Download free Estimation over Communication Networks: Performance Bounds and Achievability Results.pdf This paper considers the problem of estimation over communication networks. Suppose a sensor is taking measurements of a dynamic process. However the process needs to be estimated at a remote location connected to the sensor through a network of communication links that drop packets stochastically. We provide a framework for computing the optimal performance in the sense of expected error covariance. Using this framework we characterize the dependency of the performance on the topology of the network and the packet dropping process. For independent and memoryless packet dropping processes we find the steady-state error for some classes of networks and obtain lower and upper bounds for the performance of a general network. We also illustrate how this framework can be used in the synthesis of networks for the purpose of estimation. Finally we find a necessary and sufficient condition for the stability of the estimate error covariance for general networks with spatially correlated and Markov type dropping process. This interesting condition has a max-cut interpretation.

In recent years, systems comprising of multiple sensors cooperating with each other have received wide-spread interest (see, e.g., [1], [2]). Although such systems admittedly have a higher complexity than the strategy of using only one sensor, the increased accuracy often make these systems worthwhile. From an estimation and control perspective, such systems present many new challenges, such as dealing with data delay or data loss imposed by the communication links, fusion of data emerging from multiple nodes and so on. Most of these issues arise because of the tight coupling between the estimation and control tasks that depend on the sensed data and the communication channel effects that affect the transmission and reception of data. Communication links introduce many potentially detrimental phenomena, such as quantization error, random delays, data loss and data corruption to name a few. It is imperative to understand and counteract the effects of the communication channels.

Motivated by this, there has been a lot of work done on estimation and control over networks of communication links (see, e.g., [3], [4] and the references therein). Beginning with the seminal paper of Delchamps [5], quantization effects have been variously studied both in estimation and control context by Tatikonda [6], Nair and Evans [7], Hespanha et al [8] and many others. The effect of delayed packet delivery using various models for network delay has also been considered by many researchers.