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My father had been assigned the problem of navigating to the Moon and, as he told it to me, it was a very difficult problem, they didn't have a mathematical solution to it. It involved taking a number of different sources of information and combining them in an optimal way to get the best estimate of where your spacecraft is at any time, how fast you're going and other variables, too.
My dad invited Rudy Kalman to give a lecture at Ames, and when he did, Dad had an epiphany, rudy Kalman had written a paper about a theoretical' linear' solution to estimating a vehicle's location and speed. The problem was that this was a fundamentally' nonlinear' problem ; that's like the difference in complexity between floating down a lazy river and going over a waterfall, where your motion becomes chaotic and unpredictable. My dad then developed the equations for how to solve this nonlinear problem -- a major extension of Kalman's work.
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