A Joint Particle Filter for Quaternion-Valued $\alpha$-Stable Signals via the Characteristic Function

The filtering paradigm is revisited through the perspective of characteristic functions. This results in the derivation of a novel particle filtering technique for sequential estimation/tracking of quaternion-valued $\alpha$ -stable random signals. Importantly, the derived particle filter incorporates an efficient information fusion format and collaborative/distributed estimation framework to accommodate the push toward use of sensor networks. The distributed setting provides for the distribution of computational complexity among agents of a sensor network, while allowing each agent to retain an estimate of the state. Furthermore, the quaternion-valued structure allows for the derivation of a rigorous algorithm that is advantageous when dealing with signals of a multidimensional nature commonly encountered in sensor arrays.