Multi-target detection, tracking and classification are important problems in aerospace applications, such as reconnaissance, airborne and spaceborne sensing. These problems are correlated but are difficult to be solved simultaneously, especially for systems with multiple sensors. This paper summarized the existing work for multi-target joint detection, tracking and classification based on labeled random finite set. Furthermore, a new algorithm is proposed for multi-sensor multi-target joint detection, tracking and classification problem. A conditional multi-sensor multi-target state estimator is derived, and the optimal solution is then obtained based on the minimum Bayes risk criterion. The numerical simulations are performed, and the results are shown to be more accurate than that of the approximate solutions based on the unlabeled random finite set. It is observed that the labeled random finite set theory provides a good foundation for a joint solution for multi-target detection, tracking and classification.