This technical note considers the dynamic average consensus problem, where a group of networked agents are required to estimate the average of their time-varying reference signals. Almost all existing solutions to this problem require a specific initialization of the estimator states, and such constraints render the algorithms vulnerable to network disruptions. Here, we present three robust algorithms that do not entail any initialization criteria. Furthermore, the proposed algorithms do not rely on the full knowledge of the dynamics generating the reference signals nor assume access to its time derivatives. Two of the proposed algorithms focus on undirected networks and make use of an adaptive scheme that removes the explicit dependence of the algorithm on any upper bounds on the reference signals or its time derivatives. The third algorithm presented here provides a robust solution to the dynamic average consensus problem on directed networks. Compared to the existing algorithms for directed networks, the proposed algorithm guarantees an arbitrarily small steady-state error bound that is independent of any bounds on the reference signals or its time derivatives. The current formulation allows each agent to select its own performance criteria, and the algorithm parameters are distributedly selected such that the most stringent requirement among them is satisfied. A performance comparison of the proposed approach to existing algorithms is presented.