Trajectory-based services require continuous user location sensing. GPS is the most common outdoor location sensor on mobile devices. However, the high energy consumption of GPS sensing prohibits it to be used continuously in many applications. In this paper, we propose a Low Energy Assisted Positioning (LEAP) solution that carefully partitions the GPS signal processing pipeline and shifts delay tolerant position calculations to the cloud. The GPS receiver only needs to be on for less than a second to collect the submillisecond level propagation delay for each satellites signal. With a reference to a nearby object, such as a cell tower, the LEAP server can infer the rest of the information necessary to perform GPS position calculation. We analyze the accuracy and energy benefit of LEAP and use real user traces to show that LEAP can save up to 80% GPS energy consumption in typical trajectory-based service scenarios.