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This book explores event-based estimation problems. It shows how§several stochastic approaches are developed to maintain estimation performance§when sensors perform their updates at slower rates only when needed.§§The self-contained presentation makes this book s uitable§for readers with no more than a basic knowledge of probability analysis,§matrix algebra and linear systems. The introduction and literature review provide§information, while the main content deals with estimation problems from four§distinct angles in a stochastic setting, using numerous illustrative examples§and comparisons. The text elucidates both theoretical developments and their§applications, and is rounded out by a review of open problems.§§This book is a valuable resource for researchers and§students who wish to expand their knowledge and work in the area of§event-triggered systems. At the same time, engineers and§practitioners in industrial process control will benefit from the§event-triggering technique that reduces communication costs and improves energy§efficiency in wireless automation applications .§§ §