Proper $\beta$-Quaternion Fusion Filtering With Intermittent Observations Under Concurrent DoS–Deception Attacks

This paper investigates the problem of fusion estimation by proposing both distributed and centralized fusion filtering algorithms, developed within the framework of the $\beta$-quaternion algebra. The objective is to estimate multidimensional signals in the $\beta$-quaternion domain from sensor observations that may be degraded not only by uncertainty arising from intermittency but also by adversarial actions, including denial-of-service (DoS) and deception attacks, as well as scenarios in which both threats act concurrently. Furthermore, the proposed framework incorporates correlated observation noises, which enhances modeling fidelity under realistic sensing conditions. A key advantage of adopting the $\beta$-quaternion algebra lies in its ability to exploit first-order properness conditions, which enable a reduction of the problem dimensionality to one-fourth that of the corresponding real-valued formulation. This dimensionality reduction leads to a significant decrease in computational complexity without compromising estimation accuracy. Numerical simulation examples are presented to demonstrate the benefits of the proposed approach and to provide a comparative performance assessment achieved by proper $\beta$-quaternion distributed and centralized fusion estimation schemes.