In this paper, we propose Multi-Rate Bandwidth Available in Real Time (MR-BART) to estimate the end-to-end Available Bandwidth (AB) of a network path. The proposed scheme is an extension of the Bandwidth Available in Real Time (BART) which employs multi-rate (MR) probe packet sequences with Kalman filtering. Comparing to BART, we show that the proposed method is more robust and converges faster than that of BART and achieves a more AB accurate estimation. Furthermore, we analyze the estimation error in MR-BART and obtain analytical formula and empirical expression for the AB estimation error based on the system parameters.