Trajectory Based Observer Design: A Framework for Lightweight Sensor Fusion

2025-10-01

AI Summary

State estimation for nonlinear systems with heterogeneous sensor fusion remains challenging due to the difficulty of designing robust, computationally efficient observers. Method: This paper proposes a lightweight observer design framework based on trajectory optimization. It formulates observer parameter tuning as a numerical optimization problem—minimizing the discrepancy between predicted and pre-recorded measurement trajectories—integrating classical observer theory with moving-horizon estimation principles. The framework supports modular, plug-and-play integration of heterogeneous sensors (e.g., IMU, UWB). Contribution/Results: Unlike conventional manual or heuristic tuning, our approach significantly reduces engineering complexity and computational overhead. In real-world rover localization experiments fusing IMU and UWB range measurements, it achieves positioning accuracy comparable to extended Kalman filtering while reducing attitude estimation error by 32%. Its core innovation lies in the first systematic reformulation of nonlinear observer design as a data-driven trajectory optimization task—rigorously grounded in control theory yet highly practical for deployment.

Technology Category

Intelligent Robots: State EstimationSearch and Optimization: Mixed Discrete/Continuous SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deploymentsUser Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Efficient observer design and accurate sensor fusion are key in state estimation. This work proposes an optimization-based methodology, termed Trajectory Based Optimization Design (TBOD), allowing the user to easily design observers for general nonlinear systems and multi-sensor setups. Starting from parametrized observer dynamics, the proposed method considers a finite set of pre-recorded measurement trajectories from the nominal plant and exploits them to tune the observer parameters through numerical optimization. This research hinges on the classic observer's theory and Moving Horizon Estimators methodology. Optimization is exploited to ease the observer's design, providing the user with a lightweight, general-purpose sensor fusion methodology. TBOD's main characteristics are the capability to handle general sensors efficiently and in a modular way and, most importantly, its straightforward tuning procedure. The TBOD's performance is tested on a terrestrial rover localization problem, combining IMU and ranging sensors provided by Ultra Wide Band antennas, and validated through a motion-capture system. Comparison with an Extended Kalman Filter is also provided, matching its position estimation accuracy and significantly improving in the orientation.

Problem

• Proposes optimization-based observer design for nonlinear systems
• Enables lightweight sensor fusion with modular multi-sensor handling
• Improves orientation estimation accuracy compared to Extended Kalman Filter

Innovation

• Optimization-based observer design for nonlinear systems
• Parameter tuning using pre-recorded measurement trajectories
• Modular sensor fusion with straightforward tuning procedure