Outlier-Insensitive Kalman Filtering: Theory and Applications

TL;DR

Kalman filters excel under Gaussian assumptions but deteriorate with observation outliers. The authors introduce oikf, a parameter-free online Kalman filter that models outliers with a nuv prior and online variance estimation via EM or alternating maximization, enabling sparse outlier detection within the linear Gaussian framework. Empirical results on synthetic data and real GNSS datasets (NCLT, API) show oikf with nuv-em and nuv-am outperforming standard KF and several robust baselines in MSE/RMSE while maintaining real-time capability. The approach is computationally efficient, requires no hyperparameter tuning, and leverages all observations during filtering, offering a practical solution for robust navigation and tracking tasks.

Abstract

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers in the observations, due to the sensitivity of its convex quadratic objective function. To mitigate such behavior, outlier detection algorithms can be applied. In this work, we propose a parameter-free algorithm which mitigates the harmful effect of outliers while requiring only a short iterative process of the standard update step of the KF. To that end, we model each potential outlier as a normal process with unknown variance and apply online estimation through either expectation maximization or alternating maximization algorithms. Simulations and field experiment evaluations demonstrate competitive performance of our method, showcasing its robustness to outliers in filtering scenarios compared to alternative algorithms.

Figures (8)

• Figure 1: Factor graph of the system model at time step $t$
• Figure 2: Sub-Fig. \ref{['fig:MSE noisy']}, \ref{['fig:MSE noisy with low outliers']} and \ref{['fig:MSE noisy with high outliers']} present the mse of the estimated position for the tracking application in the kf setup. Our nuv methods were compared to different well-established robust kf algorithms in the literature.
• Figure 3: Convergence plots of the estimated outliers' variance computed using the NUV-am algorithm.
• Figure 4: The measured vehicle position in east direction obtained from the noisy gnss nclt dataset (red points), is compared to the estimated trajectory by our nuv-am (blue dashed line), which succeeded in passing the outliers and achieved performance comparable to the ground-truth (green dashed line).
• Figure 5: The measured vehicle position in north direction obtained from the noisy gnss nclt dataset (red points), is compared to the estimated trajectory by our nuv-am (blue dashed line), which succeeded in passing the outliers and achieved performance comparable to the ground-truth (green dashed line).