A switching Kalman filter approach to online mitigation and correction of sensor corruption for inertial navigation

TL;DR

This work tackles robust state estimation for inertial navigation in the presence of corrupted external sensors, notably GPS. It advances a Switching Kalman Filter augmented with parameter learning to online-detect when corruption begins and to adapt the bias model without discarding corrupted measurements. The approach maintains multiple observation models, estimates both the system state and the corruption parameters, and uses branched SKF to manage computational cost while preserving detection accuracy. Empirical results on balloon navigation and shuttle reentry demonstrate improved robustness and resilience in challenging sensing environments, with performance benefiting from larger biases, lower process noise, and higher sampling rates.

Abstract

This paper introduces a novel approach to detect and address faulty or corrupted external sensors in the context of inertial navigation by leveraging a switching Kalman Filter combined with parameter augmentation. Instead of discarding the corrupted data, the proposed method retains and processes it, running multiple observation models simultaneously and evaluating their likelihoods to accurately identify the true state of the system. We demonstrate the effectiveness of this approach to both identify the moment that a sensor becomes faulty and to correct for the resulting sensor behavior to maintain accurate estimates. We demonstrate our approach on an application of balloon navigation in the atmosphere and shuttle reentry. The results show that our method can accurately recover the true system state even in the presence of significant sensor bias, thereby improving the robustness and reliability of state estimation systems under challenging conditions. We also provide a statistical analysis of problem settings to determine when and where our method is most accurate and where it fails.

Figures (27)

• Figure 1: Diagram representing the traditional SKF operational principle. Red, green, and blue arrows represent the use of model 1, 2, or 3 respectively as an observation model. At every single instance can switch to using any of the three models. The length (left-to-right) of the blue likelihood bars represent the size of the likelihood.
• Figure 2: Diagram representing the parallel SKF operational principle. Red dots indicate the usage of a biased observation model, whereas black dots indicate an unbiased model. As an example $S=3$ indicates that the observation model is corrupted at $t=2$. The length (left-to-right) of the blue likelihood bars indicates the size of the likelihood.
• Figure 3: Diagram representing the branched SKF operational principle. Red dots indicate the usage of a biased observation model, whereas hollow dots indicate an unbiased model. At every instance a new biased branch starts from the unbiased one. The length (left-to-right) of the blue likelihood bars indicates the size of the likelihood.
• Figure 4: Diagram representing the selective branched SKF operational principle. Red dots indicate the usage of a biased observation model, whereas hollow dots indicate an unbiased model. At every instance a new biased branch starts from the unbiased one. Once there are more than three corrupted branches, the less likely one is removed. As an example, at $t_3$ the branch corrupted at $t_0$ is removed. The length (left-to-right) of the blue likelihood bars indicates the size of the likelihood.
• Figure 5: The velocity field used for the balloon drifting example problem at the initial time step