asynchronous sensor fusion

High-precision online estimation algorithms for robotics are highly sensitive to sensor timestamp accuracy; however, existing synchronization solutions struggle to simultaneously achieve real-time operation, low cost, and high temporal precision. To address this, we propose a real-time, trigger-based time synchronization system built on commodity hardware. Our approach employs a hardware-triggered mechanism to jointly schedule heterogeneous sensors operating at different frequencies, and integrates an enhanced clock synchronization protocol with nanosecond-resolution timestamping to ensure precise coordination between sensors and the onboard computer. Crucially, the system eliminates reliance on expensive dedicated timing hardware, thereby substantially mitigating the impact of timing errors on online estimation. Experimental evaluation on a physical robot platform demonstrates sub-microsecond synchronization accuracy, along with significant improvements in both estimation robustness and real-time performance.

This work addresses the challenge of wireless remote state estimation under random sensor-to-estimator delays, which degrade information utility. While conventional approaches focus solely on information freshness—typically measured by Age of Information (AoI)—they overlook the intricate coupling among delay, information content, and energy efficiency. To bridge this gap, the authors propose a unified delay-aware framework that incorporates delayed measurements via posterior-fusion Kalman updates, formulates scheduling as a Markov decision process, and introduces a proximal policy optimization (PPO)-based reinforcement learning scheduler. This scheduler jointly optimizes information gain and energy consumption without requiring prior knowledge of the delay distribution. The study further establishes, for the first time, an explicit characterization of the dependency between delay and information gain, yielding a tractable stability condition that guarantees bounded estimation error. Experiments demonstrate that the proposed method significantly outperforms random scheduling and baseline RL algorithms such as DQN and A2C under heterogeneous sensors, realistic link energy costs, and stochastic delays, achieving substantially lower estimation error at comparable energy expenditure while remaining robust to variations in measurement availability and noise.

In robot navigation, delayed measurements—such as odometry—that depend on historical states pose challenges for estimation; existing Stochastic Cloning (SC) methods address this by augmenting the state vector to model state correlations, incurring significant computational and memory overhead. Method: This paper proposes a Delayed-State Kalman Filter (DS-KF) that avoids state augmentation. Within a generalized Kalman filtering framework, we rigorously derive mean and covariance update equations for delayed observations, establishing for the first time that classical Kalman filter variants can exactly capture delayed-state correlations without augmentation. Contribution/Results: Theoretical analysis and experiments demonstrate that DS-KF achieves estimation accuracy identical to SC, while reducing computational complexity from O(n³) to O(n²) and decreasing memory usage by approximately 40% (where n is the state dimension). This work corrects the common misconception that state augmentation is necessary for handling delay-induced correlations, providing a more efficient estimation paradigm for high-dimensional real-time navigation systems.

Robot state estimation faces growing challenges from platform diversity and task complexity, while traditional discrete-time filtering and smoothing methods suffer from sampling-rate limitations and temporal misalignment. This paper proposes a unified formal framework for continuous-time state estimation, systematically integrating major modeling paradigms—including spline interpolation, Gaussian process regression, Bayesian smoothing, and continuous-time optimization—for the first time. We present the most comprehensive survey and taxonomy to date, clarifying methodological evolution, state representation strategies, and application-specific advancements. Furthermore, we identify and formally characterize key open problems, highlighting emerging research directions: differentiable modeling, asynchronous multi-sensor fusion, and real-time computation. Our framework significantly improves estimation accuracy, temporal resolution flexibility, and downstream planning and control performance. By bridging theoretical rigor with practical applicability, this work advances both the foundations and deployment of continuous-time estimation in robotics.

This paper addresses the inherent trade-off between computation and communication latency in distributed real-time state estimation. Method: We formulate the first rigorous optimization framework jointly modeling computation latency, communication latency, and estimation performance; theoretically prove that transmitting raw sensor data is generally suboptimal in heterogeneous networks; and propose a joint convex optimization algorithm for sensor subset selection and adaptive linear preprocessing—explicitly respecting per-node computational constraints and network heterogeneity. Contributions/Results: Leveraging Kalman filtering theory and heuristic subset search, we validate the approach on multivariate discrete-time systems. Experiments demonstrate that our method significantly reduces estimation error compared to full-sensor transmission, and that judicious local preprocessing substantially improves overall estimation accuracy.

This study addresses the severe degradation of inertial navigation system (INS) filtering performance caused by unknown time delays (50–300 ms) introduced by commercial GNSS receivers. For the first time, Galilean spacetime symmetry is incorporated into delayed INS modeling to construct a joint equivariant representation of navigation states and time delay, enabling the design of a corresponding equivariant filter (EqF) that achieves consistent and high-accuracy state estimation. This approach overcomes the consistency and accuracy limitations of conventional extended Kalman filters (EKF) under large time delays. Experimental results demonstrate robust performance with real-world fixed-wing UAV data exhibiting 90–120 ms delays, while simulations further confirm its significant superiority over existing EKF methods even at delays up to 500 ms.

In aided inertial navigation systems, the simultaneous identification of unknown constant measurement delays and system states is inherently challenging, significantly degrading estimation accuracy. This work addresses this issue by analyzing the continuous symmetries arising from trajectory geometry and the delayed measurement model, revealing a broader class of degenerate trajectories. For the first time, these degeneracies are attributed to symmetries under the special Galilean group. By integrating Lie group methods, identifiability theory, and Jacobian linearization analysis, the study precisely characterizes the geometric properties of unidentifiable trajectories and establishes a rigorous theoretical link between system symmetries and the loss of identifiability. These insights provide critical guidance for the design of multi-sensor fusion systems operating with time-delayed measurements.

This study addresses the non-identifiability of unknown constant time delay and initial states in aided inertial navigation systems. By integrating differential geometry with system identifiability theory, the authors formulate a delayed observation model and analyze its inherent symmetry structure. The work reveals a broader class of degenerate trajectories than previously recognized, along which the system exhibits continuous symmetries that render the time delay and initial states unrecoverable in a unique manner. The paper precisely characterizes the trajectory conditions leading to such non-identifiability, thereby establishing theoretical limits and offering principled guidance for the design of multi-sensor fusion navigation systems.

研究通过在伽利略群上使用滑动窗口滤波器，联合估计未知延迟和导航状态，以提高存在测量延迟时的惯性导航精度。

This work addresses the limited adoption of Gaussian processes (GPs) in continuous-time state estimation—primarily hindered by their high theoretical barrier—by introducing a GP modeling approach formulated within a factor graph framework. By re-expressing the GP motion prior using factor graph semantics, the proposed method naturally supports asynchronous multi-sensor fusion and trajectory interpolation while yielding smooth, continuous trajectories. The authors provide three open-source implementations built on GTSAM, significantly lowering the practical entry barrier for employing GP-based continuous-time estimation and thereby facilitating its real-world deployment and application in robotic systems.