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The available bandwidth (AB) of an end-to-end path is its remaining capacity and it is an important metric for several applications. That's why several available bandwidth estimation tools have been published recently. Most of these tools use the probe rate model. This model is based on the concept of self- induced congestion and requires that the tools send a packet train at a rate matching the available bandwidth. The main issue with this model is that these tools congest the path under study. In this paper we present a novel available bandwidth estimation tool that takes into account this issue. Our tool is based on a mathematical model that sends packet trains at a rate lower than the AB. The main drawback of this model is that it is not able to track the AB. To solve this issue we propose to apply Kalman filters (KF) to the model. By applying these filters we can produce real-time estimations of the available bandwidth and monitor its changes. In addition the KFs are able to filter the noisy (erroneous) measurements improving the overall accuracy. We also present an extensive evaluation of our tool in different network scenarios and we compare its performance with that of pathChirp (a state-of-the-art available bandwidth estimation tool).