Mathematics Colloquia and Seminars

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Abstract: The filtering problem is to take partial and noisy measurements about a dynamic process and to use them estimate in real time the complete state of the process. The filtering algorithm is constructed using models of the dynamics and measurement processes and some additional partial and noisy information about the state of the process. The algorithm must be computationally efficient enough that the state estimates can be computed in real time as the process evolves. When the dynamics and measurement processes are linear and the additional information is about the initial state of the dynamics then the method of choice is the Kalman filter which was developed in the early sixties. It and its extensions have been employed in a variety of applications ranging from aerospace to weather prediction. In a Google search, the term “Kalman Filtering” results in over half a million hits. But the additional information isn’t always just about the initial state of dynamics, it may include information about the final state of the dynamics. For example in missile defense applications one may have partial information about where the missile is coming from and also partial information about where it is going to. We present the Boundary Value Filter for linear processes about which partial boundary information is available. The Kalman Filter is a special case of the Boundary Value Filter.

Reception to follow at 5pm