5.7 Identification of weak network elements

When planning observations in a geodetic network we always try to guarantee that all observed elements are checked by other measurements. Only with redundant measurements it is possible to adjust observations and possibly remove blunders that might otherwise totaly corrupt the whole set of measurements. Apart from sufficient number of redundant observations the degree of control of single observed elements is given by the network configuration, ie. its geometry.

Less controlled observations represent weak network elements and they can in extreme cases even disable detection of gross observational errors as it is in the case of uncontrolled observations. There are two limit cases of observation control

• fully controlled observation as is for example an observed distance between two fixed points (standard deviation of the adjusted element is zero; standard deviation of the residual equals to the standard deviation if the observation) and
• uncontrolled observations as is a free polar bar for example (standard deviation of adjusted value is equal to standard deviation of observed quantity; residual and standard deviation of the residual are zero).

Weakly controlled or uncontrolled observations can result even from elimination of certain suspisios observations during analysis of adjusment.

Standard deviation of adjusted observations is less than standard deviation of the measurement. Degree of observation control in network is defined as coefficient

(8)      f = 100 (m_l - m_L)/m_l,

where m_l is standard deviation of observed quantity and m_L is standard deviation computed from a posteriori reference standard deviation m0. We consider observed network element to be

• uncontrolled if f < 0.1 (in listing marked with letter u),
• weakly controlled if 0.1 le f < 5 (in listing marked with letter w).

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