This paper investigates the remote state estimation for a cyber–physical system (CPS) where a group of (primary) sensors transmit sensing data packets to the remote estimators for state estimation via their individual channels. In view of the complexity arising from the scale of such system, it is desirable for the primary sensors to share their channels with the newly-added (potential) ones, especially when the sensing data of primary ones contains less valuable information. However, the channel sharing inevitably leads to signal interference among sensors using the same channels, and it may further degenerate the remote estimation performance. Thus, the system designer should allocate the transmission power for sensors to maximize the global estimation accuracy. We emphasize the non-cooperative nature among sensors, and solve the problem in an exchange market framework with a platform acting on behalf of the system designer, and prove that the optimal power allocation is a spontaneous outcome of the market under well-designed prices. More specifically, under (subsidized) prices announced by the platform, the primary sensors are willing to open up their channels for sharing, in which a distributed optimal power allocation is derived explicitly. To alleviate transmission interference, the platform will charge potential sensors for the use of channels, among which the mutual interaction is formulated as a non-cooperative game and the existence of a pure Nash equilibrium is proved. We also devise an algorithm for the platform to design subsidized/toll prices, which is given in an explicit recursive form with simple iterations, and therefore suited for the platform with limited computation capability.

本文研究了网络物理系统（CPS）的远程状态估计，其中一组（主要）传感器将传感数据包传输到远程估计器，以通过其各自的通道进行状态估计。考虑到这种系统的规模所带来的复杂性，希望主要传感器与新添加的（潜在的）传感器共享其信道，尤其是当主要传感器的感测数据包含有价值的信息时。然而，信道共享不可避免地导致使用相同信道的传感器之间的信号干扰，并且这可能进一步降低远程估计性能。因此，系统设计人员应为传感器分配发射功率，以使全局估计精度最大化。我们强调传感器之间的非合作性质，并以代表系统设计者的平台在交换市场框架中解决问题，并证明在合理设计的价格下，最佳功率分配是市场的自发结果。更具体地，在平台宣布的价格（补贴价）下，主要传感器愿意开放其共享渠道，在其中明确分配分布式最优功率分配。为了减轻传输干扰，该平台将为使用信道的潜在传感器充电，其中相互交互被表述为非合作博弈，并且存在一个交互作用。在平台宣布的价格（补贴价）下，主要传感器愿意开放其共享渠道，其中明确得出了分布式最优功率分配。为了减轻传输干扰，该平台将为使用信道的潜在传感器充电，其中相互交互被表述为非合作博弈，并且存在一个交互作用。在平台宣布的价格（补贴价）下，主要传感器愿意开放其共享渠道，其中明确得出了分布式最优功率分配。为了减轻传输干扰，该平台将为使用信道的潜在传感器充电，其中相互交互被表述为非合作博弈，并且存在一个交互作用。证明了纯纳什均衡。我们还为平台设计了一种算法来设计补贴/通行费价格，该算法以明确的递归形式给出，具有简单的迭代，因此适用于计算能力有限的平台。