Note on a new computational data smoothing procedure suggested by minimum mean square error estimation

Computational procedures for obtaining minimum mean square error estimates of parameters are developed for the case in which the observation functions, describing the dependence of observed data on the unknown parameters, can be accurately approximated by expansions through quadratic terms in the unknown parameters. Analytical closed-form solutions are obtained for the minimum mean square error estimates of real valued functions of the unknown parameters. It is pointed out that even in cases where the statistical assumptions are not satisfied the resulting computational procedures may be applicable. In such cases adequate, although nonoptimum, estimates may still be obtained and the computational procedure may be more convenient than iterative least-square methods.