Abstract <p>The note is devoted to the application of an optimal state filtering algorithm for Markov jump processes (MJP) to the practical problem of estimating the available bandwidth (ABW) of a network channel. The term ABW refers to the maximum additional data flow that can be transmitted through the channel under its current load without violating the existing quality of service (QoS) parameters, such as the maximum admissible packet loss rate, latency, etc. The proposed estimation algorithm belongs to the class of passive ones, as it does not rely on the generation of additional service traffic but instead utilizes the statistics of one of the existing data flows transmitting through the channel. The measurements considered include the number of packets of the observed flow currently present in the channel, as well as the occurrences of packet losses within this flow due to channel overflow. The applied problem of bandwidth estimation is thus reduced to an optimal filtering one given a set of indirect perfect (i.e., noiseless) observations and processes with counting components.</p>