Towards low-complexity state estimation for rigid bodies based on range difference measurements

The rigid body localization (RBL) technique is capable of estimating the state of a rigid body, including its translation and orientation, by utilizing the interactions between sensors and landmarks. The prevalent RBL methods employ precise time-of-flight measurements (or range measurements) to estimate the state. However, the clock offsets in range measurements in asynchronous networks are unavoidable, leading to performance degradation for state estimators. Therefore, range difference measurements have been adopted to solve the RBL problem. However, existing approaches struggle to achieve desirable performance while maintaining computational efficiency. To address this issue, a new closed-form state estimator for asynchronous networks is introduced. The proposed algorithm leverages the Taylor-series expansion technique to enhance accuracy while keeping computational overhead low. Numerical experiments demonstrate that the proposed method achieves state-of-the-art performance with high computational efficiency under small Gaussian noises. This paper proposes a lightweight rigid body localization algorithm to obtain reliable position and orientation estimators for rigid bodies. Simulations show that the closed-form algorithm achieves the CRLB performance over a small noise region.image