Diluka Moratuwage, Universidad de Chile; Martin Adams, Universidad de Chile; Leonardo Cament, Universidad de Chile
Keywords: Random Finite Set (RFS), Jump Markov System (JMS), Admissible Regions (AR), Multi-target Tracking
Abstract:
The efficient detection, tracking, and cataloging of orbiting space objects (SOs) are of paramount importance for improved Space Situational Awareness (SSA). Due to a recent collision, various SO destructions and an increased number of launches, a higher number of new SOs now exists. As a result, the demand for modern SO tracking applications to produce faster, and more efficient detection and tracking capabilities is higher than ever.
The forces acting on SOs can be considered to vary in a random manner causing their orbits to change over time. Therefore, recursive Bayesian estimation methods have been adopted to detect, track and update the states of SOs. Under this paradigm, a probability density function of the multi-target state of the set of SOs entering the Field of View (FOV) of a sensor can be propagated in time using captured observations. Traditionally, such solutions initialize the tracks of observed SOs using a procedure called Initial Orbit Determination (IOD), where an initial estimate of the orbit is refined with a set of further observations using a non-linear optimization approach. Subsequently, the estimated state of the SOs is propagated by updating a recursive Bayesian filter based on further observations.
Due to the large variance of orbital parameters, limited fields of view of the sensors and typically small numbers of observations per pass, it is challenging to initialize new tracks and update the existing tracks due to high data association uncertainty when no prior information about the measurements is available. To rectify this problem, the Admissible Region (AR) approach was proposed to limit the candidate SO orbits to be tracked by selecting either a subset of acceptable range and range rate pairs for optical observations or right ascension rate and declination rate pairs for radar observations [1]. The AR approach was further improved using additional constraints on the orbital properties such as the semi-major axis and eccentricity and then referred to as the Constrained Admissible Region (CAR). The hard constraints of the CAR approach have been replaced with a probabilistic representation, called the Probabilistic Admissible Region (PAR) method, to facilitate orbit initiation in Bayesian tracking methods using optical observations [2].
Several Bayesian SO tracking algorithms have been developed using the CAR and PAR approaches, including the recent Random Finite Set (RFS) based methods of Jones et al [3]. Almost all these solutions model SOs using a single motion model. This limits the number of trackable orbits to those that satisfy the imposed CAR or PAR constraints. Furthermore, unless prior information about the objects being observed is available, a large portion of observations may not be usable in optical observation based tracking solutions. Therefore, in this article, an RFS based SO tracking algorithm for optical observations is proposed to address these limitations using the recently introduced efficient variant of the Delta-GLMB filter based on the Gibbs sampler [4]. Instead of a single CAR, multiple disjoint CARs are defined, such that orbits ranging from Low Earth Orbit (LEO), Medium Earth Orbit (MEO), Geosynchronous Earth Orbit (GEO), Geosynchronous Transfer Orbit (GTO) to High Earth Orbit (HEO) are classified into a pre-defined set of CARs depending on their orbital properties such as semi-major axis, eccentricity, altitude, orbiting speed and orbital period. Birth SO tracks are initialized in one or more CARs using the adaptive birth approach for labeled RFSs with appropriate birth probabilities using observations from the previous timestep and CAR specific orbital parameters. The orbit tracks of SOs from LEO to HEO can, therefore, be modeled using all captured observations.
The dynamic motion of each SO track is modeled using a Jump Markov System (JMS) [5] such that each SO track is allowed to switch between different motion models corresponding to different CARs. This allows a SO track initialized in a particular CAR, with its corresponding orbital motion model, to switch to a different orbital motion model with a predefined transition probability. As a result, even with a limited number of target initializations, with increased measurement updates its track is expected to converge to the correct CAR. This approach takes into account all possible track-to-measurement associations, new track initializations, possible switching of motion models, potential track deaths, miss-detections, and measurement clutter within a single Bayesian filtering framework. The highest weighted multi-target state hypothesis in the resulting truncated Delta-GLMB distribution represents the kinematic states, labels and the most probable CARs of the SOs being tracked at any given time. The probabilities of detection and survival of a SO are modeled by taking the current orbital motion model, estimated state of the SO and the FOV of the telescope into account. The performances of the proposed solution are evaluated using a MATLAB simulation and compared with results obtained from the approach used in [3].
References
[1] A. Milani, G. F. Gronchi, M. D. M. Vitturi, and Z. Knezevic, Orbit determination with very short arcs. I admissible regions, in Celestial Mechanics and Dynamical Astronomy, vol. 90, no. 1-2, pp. 5987, Universita di Pisa, Pisa, Italy, Dec. 2004.
[2] I. Hussein, C. Roscoe, M. Wilkins, and P. Schumacher, Probabilistic Admissible Region for Short-Arc Angles-Only Observations, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, Sept. 2014.
[3] B. A. Jones, B.-T. Vo, and B.-N. Vo, Generalized Labeled Multi-Bernoulli Space-Object Tracking with Joint Prediction and Update, in AIAA/AAS Astrodynamics Specialist Conference, (Long Beach, CA, USA), pp. 1177 1194, American Institute of Aeronautics and Astronautics, Sept. 2016.
[4] B.-N. Vo, B.-T. Vo, and H. G. Hoang, An Efficient Implementation of the Generalized Labeled Multi-Bernoulli Filter, IEEE Transactions on Signal Processing, vol. 65, no. 8, pp. 19751987, June 2018.
[5] W. Yi, M. Jiang, and R. Hoseinnezhad, The Multiple Model Vo-Vo Filter, IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 2, pp. 1045 1054, Apr. 2017.
Date of Conference: September 17-20, 2019
Track: Astrodynamics