## 10. Computing the Estimate

In Chapter 7 we gave three basic procedures for parameter estimation:

**1.** The prediction-error approach in which a certain function *V*_{N}(*θ*, *Z*^{N}) is minimized with respect to *θ*.

**2.** The correlation approach, in which a certain equation *f*_{N}(*θ*, *Z*^{N}) = 0 is solved for *θ*.

**3.** The subspace approach to estimating state space models.

In this chapter we shall discuss how these problems are best solved numerically.

At time *N*, when the data set *Z*^{N} is known, the functions *V*_{N} and *f*_{N} are just ordinary functions of a finite-dimensional real parameter vector *θ*. Solving the problems therefore amounts to standard questions of nonlinear programming and numerical analysis. Nevertheless, it is worthwhile to consider the problems in our parameter ...