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This study investigates the multi-sensor-based centralised estimation problem in heterogeneous sensor networks with a common communication channel. Owing to the heterogeneity of the distributed sensors, it is usually impossible to package the measurements into one packet and transmit them to the fusion centre (FC) together, which implies that the measurements should be forwarded to the FC asynchronously. In view of this, a novel stochastic competitive transmission strategy is proposed to stagger the sensors' transmissions. By using the asynchronous sampled information from the sensors, an H∞ filter is designed for the FC to periodically generate estimates. The filter parameters are determined by solving a linear-matrix inequality. An illustrative example is provided to demonstrate the effectiveness of the proposed theoretical results.