Reversible Kalman Filter for state estimation with Manifold

2025-09-22

AI Summary

Traditional Kalman filter variants suffer from numerical divergence on synthetic data, reliance on the small-velocity assumption, and accuracy limitations imposed by motion modeling. To address these issues, this paper proposes a manifold-based invertible Kalman filter. By operating directly on the state manifold, the method eliminates the small-velocity assumption, rendering estimation accuracy dependent solely on sensor noise. A numerically stable covariance update mechanism is introduced to suppress filter divergence effectively. Additionally, a heuristic sensor quality detection module is designed to accommodate high-precision multi-sensor fusion—such as 9-axis IMUs and integrated odometry–accelerometer–barometer systems—thereby significantly improving trajectory reconstruction robustness and accuracy in challenging environments (e.g., underwater). Experimental results on both synthetic and real-world datasets demonstrate superior numerical stability and state estimation performance compared to conventional approaches.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants with arbitrary accuracy on synthetic data, something that, to the best of our knowledge, has not been addressed in prior work. To this end, we develop a new filter that exhibits favorable numerical properties, thereby correcting the divergences observed in previous Kalman filter variants. In this formulation, the achievable precision is no longer constrained by the small-velocity assumption and is determined solely by sensor noise. In addition, this new filter assumes high precision on the sensors, which, in real scenarios require a detection step that we define heuristically, allowing one to extend this approach to scenarios, using either a 9-axis IMU or a combination of odometry, accelerometer, and pressure sensors. The latter configuration is designed for the reconstruction of trajectories in underwater environments.

Problem

• Developing a Kalman filter algorithm for state estimation on manifolds
• Evaluating precision of Kalman filter variants with arbitrary accuracy
• Correcting numerical divergences in previous filter formulations

Innovation

• Reversible Kalman Filter for state estimation on manifolds
• Algorithm corrects divergences with favorable numerical properties
• Achievable precision determined solely by sensor noise