Optimal Distributed Estimation over Shared Networks

该提案涉及创新的方法来分析性能和设计最佳的分布式估计系统，在共享网络上运行。该研究计划采用了由多个遥感器组成的配置，这些遥感器评估潜在的不相似信息，并且不允许彼此通信，以及一个作为融合中心的接收器。融合中心的作用是根据传感器通过网络传输给它的信息来估计感兴趣的参数或过程。该公式的一个核心特征是网络是共享的，并且只能支持有限数量的同时传输。在多用户无线设置中，这种限制可能是每当接收机不能辨别在同一信道中发生的同时传输时引起信息丢失的干扰的结果。通常，由于安全性、监管考虑或功率和带宽限制，共享网络（可以是无线或有线）中的同时传输的数量也可能受到约束。一般来说，不可能无误差地估计感兴趣的过程，因为它可能需要所有传感器同时传输，这在所提出的公式中是不可能的。一类问题，设计的融合中心的处理。 由于传感器之间没有通信，因此可以证明所得到的范例是具有非经典信息模式的非凸团队问题。一类碰撞信道模型的同时传输的影响。在这种方法中，问题，从每个传感器的角度来看，是重铸作为一个设计一个最佳的远程估计系统跨越一个新的类的擦除链接，并在通信成本的存在。 一个连接到最佳量化理论将进行调查，以获得有效的数值优化算法。所提出的方法还导致了一类新的最优量化问题，其成本在表示符号之间是不均匀的。我们将探讨如何使用上述思想来找到特定情况下的问题的最佳解决方案。这包括测量在传感器之间独立和相关的设置，以及单步和顺序情况。两个传感器的框架，显示在传感器与高斯测量的非对称阈值政策的最优性，并在测量噪声的存在下扩展到多个传感器将进行研究。此外，将开发有效的软件工具，以实现设计和性能分析的算法。作为任何网络化监测或控制层的重要组成部分，在传感器和融合中心执行的估计算法必须统一设计，以保证整个系统的性能。 该方法将允许实施最佳策略，并分析一系列应用的性能权衡，其中传输传感器的数量超过了底层网络可以利用的数量。例子包括建筑物中的传感器网络、大型可再生能源发电基础设施和配电网络。

The proposal deals with innovative methods to analyze the performance and design optimal distributed estimation systems that operate over shared networks. The research plan adopts a configuration formed by multiple remote sensors, which assess potentially dissimilar information and are not allowed to communicate with each other, and one receiver that acts as fusion center. The role of the fusion center is to estimate a parameter or process of interest based on information that is transmitted to it through the network by the sensors. A central feature of the formulation is the constraint that the network is shared and can support only a finite number of simultaneous transmissions. In a multi-user wireless setting, such a limitation may be the result of interference that causes information loss whenever a receiver cannot discern simultaneous transmissions occurring in the same channel. In general, the number of simultaneous transmissions in a shared network, which can be wireless or wireline, may also be constrained due to security, regulatory considerations or power and bandwidth limitations. In general, it is not possible to estimate the process of interest with no error because it could require simultaneous transmissions by all sensors, which is not possible in the proposed formulation. A class of problems to design the processing at the fusion center is considered. Since there is no communication among the sensors, it can be shown that the resulting paradigm is a non-convex team problem with a non-classical information pattern. A class of collision channels to model the effect of simultaneous transmissions is considered. In this approach, the problem, from the point of view of each sensor, is recast as one of designing an optimal remote estimation system across a new class of erasure links, and in the presence of communication costs. A connection to optimal quantization theory will be investigated to obtain effective numerical optimization algorithms. The proposed approach also leads to a new class of optimal quantization problems for which the cost is non-uniform across representation symbols. We explore how the ideas above can be used to find the optimal solution to particular cases of the problem. This includes the settings in which measurements are independent and dependent across sensors, and the one-step and sequential cases. The two-sensor framework that shows the optimality of asymmetric threshold policies at the sensors with Gaussian measurements, and extensions to multiple sensors in the presence of measurement noise will be investigated. In addition, efficient software tools to implement the algorithms for design and performance analysis will be developed. An important component of any networked monitoring or control layer, estimation algorithms executed at the sensors and fusion centers must be designed in unison to guarantee the performance of the overall system. The methods will allow implementation of optimal policies, and analyze the tradeoffs of performance for a range of applications for which the number of transmitting sensors exceeds what the underlying network can utilize. Examples include sensor networks in buildings, large renewable energy generation infrastructure and power distribution networks.