{@linkplain org.opengis.metadata.quality.DataQuality Data quality} and {@linkplain org.opengis.metadata.quality.PositionalAccuracy positional accuracy}. The following is adapted from OpenGIS® Spatial Referencing by Coordinates (Topic 2) specification.

The parameters that define a coordinate reference system are chosen rather than measured to satisfy the degrees-of-freedom problem in the changeover from observation to coordinate quantities. Coordinate reference systems are therefore by definition error-free (i.e., non-stochastic). A coordinate reference system is realised through a network of control points. The coordinates of those control points, derived from surface and/or from satellite observations, are stochastic. Their accuracy can be expressed in a covariance matrix, which, due to the degrees-of-freedom problem, will have a rank deficiency, described in geodetic literature.

Coordinate transformations between coordinate reference systems usually have parameter values derived from two sets of point coordinates, one set in system 1, the other set in system 2. As these coordinates are stochastic (i.e., have random-error characteristics) the derived transformation parameter values will also be stochastic. Their covariance matrix can be calculated.

Coordinates that have not been "naturally" determined in coordinate reference system 2, but have been determined in coordinate system 1 and then transformed to system 2, have the random error effects of the transformation superimposed on their original error characteristics. It may be possible in well-controlled cases to calculate the covariance matrices of the point coordinates before and after the transformation, and thus isolate the effect of the transformation, but in practice a user will only be interested in the accuracy of the final transformed coordinates.

Nevertheless the option is offered to specify the covariance matrix of point coordinates resulting exclusively from the transformation. It is outside the scope of this specification to describe how that covariance matrix should be used. Because a covariance matrix is symmetrical, only the upper or lower diagonal part (including the main diagonal) needs to be specified.

For some transformations, this accuracy information is compacted in some assessment of an average impact on horizontal position and vertical position, allowing specification of average absolute accuracy and, when relevant and available, average relative accuracy. Hence separate quality measures may be specified for horizontal and for vertical position in those objects.