Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Bayesian Approach to Low-Thrust Maneuvering Spacecraft Tracking

Enrico M. Zucchelli, Brandon A. Jones

Abstract

Bayesian estimation with an explicit transitional prior is required for a tracking algorithm to be embedded in most multi-target tracking frameworks. This paper describes a novel approach capable of tracking maneuvering spacecraft with an explicit transitional prior and in a Bayesian framework, with fewer than two observations passes per day. The algorithm samples thrust profiles according to a multivariate Laplace distribution. It is shown that multivariate Laplace distributions are particularly suited to track maneuvering spacecraft, leading to a log probability function that is almost linear with the thrust. Principles from rare event simulation theory are used to propagate the tails of the distribution. Fast propagation is enabled by multi-fidelity methods. Because of the diffuse transitional prior, a novel k-nearest neighbor-based ensemble Gaussian mixture filter is developed and used.The method allows Bayesian tracking of maneuvering spacecraft for several scenarios with fewer than two measurement passes per day, and with a mismatch between the true and expected thrust magnitude of up to a factor of 200. The validity domain and statistical significance of the method are shown by simulation through several Monte Carlo trials in different scenarios and with different filter settings.

A Bayesian Approach to Low-Thrust Maneuvering Spacecraft Tracking

Abstract

Bayesian estimation with an explicit transitional prior is required for a tracking algorithm to be embedded in most multi-target tracking frameworks. This paper describes a novel approach capable of tracking maneuvering spacecraft with an explicit transitional prior and in a Bayesian framework, with fewer than two observations passes per day. The algorithm samples thrust profiles according to a multivariate Laplace distribution. It is shown that multivariate Laplace distributions are particularly suited to track maneuvering spacecraft, leading to a log probability function that is almost linear with the thrust. Principles from rare event simulation theory are used to propagate the tails of the distribution. Fast propagation is enabled by multi-fidelity methods. Because of the diffuse transitional prior, a novel k-nearest neighbor-based ensemble Gaussian mixture filter is developed and used.The method allows Bayesian tracking of maneuvering spacecraft for several scenarios with fewer than two measurement passes per day, and with a mismatch between the true and expected thrust magnitude of up to a factor of 200. The validity domain and statistical significance of the method are shown by simulation through several Monte Carlo trials in different scenarios and with different filter settings.

Paper Structure

This paper contains 28 sections, 41 equations, 15 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Multi-Fidelity Stochastic Collocation
  3. High-Level Description of multi-fidelity stochastic collocation
  4. Interpolation Nodes Selection
  5. Model Synthesis
  6. Multi-fidelity Stochastic Collocation for Maneuvering Spacecraft
  7. Thrust Profile Distribution
  8. Rare Event Simulation Particle Filter
  9. Rare Event Simulation for State Estimation
  10. Rare Event Simulation Filter with Laplace Prior
  11. Results
  12. Nearest-Neighbor Ensemble Gaussian Mixture Filter
  13. Proposed Approach
  14. Filter Architecture
  15. Construction of the Transitional Prior
  16. ...and 13 more sections

Figures (15)

  • Figure 1: Example of problematic multi-fidelity maneuvering spacecraft trajectories.
  • Figure 2: Example of thrust profile sample between two measurement passes.
  • Figure 3: Expected logarithm of the RMSE according to Eq. \ref{['eq:RMSEq']}.
  • Figure 4: RMSE for Monte Carlos of particle filters.
  • Figure 5: Transitional prior without (left) and with (right) importance sampling.
  • ...and 10 more figures