Iteratively Saturated Kalman Filtering

TL;DR

The paper introduces the iteratively saturated Kalman filter (ISKF), a robust variant that effectively handles outliers in linear-Gaussian systems while maintaining low computational cost and real-time applicability.

Contribution

It proposes a novel robust Kalman filtering method derived as a scaled gradient approach, enhancing outlier resilience with minimal additional complexity.

Findings

Achieves outlier robustness with only one or two iterations.

Maintains low per-step computational cost similar to standard KF.

Includes a steady-state variant suitable for real-time systems.

Abstract

The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise. We introduce the iteratively saturated Kalman filter (ISKF), which is derived as a scaled gradient method for solving a convex robust estimation problem. It achieves outlier robustness while preserving the KF's low per-step cost and implementation simplicity, since in practice it typically requires only one or two iterations to achieve good performance. The ISKF also admits a steady-state variant that, like the standard steady-state KF, does not require linear system solves in each time step, making it well-suited for real-time systems.