This work proposes a distributed and decentralized observer for position estimation (localization) of a moving target being tracked by multiple mobile sensors. The possibly time-varying set of sensors that have the target in their field of view, is used to create an energy-like quantity that depends on errors in the estimated relative positions and relative velocities of the target as measured by the mobile sensors. The relative velocities need not be measured directly, and can be obtained by filtering the observed relative positions. Each sensor then implements a local version of this distributed observer, and shares relative position information with the other sensors that are tracking the target. The observer is in the form of a variational estimator that is obtained by taking an action functional constructed from the energy-like quantity and dissipating this energy. As a result, the observer is shown to be asymptotically stable. Numerical simulations confirm this stability property and indicate robustness of the distributed observer to bounded measurement errors.