The iterated Kalman smoother as a Gauss-Newton method
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.