9.20 LEAST-SQUARES ESTIMATION

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

(9.309) Numbered Display Equation

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

(9.310) Numbered Display Equation

where and

(9.311) Numbered Display Equation

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 ...

Get Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.