On Embedding B-Splines in Recursive State Estimation

In this article, we present a principled study on establishing a recursive Bayesian estimation scheme using B-splines in Euclidean spaces. The use of recurrent control points as the state vector is first conceptualized in a recursive setting. This enables the embedding of B-splines into the state-space model as a continuous-time intermediate, bridging discrete-time state transition with asynchronous multisensor observations. Building on this spline-state-space model, we propose the spline-embedded recursive estimation scheme for general multisensor state estimation tasks. Extensive evaluations are conducted on motion tracking in sensor networks with time-difference-of-arrival and time-of-arrival-inertial settings using real-world and real-world-based synthetic datasets, respectively. Numerical results evidently demonstrate several advantages of spline embedding in recursive state estimation over classical discrete-time filtering approaches in terms of tracking accuracy, robustness, and memory efficiency.