优化网络传输以最小化状态估计误差和信道使用

Sayeh Rezaee, César Nieto, Abhyudai Singh
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引用次数: 3

摘要

研究了动态系统状态值在通信网络中的传输问题。状态估计误差的动态采用随机混合系统形式建模,其中误差随时间呈指数增长。传输在特定的时间通过网络进行,以获取系统的状态,每当触发传输时,误差被重置为零均值随机变量。我们的目标是揭示传输策略,使稳态误差方差和每单位时间的平均传输数的组合最小化。我们发现,恒定的泊松传输速率会导致估计误差的重尾分布。接下来,我们考虑一个随机的非阈值传输速率,它随误差的幂律而变化。最后,我们探索了一个基于阈值的速率,在这个速率中,当错误达到阈值时,传输就会发生。我们的研究结果表明,如果传输后的误差方差足够小,基于阈值的策略是最优范式。另一方面,如果该方差较大,且误差增长不够快,则随机无阈值传输策略为最优。这些分析结果通过随机混合系统的仿真得到了验证。
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Optimal network transmission to minimize state-estimation error and channel usage
We consider the problem of transmitting the state value of a dynamical system through a communication network. The dynamics of the error in state estimation is modeled using a stochastic hybrid system formalism, where the error grows exponentially over time. Transmission occurs over the network at specific times to acquire the system's state, and whenever a transmission is triggered, the error is reset to a zero-mean random variable. Our goal is to uncover transmission strategies that minimize a combination of the steady-state error variance and the average number of transmissions per unit of time. We found that a constant Poisson rate of transmission results in a heavy-tailed distribution for the estimation error. Next, we consider a random non-threshold transmission rate that varies as a power law of the error. Finally, we explore a threshold-based rate in which transmission occurs exactly when the error reaches a threshold. Our results show that if the error's variance after transmission is small enough, a threshold-based strategy is the optimal paradigm. On the other hand, if this variance is large, and the error does not grow fast enough, the random non-threshold transmission strategy emerges as optimal. These analytical results are verified by simulations of the stochastic hybrid system.
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