9.20 LEAST-SQUARES ESTIMATION

Assume that information about the parameter vector is obtained via the following measurement model:

(9.309)

where Y is a random variable, a is a known vector, and V is an unobservable additive noise random variable. This is a generalization of the simpler model Y = X+V discussed previously where X is a random variable. If happens to be a random vector, its distribution will not be taken into account in least-squares (LS) estimation. Assume there are N iid samples such that

where and

Usually, the number of samples far exceeds the number of parameters, that is, so that a is a tall narrow matrix. Let be an estimate of the measurements based ...

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