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

TL;DR

This paper evaluates a reversible Kalman filter on real data, addressing previous limitations by developing a methodology to determine when it outperforms classical filters, with implications for more accurate state estimation on manifolds.

Contribution

It introduces a methodology to identify optimal switching points between reversible and classical Kalman filters on real data, improving state estimation accuracy.

Findings

Reversible Kalman filter shows improved accuracy at certain detection points.

Heuristic event detection mitigates measurement noise issues.

Methodology enables precise evaluation of filter performance on real data.

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.