On State Estimation in Multi-Sensor Fusion Navigation: Optimization and Filtering

TL;DR

This paper analyzes the theoretical and practical differences between optimization and filtering methods in multi-sensor fusion navigation, showing that strategy adjustments can make filtering approaches equivalent to optimization in real-time applications.

Contribution

It reveals the theoretical equivalence of optimization and filtering in multi-sensor fusion and demonstrates how strategy adjustments in filtering can match optimization performance.

Findings

Optimization outperforms filtering in accuracy.

Adjusting filtering strategies makes it equivalent to optimization.

Theoretical equivalence is disrupted by real-time strategies.

Abstract

The essential of navigation, perception, and decision-making which are basic tasks for intelligent robots, is to estimate necessary system states. Among them, navigation is fundamental for other upper applications, providing precise position and orientation, by integrating measurements from multiple sensors. With observations of each sensor appropriately modelled, multi-sensor fusion tasks for navigation are reduced to the state estimation problem which can be solved by two approaches: optimization and filtering. Recent research has shown that optimization-based frameworks outperform filtering-based ones in terms of accuracy. However, both methods are based on maximum likelihood estimation (MLE) and should be theoretically equivalent with the same linearization points, observation model, measurements, and Gaussian noise assumption. In this paper, we deeply dig into the theories and existing strategies utilized in both optimization-based and filtering-based approaches. It is demonstrated that the two methods are equal theoretically, but this equivalence corrupts due to different strategies applied in real-time operation. By adjusting existing strategies of the filtering-based approaches, the Monte-Carlo simulation and vehicular ablation experiments based on visual odometry (VO) indicate that the strategy adjusted filtering strictly equals to optimization. Therefore, future research on sensor-fusion problems should concentrate on their own algorithms and strategies rather than state estimation approaches.