Remarks on stochastic cloning and delayed-state filtering

2025-08-28

AI Summary

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.

Technology Category

Intelligent Robots: State EstimationReasoning under Uncertainty: Stochastic OptimizationPlanning, Routing, and Scheduling: Model-Based Reasoning

Application Category

Security and Privacy: Large-scale security measurementsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Many estimation problems in robotics and navigation involve measurements that depend on prior states. A prominent example is odometry, which measures the relative change between states over time. Accurately handling these delayed-state measurements requires capturing their correlations with prior state estimates, and a widely used approach is stochastic cloning (SC), which augments the state vector to account for these correlations. This work revisits a long-established but often overlooked alternative--the delayed-state Kalman filter--and demonstrates that a properly derived filter yields exactly the same state and covariance update as SC, without requiring state augmentation. Moreover, the generalized Kalman filter formulation provides computational advantages, while also reducing memory requirements for higher-dimensional states. Our findings clarify a common misconception that Kalman filter variants are inherently unable to handle correlated delayed-state measurements, demonstrating that an alternative formulation achieves the same results more efficiently.

Problem

• Handling delayed-state measurements in robotics and navigation
• Capturing correlations between measurements and prior state estimates
• Efficiently managing computational and memory requirements for estimation

Innovation

• Delayed-state Kalman filter without state augmentation
• Computational efficiency with generalized Kalman formulation
• Equivalent performance to stochastic cloning method