## Survey control networks: proceedingsWissenschaftlicher Studiengang Vermessungswesen, Hochschule der Bundeswehr München, 1982 - Nets (Geodesy) - 428 pages |

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Page 166

(12) Ah i j ij a network is bound to satisfy its design criteria if the variances in the

covariance matrix are forced to be smaller than those in the

conversely, the covariances larger. Since (6) involves an inversion of the

inequalities were reversed and the linear programming constraint equations

written as: (A^ O A^)w ^ vech Qa (diagonal elements) (13) (AT O AT)w £ vech Qa.

(off-diagonal ...

(12) Ah i j ij a network is bound to satisfy its design criteria if the variances in the

covariance matrix are forced to be smaller than those in the

**criterion matrix**and,conversely, the covariances larger. Since (6) involves an inversion of the

**criterion****matrix**, and since inversion is the matrix equivalent of a reciprocal, theseinequalities were reversed and the linear programming constraint equations

written as: (A^ O A^)w ^ vech Qa (diagonal elements) (13) (AT O AT)w £ vech Qa.

(off-diagonal ...

Page 245

proceedings International Federation of Surveyors. Study Group 5B. Meeting, Kai

Borre, Walter Welsch. CRITERI0N MATRICES F0R ESTIMABLE QUANTITIES F.

KRUMM Stuttgart, Federal Republic of Germany ABSTRACT Within the concept

of the analysis of geodetic networks often use is made of idealized variance-

covariance matrices (

estimable quantities can be developed as a starting point for the procedure of

analysing.

proceedings International Federation of Surveyors. Study Group 5B. Meeting, Kai

Borre, Walter Welsch. CRITERI0N MATRICES F0R ESTIMABLE QUANTITIES F.

KRUMM Stuttgart, Federal Republic of Germany ABSTRACT Within the concept

of the analysis of geodetic networks often use is made of idealized variance-

covariance matrices (

**criterion matrices**). According to that,**criterion matrices**forestimable quantities can be developed as a starting point for the procedure of

analysing.

Page 269

The designed network with covariance matrix C is "at least as good" as the

If vimax « 1 the standard ellipses lie all within the standard ellipses derived from

the

the minimum general eigenvalue of C and K. As an average measure for the

precision can serve ; .Ix i Tr (rt) . The geometric mean of the general eigenvalue

can also be ...

The designed network with covariance matrix C is "at least as good" as the

**criterion matrix**K if the general maximum eigenvalue of C and K p <s 1. 3 3 max vIf vimax « 1 the standard ellipses lie all within the standard ellipses derived from

the

**criterion matrix**(the converse is not true). It is also advantageous to computethe minimum general eigenvalue of C and K. As an average measure for the

precision can serve ; .Ix i Tr (rt) . The geometric mean of the general eigenvalue

can also be ...

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### Contents

Introduction | 34 |

BAN0V B A special method to derive a criterion | 65 |

UNGUEND0LI M Analysis of some densi | 79 |

9 other sections not shown

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### Common terms and phrases

accuracy additional parameters adjustment algorithm alternative hypothesis angles applied B-method BAARDA blocks boundary values cadastral calculated coefficients components computed condition equations constraints control networks coordinate system corrections correlation corresponding covariance matrix covariance transformation criterion matrix data snooping defined deformation densification networks derived determined direction distance eigenvalues eigenvector error ellipses essential eigenvector estimate example formula free network functional model Geod Geodesy geodetic networks geometric given GRAFAREND homogeneous inverse land uplift least squares linear programming mathematical model matrix Q mean square error means measurements method misclosures nets normal equations normal matrix observations obtained optimization orthogonal PELZER photogrammetric plot points possible precision problem reliability respect rotation S-system S-transformation scale SCHAFFRIN second order design solution Sopron standard ellipses stations stochastical model substitute matrix systematic errors techniques transformation traverses triangulation variance variance-covariance matrix variations vech vector vertices weight zero