[Paper Review] Robust Gaussian Filtering.

Manuel Wüthrich, Cristina Garcia Cifuentes+2 more|arXiv (Cornell University)|Sep 14, 2015

Target Tracking and Data Fusion in Sensor Networks20 references3 citations

TL;DR

This paper proposes a robust Gaussian filtering method that enables standard Gaussian Filters to handle fat-tailed measurement noise by mapping measurements into an optimal feature space. The approach maintains the computational efficiency of existing filters while significantly improving robustness to outliers in both linear and nonlinear systems.

ABSTRACT

Most widely-used state estimation algorithms, such as the Extended Kalman Filter and the Unscented Kalman Filter, belong to the family of Gaussian Filters (GF). Unfortunately, GFs fail if the measurement process is modelled by a fat-tailed distribution. This is a severe limitation, because thin-tailed measurement models, such as the analytically-convenient and therefore widely-used Gaussian distribution, are sensitive to outliers. In this paper, we show that mapping the measurements into a specific feature space enables any existing GF algorithm to work with fat-tailed measurement models. We find a feature function which is optimal under certain conditions. Simulation results show that the proposed method allows for robust filtering in both linear and nonlinear systems with measurements contaminated by fat-tailed noise.

Motivation & Objective

• To address the limitation of Gaussian Filters in handling fat-tailed measurement noise, which leads to poor performance when outliers are present.
• To enable existing Gaussian Filter algorithms to operate robustly under fat-tailed measurement models without requiring algorithmic redesign.
• To identify an optimal feature function that transforms measurements in a way that preserves filter performance under heavy-tailed noise.
• To demonstrate the effectiveness of the proposed method in both linear and nonlinear systems with contaminated measurements.

Proposed method

• Mapping raw measurements into a specific feature space to transform fat-tailed noise into a form compatible with Gaussian filtering assumptions.
• Deriving an optimal feature function under certain statistical conditions to ensure robustness and consistency in filtering performance.
• Applying standard Gaussian Filter algorithms (e.g., Extended or Unscented Kalman Filters) in the transformed feature space.
• Using the feature space transformation to stabilize the filter against outliers while retaining the computational efficiency of traditional GFs.
• Leveraging the structure of the feature space to maintain the mean and covariance updates of standard Gaussian Filters.
• Ensuring that the transformation preserves the statistical properties needed for filtering, particularly under non-Gaussian measurement noise.

Experimental results

Research questions

• RQ1 Can standard Gaussian Filters be made robust to fat-tailed measurement noise through a suitable transformation of the measurement space?
• RQ2 What is the optimal feature function that enables robust filtering under fat-tailed measurement models?
• RQ3 Does the proposed method maintain the performance and efficiency of existing Gaussian Filters in nonlinear systems?
• RQ4 How does the feature space mapping improve filtering accuracy when measurements are contaminated by outliers?

Key findings

• The proposed feature space mapping enables standard Gaussian Filters to effectively handle fat-tailed measurement noise, overcoming a key limitation of traditional approaches.
• The derived feature function is optimal under specific statistical conditions, ensuring robustness and consistency in filtering performance.
• Simulation results confirm that the method achieves robust filtering in both linear and nonlinear systems under fat-tailed noise.
• The approach maintains the computational efficiency of existing Gaussian Filters while significantly improving resilience to outliers.
• The method outperforms standard Gaussian Filters in scenarios with heavy-tailed measurement noise, as demonstrated by reduced estimation error.