Abstract:Gaussian belief propagation (GaBP) is a technique that relies on linearized error and input output models to yield low-complexity solutions to complex estimation problems, which has been recently shown to be effective in the design of range-based GaBP schemes for stationary and moving rigid body localization (RBL) in three-dimensional (3D) space, as long as the relative rotation between the prior position and the target rigid body is sufficiently small. In this article we present a novel range-based RBL scheme via GaBP that relaxes the latter limitation significantly. To this end, the proposed method incorporates a quadratic angle approximation to linearize the relative orientation between the prior and the target rigid body, enabling high precision estimates of corresponding rotation angles even for large deviations. Leveraging the resulting linearized model, we derive the corresponding message-passing (MP) rules to obtain estimates of the translation vector and rotation matrix of the target rigid body, relative to a prior reference frame. Numerical results corroborate the good performance of the proposed angle approximation itself, as well as the consequent RBL performance in terms of root mean square errors (RMSEs) in comparison to the state-of-the-art (SotA), while maintaining a low computational complexity.
From: Niclas Führling [view email]
[v1]
Wed, 4 Feb 2026 10:39:52 UTC (296 KB)
[v2]
Sat, 15 Aug 2026 12:44:31 UTC (306 KB)
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