We present a novel time-based positioning scheme (TPS) for efficient location discovery in outdoor sensor networks. TPS relies on TDoA (time-difference-of-arrival) of RF signals measured locally at a sensor to detect range differences from the sensor to three base stations. These range differences are averaged over multiple beacon intervals before they are combined to estimate the sensor location through trilateration. A nice feature of this positioning scheme is that it is purely localized: sensors independently compute their positions. We present a statistical analysis of the performance of TPS in noisy environments. We also identify possible sources of position errors with suggested measures to mitigate them. Our scheme requires no time synchronization in the network and minimal extra hardware in sensor construction. TPS induces no communication overhead for sensors, as they listen to three beacon signals passively during each beacon interval. The computation overhead is low, as the location detection algorithm involves only simple algebraic operations over scalar values. TPS is not adversely affected by increasing network size or density and thus offers scalability. We conduct extensive simulations to test the performance of TPS when TDoA measurement errors are normally distributed or uniformly distributed. The obtained results show that TPS is an effective scheme for outdoor sensor self-positioning.