The state estimation plays an irreplaceable role in many real applications since it lays the foundation for decision-making and control. This paper studies the multi-sensor estimation problem for a contention-based unreliable wireless network. At each time step, no more than one sensor can communicate with the base station due to the potential contention and collision. In addition, data packets may be lost during transmission since wireless channels are unreliable. A novel packet arrival model is proposed which simultaneously takes into account the above two issues. Two scenarios of wireless sensor networks (WSNs) are considered: the sensors transmit the raw measurements directly and the sensors send the local estimation instead. Based on the obtained packet arrival model, necessary and sufficient stability conditions of the estimation at the base station side are provided for both network scenarios. In particular, all offered stability conditions are expressed by simple inequalities in terms of the packet arrival rates and the spectral radius of the system matrix. Their relationships with existing related results are also discussed. Finally, the proposed results are demonstrated by simulation examples and an environment monitoring prototype system.