Sensor Power Control for Remote State Estimation with Historical Data Re-Transmission

In this article, the problem of sensor transmission power control for remote state estimation is considered, where packet drops may occur. In most existing literature, the task is to choose the transmission power level for sending the latest data packet at each time step. However, only transmitting the latest packet may not fully compensate the estimation performance degradation due to the drops of historical packets. Therefore, in this paper, we propose a new sensor transmission power control scheme, where the power for sending the latest packet in the fixed sensor transmission power control scheme is split into two parts: one for the transmission of the latest packet and the other one for the re-Transmission of the historical packet. Specifically, we derive an explicit recursion expression of the estimation error covariance and the steady-state analysis of the proposed scheme. Additionally, we provide a sufficient condition such that the proposed scheme outperforms the fixed sensor transmission power control scheme. Moreover, the analytical properties of the proposed scheme and further results are derived from the special case of sensor scheduling problems. Finally, numerical simulations illustrate the validity of the proposed theoretical methods. Note to Practitioners-There are some scenarios in practice where the packet dropped in the transmission, resulting in degraded estimation and control performance. However, only sending current data in most literature may not compensate for the estimated performance degradation caused by historically dropped data. Motivated by this, we consider a new sensor transmission power control scheme using both drops of historical packets and the current information, which further improves the accuracy of the state estimation. In addition, we allocate the transmission power wisely to send the current data and the drops of historical packets for efficient use of energy due to the limited transmission power in practice. Specifically, we allocate part of the transmission power of the current data to the drops of historical packets for transmission when the packet is dropped under the same energy constraint. The effectiveness of the scheme is illustrated based on simulation study.