有限测量与噪声通信下的最优估计
Optimal Estimation with Limited Measurements and Noisy Communication
AI总结：
本文研究了一种单传感器与单估计器的顺序估计和传感器调度问题，考虑了噪声信道下的最优编码与传输策略，发现噪声存在时出现相变现象。
摘要：
本文考虑了一个传感器和一个估计器的顺序估计和传感器调度问题。传感器对底层无记忆随机过程的状态进行顺序观测，并决定是否将该测量发送给估计器。传感器和估计器共同目标是在有限时间内最小化估计状态的期望失真，且传感器只能有限次传输。与之前假设通信无噪声的工作不同，本文考虑了具有固定功率约束的加性噪声信道，因此传感器需在传输前编码信息。对于某些特定的源噪声和信道噪声密度，我们得到了最优编码和估计策略及最优传输调度。通过动态规划分析噪声信道的影响，得出了一些出人意料的结果，如使用的传输机会数量出现相变现象，这在无噪声通信设置中未曾出现。
英文摘要：
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon, with the constraint that the sensor can transmit its observation only a limited number of times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. For some specific source and channel noise densities, we obtain the optimal encoding and estimation policies in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase-transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
