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The minimum-variance smoother solution for input estimation is described and it is shown that the resulting estimates are unbiased. The smoothed input and state estimates are used to iteratively identify unknown process noise variances. The use of smoothed estimates, as opposed to filtered estimates, leads to improved approximate Cramér-Rao lower bounds for the unknown parameters. It is also shown that the sequence of iterates are monotonic and asymptotically approach the actual values under prescribed conditions. A nonlinear mining navigation application is described in which unknown parameters are estimated.