State-of-the-art trajectory compression methods usually involve high space-time complexity or yield unsatisfactory compression rates, leading to rapid exhaustion of memory, computation, storage, and energy resources. Their ability is commonly limited when operating in a resource-constrained environment especially when the data volume (even when compressed) far exceeds the storage limit. Hence, we propose a novel online framework for error-bounded trajectory compression and ageing called the Amnesic Bounded Quadrant System (ABQS), whose core is the Bounded Quadrant System (BQS) algorithm family that includes a normal version (BQS), Fast version (FBQS), and a Progressive version (PBQS). ABQS intelligently manages a given storage and compresses the trajectories with different error tolerances subject to their ages. In the experiments, we conduct comprehensive evaluations for the BQS algorithm family and the ABQS framework. Using empirical GPS traces from flying foxes and cars, and synthetic data from simulation, we demonstrate the effectiveness of the standalone BQS algorithms 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 45 percent). We also show that the operational time of the target resource-constrained hardware platform can be prolonged by up to 41 percent. We then verify that with ABQS, given data volumes that are far greater than storage space, ABQS is able to achieve 15 to 400 times smaller errors than the baselines. We also show that the algorithm is robust to extreme trajectory shapes.