© 2020 IEEE. Deployment of unmanned aerial vehicles (UAVs) performing as flying aerial base stations (BSs) has a great potential of adaptively serving ground users during temporary events, such as major disasters and massive events. However, planning an efficient, dynamic, and 3D deployment of UAVs in adaptation to dynamically and spatially varying ground users is a highly complicated problem due to the complexity in air-to-ground channels and interference among UAVs. In this paper, we propose a novel distributed 3D deployment method for UAVBSs in a downlink network for on-demand coverage. Our method consists mainly of the following two parts: sensing-aided crowd density estimation and distributed push-sum algorithm. The first part estimates the ground user density from its observation through on-ground sensors, thereby allowing us to avoid the computationally intensive process of obtaining the positions of all the ground users. On the basis of the estimated user density, in the second part, each UAV dynamically updates its 3D position in collaboration with its neighboring UAVs for maximizing the total coverage. We prove the convergence of our distributed algorithm by employing a distributed push-sum algorithm framework. Simulation results demonstrate that our method can improve the overall coverage with a limited number of ground sensors. We also demonstrate that our method can be applied to a dynamic network in which the density of ground users varies temporally.