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Monitoring movement of high-dimensional points is essential for environmental databases, geospatial applications, and biodiversity informatics as it reveals crucial information about data evolution, provenance detection, pattern matching etc. Despite recent research interest on processing continuous queries in the context of spatiotemporal data streams, the main focus is on managing the current location of numerous moving objects. In this paper, we turn our attention onto a historical perspective of movement and examine trajectories generated by streaming positional updates. The key challenge is how to maintain a concise, yet quite reliable summary of each object's movement, avoiding any superfluous details and saving in processing complexity and communication cost. We propose two single-pass approximation techniques based on sampling that take advantage of the spatial locality and temporal timeliness …