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Likelihood Scouting Via Map Inversion For A Posterior-Sampled Particle Filter

Simone Servadio

TL;DR

This work introduces the Scout Particle Filter (SPF), a Sequential Importance Sampling approach that leverages Differential Algebra to construct invertible polynomial maps linking state deviations to measurement deviations. By sampling scout particles from the measurement noise and mapping them back to the state space via map inversion, SPF produces a measurement-informed proposal that concentrates particles in high-likelihood regions, improving both accuracy and efficiency. The method handles non-square measurement models with fictitious observations and demonstrates superior performance across multiple aerospace-relevant scenarios, including range-angle tracking, range-only estimation, projectile tracking, perturbed orbit determination, and bimodal posteriors. Results show higher effective sample sizes and reduced particle counts needed for comparable accuracy, highlighting SPF’s potential for robust nonlinear filtering in high-noise and long-horizon contexts.

Abstract

An exploit of the Sequential Importance Sampling (SIS) algorithm using Differential Algebra (DA) techniques is derived to develop an efficient particle filter. The filter creates an original kind of particles, called scout particles, that bring information from the measurement noise onto the state prior probability density function. Thanks to the creation of high-order polynomial maps and their inversions, the scouting of the measurements helps the SIS algorithm identify the region of the prior more affected by the likelihood distribution. The result of the technique is two different versions of the proposed Scout Particle Filter (SPF), which identifies and delimits the region where the true posterior probability has high density in the SIS algorithm. Four different numerical applications show the benefits of the methodology both in terms of accuracy and efficiency, where the SPF is compared to other particle filters, with a particular focus on target tracking and orbit determination problems.

Likelihood Scouting Via Map Inversion For A Posterior-Sampled Particle Filter

TL;DR

This work introduces the Scout Particle Filter (SPF), a Sequential Importance Sampling approach that leverages Differential Algebra to construct invertible polynomial maps linking state deviations to measurement deviations. By sampling scout particles from the measurement noise and mapping them back to the state space via map inversion, SPF produces a measurement-informed proposal that concentrates particles in high-likelihood regions, improving both accuracy and efficiency. The method handles non-square measurement models with fictitious observations and demonstrates superior performance across multiple aerospace-relevant scenarios, including range-angle tracking, range-only estimation, projectile tracking, perturbed orbit determination, and bimodal posteriors. Results show higher effective sample sizes and reduced particle counts needed for comparable accuracy, highlighting SPF’s potential for robust nonlinear filtering in high-noise and long-horizon contexts.

Abstract

An exploit of the Sequential Importance Sampling (SIS) algorithm using Differential Algebra (DA) techniques is derived to develop an efficient particle filter. The filter creates an original kind of particles, called scout particles, that bring information from the measurement noise onto the state prior probability density function. Thanks to the creation of high-order polynomial maps and their inversions, the scouting of the measurements helps the SIS algorithm identify the region of the prior more affected by the likelihood distribution. The result of the technique is two different versions of the proposed Scout Particle Filter (SPF), which identifies and delimits the region where the true posterior probability has high density in the SIS algorithm. Four different numerical applications show the benefits of the methodology both in terms of accuracy and efficiency, where the SPF is compared to other particle filters, with a particular focus on target tracking and orbit determination problems.
Paper Structure (17 sections, 56 equations, 13 figures)

This paper contains 17 sections, 56 equations, 13 figures.

Table of Contents

  1. Introduction
  2. The Use of Differential Algebra For Deviation Mapping
  3. Importance Sampling
  4. Sequential Importance Sampling
  5. Filtering with Scouting Particles: the Scout Particle Filter
  6. The Prediction Step
  7. The Correction Step
  8. The Scout Particle Filter for Non-Square Applications
  9. Software Architecture
  10. Numerical Applications
  11. Range-Angle Measurement
  12. Range Measurement
  13. Projectile Tracking
  14. Perturbed Orbit Determination
  15. Bimodal Distribution
  16. ...and 2 more sections

Figures (13)

  • Figure 1: Scout Particle Filter Software Architecture.
  • Figure 2: Prior, likelihood, and true posterior probability density functions.
  • Figure 3: RMSE and efficiency comparison among particle filters.
  • Figure 4: Different particle filter approximation of the true posterior distribution.
  • Figure 5: RMSE and efficiency comparison among particle filters: range only
  • ...and 8 more figures