By leveraging the sensing capabilities of consumer mobile devices, mobile crowdsensing (MCS) systems enable a number of new applications for Internet of Things (IoT), such as traffic management, environmental monitoring, and localisation. However, the sensing data collected from the crowd workers are of various qualities, making it difficult to discover the ground truth and maintain the fairness of incentivisation schemes. In this paper, we propose a truth discovery algorithm based on a two-stage Maximum Likelihood Estimator (MLE), which explicitly characterises the heterogeneous sensing capabilities of the crowd and is able to estimate ground truth accurately using only a small amount of data from IoT infrastructures. Moreover, based on the truth discovery algorithm, two reward distribution schemes, LRDS and MRDS, are proposed to ensure fairness of rewarding the crowd according to their effort levels. We evaluate the estimation accuracy of the truth discovery algorithm and the fairness of the reward distribution schemes using both simulations and real-world MCS campaigns. The evaluation results indicate that the proposed methods achieve superior performance compared with state-of-the-art methods in terms of estimation accuracy and fairness of reward distribution. © 2018 Elsevier B.V.