β-Quaternion Centralized Fusion Estimation Problem Under First-Order Properness Conditions

The linear least mean-squared error (LLMSE) centralized fusion filtering and one-stage prediction problem is addressed in the β -quaternion domain, by using observations provided by multiple sensors. With the aim of reducing the computational burden of the estimation recursive algorithm, the first-order properness conditions have been studied, leading to a reduction in the augmented state-space model. A numerical simulation example illustrates the improvement in the estimations obtained with the proposed algorithm compared to those calculated with its quaternion counterpart when first-order properness conditions are satisfied.