线性状态估计的自适应采样
Adaptive sampling for linear state estimation
AI总结：
针对传感器通过有限速率网络传输测量值以估计状态的问题，研究了因果采样策略的最优设计，通过将问题转化为最优停时序列，证明了Delta采样性能较差，并给出了布朗运动情形下的解析解。
摘要：
当传感器具有连续测量值但通过数据网络向估计状态的监督器发送有限消息时，可用的数据包速率决定了状态估计的可实现质量。当这种速率限制变得严格时，传感器的消息策略需要重新设计。什么是好的因果消息策略？消息数据包应包含什么？监督器处因果估计的最低可能失真是什么？Delta采样是否优于周期性采样？我们在网络的理想化模型和传感器完美测量的假设下回答这些问题。对于标量线性扩散过程，我们研究选择因果采样时间以最小化总平方误差失真的问题。我们坚持有限时域，并对允许的样本数量施加硬上限。我们将设计问题转化为选择最优停时序列的问题。我们将其简化为一个嵌套序列问题，每个问题要求一个单一的最优停时。在监督器处最小二乘估计的一个未经证明但自然的假设下，这些单一停时问题中的每一个都是标准形式。最优停时是估计误差超过设计包络的随机时间。对于状态是布朗运动的情况，我们解析地给出：最优采样包络的形状、最优Delta采样下的包络形状及其性能。令人惊讶的是，我们发现Delta采样表现不佳。因此，当速率约束是有限时域内样本数量的硬限制时，我们不应使用Delta采样。
英文摘要：
When a sensor has continuous measurements but sends limited messages over a data network to a supervisor which estimates the state, the available packet rate fixes the achievable quality of state estimation. When such rate limits turn stringent, the sensor's messaging policy should be designed anew. What are the good causal messaging policies ? What should message packets contain ? What is the lowest possible distortion in a causal estimate at the supervisor ? Is Delta sampling better than periodic sampling ? We answer these questions under an idealized model of the network and the assumption of perfect measurements at the sensor. For a scalar, linear diffusion process, we study the problem of choosing the causal sampling times that will give the lowest aggregate squared error distortion. We stick to finite-horizons and impose a hard upper bound on the number of allowed samples. We cast the design as a problem of choosing an optimal sequence of stopping times. We reduce this to a nested sequence of problems each asking for a single optimal stopping time. Under an unproven but natural assumption about the least-square estimate at the supervisor, each of these single stopping problems are of standard form. The optimal stopping times are random times when the estimation error exceeds designed envelopes. For the case where the state is a Brownian motion, we give analytically: the shape of the optimal sampling envelopes, the shape of the envelopes under optimal Delta sampling, and their performances. Surprisingly, we find that Delta sampling performs badly. Hence, when the rate constraint is a hard limit on the number of samples over a finite horizon, we should should not use Delta sampling.
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。
