2.3 Errors of mathematical model, data errors and reliability

For adjustment of observation equations, a normal distribution with known variances is assumed. The adjustment model does not consider gross errors and asserts that the introduced standard deviations are correct. In reality, however, gross errors do occur. Also, the assumptions regarding the spread of measurement values do not always prove true. Therefore, errors of mathematical models (wrong standard deviations) or data errors may appear, or both.

Apart from wrong standard deviations errors of mathematical models can also result from wrong assumptions regarding contexts and characteristics within the block. Some examples will illustrate this.

• A bundle block adjustment with photos taken by an amateur camera with poor block geometry and poor redundancy may very well achieve "good" results in the form of small standard deviations and small residuals. The assumed model of central projection and constant interior orientation is not fulfilled, however, so that not only the assumed model but also the adjustment result does not conform to reality.
• The entire adjustment result can be falsified by assuming stereo metric camera conditions for non-synchronously released stereo metric photo-pairs
• Object conditions, for example plane conditions with wrong assumptions regarding tolerance of flatness, also lead to incorrect adjustment models.

Consequently, if large residuals occur in relation to the standard deviations, a data error as well as an error in the mathematical model may exist. As data errors and errors of mathematical models influence each other, separation requires extensive computations in the program, and as well careful attention by the user.