In a multisensor target tracking application running on a shared network, at what bit rates should the sensors send their measurements to the tracking fusion center? Clearly, the sensors cannot use arbitrary rates in a shared network, and a standard network rate control algorithm may not provide rates amenable to effective target tracking. For Kalman filter-based multisensor target tracking, we derive a utility function that captures the tracking quality of service as a function of the sensor bit rates. We incorporate this utility function into a network rate resource allocation framework, deriving a distributed rate control algorithm for a shared network that is suitable for current best effort packet networks, such as the Internet. In simulation studies, the new rate control algorithm engenders significantly better tracking performance than a standard rate control method, while the ordinary data transfer flows continue to effectively operate while using their standard rate control methods.