It is important to note that while the correlation matrix C is a symmetric matrix, the dependency matrix D is nonsymmetrical D ( i, j ) \ ne D ( j, i ) since the influence of node " j " on node " i " is not equal to the influence of node " i " on node " j ".
42.
The square of the coefficient of multiple correlation can be computed using the vector \ mathbf { c } = { ( r _ { x _ 1 y }, r _ { x _ 2 y }, \ dots, r _ { x _ N y } ) } ^ \ top of correlations r _ { x _ n y } between the predictor variables x _ n ( independent variables ) and the target variable y ( dependent variable ), and the correlation matrix R _ { xx } of correlations between predictor variables.
43.
This formula for Q arises from applying Best Linear Unbiased Estimation to a linearized version of the sensor measurement residual equations about the current solution \ Delta \ underline { x } =-Q * ( J _ x ( J _ d C _ d J _ d ^ T ) ^ {-1 } f ), except in the case of B . L . U . E . C _ d is a noise covariance matrix rather than the noise correlation matrix used in DOP, and the reason DOP makes this substitution is to obtain a relative error.
44.
In general : Q = ( J _ x ^ T ( J _ d C _ d J _ d ^ T ) ^ {-1 } J _ x ) ^ {-1 } where J _ x is the Jacobian of the sensor measurement residual equations f _ i ( \ underline { x }, \ underline { d } ) = 0, with respect to the unknowns, \ underline { x }; J _ d is the Jacobian of the sensor measurement residual equations with respect to the measured quantities \ underline { d }, and C _ d is the correlation matrix for noise in the measured quantities.
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