Differential distortions in photogrammetric block adjustment

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The self-calibrating photogrammetric bundle-block ad adjustment program UNBASC2 is revised. Its design matrices rederived to account for the additional parameters being a function of the radial distance of image points. The revision improved the adjusted image coordinates by up to two micrometers. Similar revisions were made to the program GEBAT. With improved mathematical modelling, further differential increase in the precision of photogrammetric densification may be achieved by improving the weighting scheme. Ignoring correlation in the weight matrices of observations and known parameters can lead to differential distortions. Weights for observed image coordinates and for known coordinates of ground control points are examined. It is shown that in the presence of additional parameters, image weights transformed from the observation space to the model space will always be correlated. A test adjustment shoes the maximum correlation to be 2.5%, resulting in changes to the adjusted coordinates of not more than 0.5 micrometers. A similar improvement is obtained with the proper weighting of the ground control points in UNBASC2. Although many bundle adjustment programs can treat ground control points as stochastic, they are not designed to accept their full covariance matric event though there can be very high correlations. Evidence of highly correlated covariance matrices of the adjusted coordinates from weighted station adjustments of control networks are presented. It is shown that similar high correlation patterns can also occur in photogrammetric densification adjustments. The implications of the high correlation on geodetic densification are illustrated by the global ripple effects and the importance of relative precision. Alternative apriori covariance matrices are proposed. Although these are not suitable for rigorous statistical assessment, they produce coordinates with acceptable distortions. When a matrix inverse is involved, the effects of a distortion on the least squares solution may not be readily apparent. Therefore, the method of differential distortion analysis is developed to clarify the effects of each distorting variable.