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The Kalman filter is a mathematical power tool that is playing an increasingly important role in computer graphics as we include sensing of the real world in our systems. The good news is you don’t have to be a mathematical genius to understand and effectively use Kalman filters. This tutorial is designed to provide developers of graphical systems with a basic understanding of this important mathematical tool.

The celebrated Kalman filter, rooted in the state-space formulation or linear dynamical systems, provides a recursive solution to the linear optimal filtering problem. It applies to stationary as well as nonstationary environments. The solution is recursive in that each updated estimate of the state is computed from the previous estimate and the new input data, so only the previous estimate requires storage. In addition to eliminating the need for storing the entire 1 past observed data, the Kalman filter is computationally more efficient than computing the estimate directly from the entire past observed data at each step of the filtering process.

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