T-Proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on T-k, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or a widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the T-k linear estimators over their counterparts in the quaternion domain is apparent.

Automated summary

This study analyzes the centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises. New centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised, offering optimal estimators with reduced computational cost compared to traditional methods. Simulation examples demonstrate the effectiveness and superiority of the proposed T-k linear estimators over their counterparts in the quaternion domain.