One of the major problems in sensor fusion is that sensors frequently provide spurious observations which are difficult to predict and model. The spurious data from sensors must be identified and eliminated from the sensor fusion since its incorporation in the fusion pool might lead to inaccurate estimation. This paper presents a sensor fusion strategy based on Bayesian approach that can automatically identify the inconsistency in sensor data so that the spurious sensor data can be eliminated from the sensor fusion process. The proposed method adds a term to the commonly used Bayesian technique that represents the probabilistic estimate corresponding to the event that the data is not spurious conditioned upon the data and the true state. This term has the effect of increasing the variance of the posterior distribution when data from one of the sensors is inconsistent with respect to the other. The proposed strategy was verified with the help of extensive computations performed on simulated data from three sensors. A comparison was made between two different fusion schemes: centralized fusion in which data from all sensors were fused at once, and decentralized or sequential Bayesian method which provided opportunity to identify and eliminate spurious data from the fusion process. The simulations verified that the proposed strategy was able to identify spurious data, and its elimination from the fusion process led to better estimation.