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The past few years have witnessed the emergence of an increasing number of applications for tracking and tracing based on radio frequency identification (RFID) technologies. However, raw RFID readings are usually of low quality and may contain numerous anomalies. An ideal solution for RFID data cleansing should address the following issues. First, in many applications, duplicate readings of the same object are very common. The solution should take advantage of the resulting data redundancy for data cleaning. Second, prior knowledge about the environment may help improve data quality, and a desired solution must be able to take into account such knowledge. Third, the solution should take advantage of physical constraints in target applications to elevate the accuracy of data cleansing. There are several existing RFID data cleansing techniques. However, none of them support all the aforementioned features. In this paper, we propose a Bayesian inference-based framework for cleaning RFID raw data. We first design an n-state detection model and formally prove that the three-state model can maximize the system performance. Then, we extend the n-state model to support two-dimensional RFID reader arrays and compute the likelihood efficiently. In addition, we devise a Metropolis-Hastings sampler with constraints, which incorporates constraint management to clean RFID data with high efficiency and accuracy. Moreover, to support real-time object monitoring, we present the streaming Bayesian inference method to cope with realtime RFID data streams. Finally, we evaluate the performance of our solutions through extensive experiments.