不完全确认条件下丢包链路卡尔曼滤波的最优传输策略
An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements
摘要：
本文提出了一种新的设计方法，在智能传感器的最佳传输策略，远程估计一个稳定的线性随机动力系统的状态。传感器测量过程，并使用本地卡尔曼滤波器形成状态估计。传感器通过分组丢弃链路向远程接收器发送量化信息。接收器经由错误的反馈通信信道将分组接收确认发送回传感器，该错误的反馈通信信道本身是分组丢弃。该公式的关键新颖性在于，智能传感器在每个离散时刻决定是否传输其局部状态估计或其局部创新的量化版本。目标是设计最优的传输策略，以最小化作为接收器的预期估计误差协方差和传输分组所需的能量的凸组合的长期平均费用函数。利用动态规划技术得到最优输电策略。利用子模块度的概念，证明了在具有完美分组接收间隔的标量系统中阈值策略的最优性。次优解及其结构结果也进行了讨论。数值结果说明了最佳和次优传输策略的性能。
英文摘要：
This paper presents a novel design methodology for optimal transmission policies at a smart sensor to remotely estimate the state of a stable linear stochastic dynamical system. The sensor makes measurements of the process and forms estimates of the state using a local Kalman filter. The sensor transmits quantized information over a packet dropping link to the remote receiver. The receiver sends packet receipt acknowledgments back to the sensor via an erroneous feedback communication channel which is itself packet dropping. The key novelty of this formulation is that the smart sensor decides, at each discrete time instant, whether to transmit a quantized version of either its local state estimate or its local innovation. The objective is to design optimal transmission policies in order to minimize a long term average cost function as a convex combination of the receiver's expected estimation error covariance and the energy needed to transmit the packets. The optimal transmission policy is obtained by the use of dynamic programming techniques. Using the concept of submodularity, the optimality of a threshold policy in the case of scalar systems with perfect packet receipt acknowledgments is proved. Suboptimal solutions and their structural results are also discussed. Numerical results are presented illustrating the performance of the optimal and suboptimal transmission policies.
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