Lesson 9 Best Linear Unbiased Estimation

Summary

The main purpose of this lesson is to develop our second estimator. It is both unbiased and efficient by design and is a linear function of the measurements Z(k). It is called a best linear unbiased estimator (BLUE).

As in the derivation of the WLSE, we begin with our generic linear model; but now we make two assumptions about this model: (1) H(k) must be deterministic, and (2) V(k) must be zero mean with positive definite known covariance matrix R(k). The derivation of the BLUE is more complicated than the derivation of the WLSE because of the design constraints; however, its performance analysis is much easier because we build good performance into its design.

A very remarkable connection exists ...

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