Multi-Sensor, Multi-Space Object, Poisson Labelled Multi-Bernoulli Tracking using Lie Algebra and Low Cost Telescopes
Abstract
The number of space objects (SOs) in orbit has increased dramatically in recent years making methodologies to improve track catalogs crucial for the avoidance of collisions. The efficient detection, tracking, and cataloging of orbiting SOs are therefore of paramount importance for improved Space Situational Awareness (SSA), and the demand for modern SO tracking applications to produce more accurate and more computationally efficient tracking capabilities is higher than ever.Due to the random nature of various forces which act on SOs, their orbits can change significantly over time. Therefore, state of the art concepts for tracking multiple SOs have focused on stochastic estimation methods for updating the track catalogs of SOs. Such approaches usually initialize the tracks of observed SOs using Initial Orbit Determination (IOD), where an initial estimate of the orbit is refined with observations. The estimated states of the SOs are propagated via a recursive Bayesian filter based on subsequent observations.Advances in the current technology associated with cataloging space debris are proposed by fusing image data from multiple disparate low-cost telescopes with new algorithms. Specifically, this proposal hypothesizes that the accuracy of multi-target SO tracking, based on telescopic observations, can be significantly improved beyond the state of the art.This proposed research will demonstrate improvements in advances beyond the state of the art in the following three areas 1. Multi SO target tracking algorithms, 2. Single SO target tracking models and 3. SO measurement models.1. Advances Beyond State-of-the-Art Multi SO Target Tracking AlgorithmsDue to the large variance of various orbital parameters, limited Fields of View (FoVs) of the sensors and typically small numbers of observations per SO pass, it is challenging to initialize new tracks and update existing tracks due to high data association uncertainty when no prior information about the SOs is available. This research will generate a Multi-SO target tracking algorithm improved based on the combination of the RFS based Poisson Labelled Multi-Bernoulli (PLMB) filter, together with a Partially Uniform Birth (PUB) - Probabilistic Admissible Regions (PAR) Initial Orbit Determination (IOD) concept.Recently in the RFS multi-target tracking literature, multi- Bernoulli filters that utilize a Poisson process birth model have been proposed, a computationally tractable version of which is the Poisson Labelled Multi-Bernoulli (PLMB) filter. The advantages of using a Poisson process birth model within LMB filters include-a. The ability to model the birth of any number of targets at a given time step,b. The ability to model a birth rate, thus allowing filter predictions with varying time steps,c. Poisson based birth filters can make meaningful use of existing Initial Orbit Determination (IOD) methods such as the Partially Uniform Birth (PUB) - Probabilistic Admissible Regions (PAR) approach as proposed in this project.2. Advances Beyond State-of-the-Art Single SO Target Tracking Models- Single SO target dynamic motion modelling based on Lie manifolds, is hypothesized to yield more computationally efficient predictors than state of the art concepts based on Cartesian coordinate systems. State uncertainty in Lie Manifolds can be mathematically modelled as Concentrated Gaussian Distributions (CGD), allowing single Gaussian components to model SO orbital motion. This will reduce the computational complexity of state-of-the-art SO orbital motion prediction due to the necessity of less parameters to represent SO states and their uncertainties. Single SO target dynamic motion modelling requires a propagation integrator, for relating the various forces which act on SOs to the prediction of their position and, if used, angular velocity states.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2024
- Source ID
- FA95502310592
Entities
People
- Martin Adams
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Chile