Validation methodology on real data of reversible Kalman Filter for state estimation with Manifold

TL;DR

This work targets the challenge of validating state-estimation filters on manifolds using real data by formalizing a reversible Kalman framework and a metric-based switching strategy between Rev-MEKF and MEKF. It introduces a geometric constraint step that leverages known surface normals to correct accelerometer and magnetometer information, and defines a strong notion of reversibility to enable precise, backward-compatibility testing. A tailored heuristic governs when the reversible corrections are applied, with a metric $\Lambda$ to quantify improvement relative to ground truth across several real-world datasets. The results show that, when correctly triggered, Rev-MEKF can outperform MEKF in dynamic phases and provides a principled path toward robust, manifold-aware attitude and pose estimation in robotics and underwater navigation.

Abstract

This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter was designed to provide a methodology for evaluating the accuracy of existing Kalman filter variants with arbitrary precision on synthetic data. It has favorable numerical properties on synthetic data, achieving arbitrary precision without relying on the small-velocity assumption and depending only on sensor noise. However, its application to real data encountered difficulties related to measurement noise, which was mitigated using a heuristic. In particular, the heuristic involved an event detection step switching between reversible Kalman filter and classical Kalman variant at chosen moments. In the present work, we propose a study of this detection step and propose a methodology to prove at which moment the reversible Kalman approach improves on classical multiplicative variant.

Figures (16)

• Figure 1: Example of rotations of acceleration around the $X$ axis and their intersection with a plane.
• Figure 2: $\max(\Lambda(X_{\text{MEKF}},\mathcal{T}))$ as a function of average acceleration variations during $dt=1/100s$.
• Figure 3: $\max(\Lambda(X_{\text{Rev-MEKF}},\mathcal{T}))$ as a function of average acceleration variations during $dt=1/100s$.
• Figure 4: $\max(\Lambda(X_{\text{Rev-MEKF}},\mathcal{T}))$ as a function of measurement noise matrix coefficients.
• Figure 5: Typical $h_k$ with $\text{std}(\mathbf{A}^\mathcal{R})/\text{freq}$ equal to $10^{-3}$ on the right and $10^{-5}$ on the left.

Theorems & Definitions (4)

• Definition 1: Distance Function
• Remark 1: Uniqueness of Angle
• Remark 2: Non planar movement
• Definition 2: Metric function