Combination of correlated random measures for improving the estimation of a variable

The following problem is treated: we consider two different measures of a random variable. These two measures yield a random result. This couple of variables is Gaussian,characterized by the mean values (m1,m2),the variances (omega2,omega1) and the correlation coefficient r. This correlation coefficient is supposed to be positive. 1. How is it conceivable to combine these two measures in order to improve the accuracy of the measured variable estimation? (A typical situation is the following: a phenomenon is measured by two different methods; the first one yields a result (the mean) with a given incertitude (the variance); the second yields a different result with a different incertitude; these two measurements are correlated and the correlation coefficient is also known.). 2. Furthermore show that this combination yields the minimal variance estimation of the measured variable.

Mots-clés : Kalman filter,filtre de Kalman,Gaussian variable,variable gaussienne,quadratic form,forme quadratique,optimal control,commande optimale,fuscia
Type de document : texte
Type de ressource : exercise
Niveau : higher education,bac+3,bac+4
Publics visés : learner
Auteurs ou éditeurs : Joël Le Roux,Université de Nice