Error Analysis of a Dual Quaternion Batch Estimator

This study presents an error analysis for a single-frame dual quaternion batch estimator that utilizes point and unit vector measurements. This estimator addresses a constrained least-squares problem by minimizing a cost function that aggregates orientation and position errors, analogous to the q-method for rotation quaternions. An error analysis of this dual quaternion method is developed based on the eigenvalue principle for the first time, deriving the closed-form expressions for the three-dimensional attitude and translation error vectors, along with their covariance matrices. Extensive Monte Carlo simulations validate the precision of these expressions. Moreover, we explore the algorithm’s sensitivity to variations in batch sizes and cost weights, revealing the balance between computational efficiency and estimation accuracy.