Optimal Distributed Estimation over Shared Networks

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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.