Fundamentals on Estimation Theory

Under the estimation theory title a doctrinal body is collected which treats to solve a problem with very simple formulation: given a set of noisy observations from reality to guess the value a magnitude has taken is under consideration departing from those observations. Obviously, we have got no direct access to that magnitude but it has some functional relationship with the obtained observations. The importance of the noisy adjective in the previous paragraph must be realized. If the obtained observations taken from reality have not got any degree of uncertainty, the unknown magnitude would be determined without no error from solving, in favor of that magnitude, the functional relationship mentioned beforehand. As many times as the experiment being repeated, as many times the same value would be obtained. However, the nature do not behave like that; let repeat any measurement of any magnitude several times and surely different values will be obtained. The fluctuations shall be with higher or lower amplitude depending on the random factors which affect the problem, and thus averaging all those measurements, the fluctuation will decrease as the number of averaged measurements increase. The estimation theory deals then with, from given observations, building a function of them which allows achieving a value for the unknown magnitude as accurate as possible.