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This paper aims to introduce an application to Kalman Filtering Theory, whichis rather unconventional. Recent experiments have shown that many naturalphenomena, especially from ecology or meteorology, could be monitored andpredicted more accurately when accounting their evolution over somegeographical area. Thus, the signals they provide are gathered together into acollection of distributed time series. Despite the common sense, such timeseries are more or less correlated each other. Instead of processing each timeseries independently, their collection can constitute the set of measurablestates provided by some open system. Modeling and predicting the system statescan take benefit from the family of Kalman filtering algorithms. The articledescribes an adaptation of basic Kalman filter to the context of distributedsignals collections and completes with an application coming from Meteorology.

Kalman Filtering of Distributed Time Series