[Paper Review] The Progressive Proposal Particle Filter: Better Approximations to the Optimal Importance Density

Pete Bunch, Simon Godsill|arXiv (Cornell University)|Jan 13, 2014

Target Tracking and Data Fusion in Sensor Networks29 references3 citations

TL;DR

This paper introduces the progressive proposal particle filter, a novel method for approximating the optimal importance density in particle filters by progressively incorporating observations through sequential local Gaussian approximations. It significantly improves performance in nonlinear and non-Gaussian state estimation tasks, reducing particle degeneracy and filter tracking failure compared to standard methods.

ABSTRACT

The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated analytically in most case. In practice, approximations of this density are used, particularly Gaussian densities based on linearisation or the unscented transform. For many highly nonlinear or non-Gaussian models, these approximations can be poor, leading to degeneracy of the particle approximation or even the filter "losing track" completely. In this paper, we develop a new mechanism for approximating the optimal importance density, which we call the progressive proposal method. This works by introducing the observation progressively and performing a series of state updates, each using a local Gaussian approximation to the optimal importance density. A number of refinements and extensions to the basic algorithm are also introduced. Simulations are used to demonstrate an improvement in performance over simpler particle filters on a number of applications.

Motivation & Objective

• To address the challenge of poor performance in standard particle filters due to inaccurate importance density approximations in nonlinear and non-Gaussian models.
• To develop a more accurate approximation of the optimal importance density, which is analytically intractable in most practical cases.
• To reduce particle degeneracy and filter tracking failure in complex dynamic systems.
• To improve the robustness and accuracy of particle filtering through a refined, progressive approximation strategy.

Proposed method

• The method progressively introduces observations into the state update process, allowing for a sequence of local approximations to the optimal importance density.
• At each step, a local Gaussian approximation is used to estimate the importance density based on the current partial observation.
• The algorithm performs multiple state updates, each refining the particle set using the locally approximated importance density.
• The approach avoids global linearisation or unscented transform by focusing on local, observation-incremental updates.
• Refinements include adaptive step sizes and improved proposal tuning to enhance convergence and stability.
• The method is designed to better capture the true posterior structure than standard extended or unscented Kalman-based proposals.

Experimental results

Research questions

• RQ1 How can the optimal importance density be more accurately approximated in nonlinear and non-Gaussian state-space models?
• RQ2 Can progressive observation incorporation lead to better particle filter performance than single-step approximations?
• RQ3 Does using local Gaussian approximations at each step reduce particle degeneracy compared to global linearisation methods?
• RQ4 To what extent does the progressive proposal method improve tracking accuracy in challenging nonlinear systems?

Key findings

• The progressive proposal particle filter achieves significantly better performance than standard particle filters in highly nonlinear and non-Gaussian models.
• It reduces particle degeneracy by maintaining a more accurate approximation of the posterior distribution throughout the filtering process.
• The method prevents the filter from 'losing track' in complex systems where standard filters fail.
• Simulations demonstrate consistent improvements across multiple test applications, particularly in scenarios with strong nonlinearity or non-Gaussian noise.