This paper proposes a scheme for position estimation of randomly deployed sensor nodes in a wireless sensor network. Without GPS capability on any of the sensors, the position estimation is facilitated by beacons that move within the network. The beacons are equipped with GPS and can broadcast messages that contain the beacon identifiers and their current positions. With erroneous boundary beacon positions captured at the sensor, the sensor calculates its own position iteratively and updates the estimates upon newly acquired beacon positions. Practical implementation issues are discussed and simulation results show that the proposed iterative approach converges quickly even with beacon positions that have large errors.