<p>This paper studies the adaptive mean-square output consensus problem of heterogeneous multi-agent systems with different multiplicative noises under a directed graph. Specifically, due to the presence of packet losses, the optimal estimator is first derived for the continuous-time stochastic system through discretization to estimate each agent’s state. Based on this, the authors design an edge-based distributed adaptive control protocol that is independent of global information of the communication topology. With the aid of the distributed feedforward control approach and stochastic stability theory, the sufficient condition for achieving mean-square output consensus is derived. Moreover, the convergence of the optimal estimator is analyzed through rigorous mathematical derivation. Finally, a numerical simulation verifies the validity of the obtained results.</p>