ABSTRACT

This chapter introduces linear, least mean square estimation of an unknown value from noisy measurements. It estimates the mean value of some unknown quantity, f, from a series of noisy measurements which can be called as the pj. The random variable notation can be used to describe this model of the measurement process. The statistical properties of the model deal with the different experiments, not with the individual measurements in a single experiment. The goal of estimation is to minimize the error with regard to some criteria. In order to better understand the difference between estimation of the data and estimation of the unknown, it is useful to define various vector spaces associated with the estimation process. The unknown space, associated with the unknown, f, has one dimension. The measurement space, associated with the measurement, p, has a number of dimensions equal to the number of measurements.