With the recent proliferation of sensor data, there is an increasing need for the efficient evaluation of analytical queries over multiple sensor datasets. The magnitude of such datasets makes exact query answering infeasible, leading researchers into the development of approximate query answering approaches. However, existing approximate query answering algorithms are not suited for the efficient processing of queries over sensor data, as they exhibit at least one of the following shortcomings: (a) They do not provide deterministic error guarantees, resorting to weaker probabilistic error guarantees that are in many cases not acceptable, (b) they allow queries only over a single dataset, thus not supporting the multitude of queries over multiple datasets that appear in practice, such as correlation or cross-correlation and (c) they support relational data in general and thus miss speedup opportunities created by the special nature of sensor data, which are not random but follow a typically smooth underlying phenomenon. To address these problems, we propose PlatoDB; a system that exploits the nature of sensor data to compress them and provide efficient processing of queries over multiple sensor datasets, while providing deterministic error guarantees. PlatoDB achieves the above through a novel architecture that (a) at data import time pre-processes each dataset, creating for it an intermediate hierarchical data structure that provides a hierarchy of summarizations of the dataset together with appropriate error measures and (b) at query processing time leverages the pre-computed data structures to compute an approximate answer and deterministic error guarantees for ad hoc queries even when these combine multiple datasets.