Optimal Distributed Estimation-Deterministic Framework
Estimation Theory has always been a very important and necessary tool in dealing with complex systems and control engineering, from its birth in 18th century. In the last decades, and by raising the hot topics of distributed systems, estimation over networks has been of great interest among the scientists, and lots of effort has been made to solve the various aspects of this problem.
An important question in solving the estimation problems, either over networks or a single system, is how much the obtained estimation is reliable, or in the other words, how much close our estimation is to the subject being estimated. Undoubtedly, a good estimation is an estimation which produces the least error. This leads us to combine the estimation theory with optimization techniques to obtain the best estimation of a given variable, which it is called Optimal Estimation.
In control systems theory, we can have the optimal estimation problem in a static system, which is not progressing in time, and also, we can have the optimal estimation problem in a dynamic system, which is changing by time. Moreover, from another point of view, we can divide the common problems into two different frameworks, Stochastic Estimation Problem, and Deterministic Estimation Problem, which less attention has been made on the latter. Actually, treating a problem in deterministic framework is tougher than stochastic case, since in deterministic case we are not allowed to use the nice properties of stochastic random variables.
In this Master thesis, the optimal estimation problem over distributed systems consist of a finite number of players, in deterministic framework, and in static setting has been treated. We assume a special case of estimation problem, in which the measurements available for different players are completely decoupled from each other. In the other words, no player can have access to the other players’ information space. We will derive the mathematical conditions for this problem as well as the optimal estimation minimizing the given cost function. For ease of understanding, some numerical examples are also provided, and the performance of the given approach is derived.
This thesis consists of five chapters. In chapter 1, a brief introduction about the considered problems in this thesis and their history is given. Chapter 2 introduces the reader with the mathematical tools used in the thesis through the solving a very classic problem in estimation theory. In chapter 3, we have treated the main part of this thesis which is static team estimation problem. In chapter 4, we have looked at the performance of derived estimators, and compare our results with the available numerical solutions. Chapter 5 is a short conclusion, stating the main results, and summarizing the main points of the thesis.
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