimization technique to estimate an essential ballistic parameter EBP k × B is presented in this paper. Here, B is the ballistic parameter and k is a factor that will absorb the uncertainties in themeasurements, models, and other inputs. In this approach, the orbital parameters are computed from TLEs using Simplified General Perturbations No.4 (SGP4) theory at their epoch and are used as the observations to predict the EBP. In this study, the high-precision orbit propagator (HPOP) utility of the Satellite Tool Kit (STK) is integrated with an optimization technique for estimating the optimal EBP. States from a pivot TLE are propagatedwith a set of ballistic parameters to generate the predictions of orbital parameters at all other TLE epochs. The innovations (observation–prediction) are then minimized to estimate the best EBP. A multi-objective function, combining the innovations on apogee and perigee altitudes, is minimized to arrive at the best EBP. Least-square errors, weighted least-square errors, considering the expected remaining life as weights, and normalized nondimensioned errors are taken as the components of the multi-objective function. In thismodel, the inaccuracies inTLEs, uncertainties inparameters likeF10.7andAp values, the inaccuracies in the atmosphericmodel, and the propagation model are all absorbed in the estimatedEBP.TheestimatedEBP isused to predict the reentry time of the object from the pivot TLE. The effectiveness of themodel is shown through the reentry time prediction ofdecayedobjects, PhobosGrunt andROSAT.This novel idea of using a multi-objective function minimization to estimate the optimal essential ballistic parameter in the reentry prediction has proven to be very effective. The present approach is different from the earlier approaches because of this novelty.