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The iterated Kalman smoother as a Gauss-Newton method

Abstract
The Kalman smoother is known to be the maximum likelihood estimator when the measurement and transition functions are affine; i.e., a linear function plus a constant. A new proof of this result is presented that shows that the Kalman smoother decomposes a large least squares problem into a sequence of much smaller problems. The iterated Kalman smoother is then presented and shown to be a Gauss-Newton method for maximizing the likelihood function in the nonaffine case. The method takes advantage of the decomposition obtained with the Kalman smoother.

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