Long-term location tracking, where trajectory compression is commonly used, has gained high interest for many applications in transport, ecology, and wearable computing. However, state-of-the-art compression methods involve high space-time complexity or achieve unsatisfactory compression rate, leading to rapid exhaustion of memory, computation, storage and energy resources. We propose a novel online algorithm for error-bounded trajectory compression called the Bounded Quadrant System (BQS), which compresses trajectories with extremely small costs in space and time using convex-hulls. In this algorithm, we build a virtual coordinate system centered at a start point, and establish a rectangular bounding box as well as two bounding lines in each of its quadrants. In each quadrant, the points to be assessed are bounded by the convex-hull formed by the box and lines. Various compression error-bounds are therefore derived to quickly draw compression decisions without expensive error computations. In addition, we also propose a light version of the BQS version that achieves $\mathcal{O}(1)$ complexity in both time and space for processing each point to suit the most constrained computation environments. Furthermore, we briefly demonstrate how this algorithm can be naturally extended to the 3-D case. Using empirical GPS traces from flying foxes, cars and simulation, we demonstrate the effectiveness of our algorithm in significantly reducing the time and space complexity of trajectory compression, while greatly improving the compression rates of the state-of-the-art algorithms (up to 47%). We then show that with this algorithm, the operational time of the target resource-constrained hardware platform can be prolonged by up to 41%.