As for multi-sensor systems with correlated noises, eventtriggered sequential and distributed fusion state estimation algorithms are studied, whereas measurement noises of different sensors are correlated with each other at the same time step and also correlated with the process noise at the previous time step. In order to save communication energy, an eventtriggered transmission mechanism is adopted based on observations at current instant and the latest triggered instant of each sensor. Sequential fusion and distributed fusion estimation algorithms are proposed in the sense of linear minimum variance under condition of eventtriggered situation. The data processing can be made by the proposed sequential fusion algorithm in real time in accordance with the order of measurements of sensors arriving at the fusion center, and the algorithms have a little burden to computation. The proposed distributed fusion algorithm can process in parallel measurements of sensors, and has a good reliability. The two kinds of algorithms are as good in estimation accuracy as the eventtriggered centralized fusion estimator. The simulation result shows that the proposed algorithms are valid.