Fig 1.
Flowchart of the algorithm to compute the probability levels of Iterative Data Snooping (IDS) for each measurement in the presence of an outlier [44].
Fig 2.
Digital level—Bar-code staff system.
Example of a digital level—bar-code staff system [44].
Fig 3.
Different constraint scenarios.
Leveling geodetic network subject to different constraint scenarios.
Table 1.
Local redundancy (ri), standard deviation of the least-squares (LS)-estimated outlier and the maximum absolute correlation (
) for each scenario of hard constraint.
Fig 4.
and
for the case of hard constraints and for α′ = 0.001.
Cluster 1(A,b), Cluster 2(c,d), Cluster 3(e,f) and Cluster 4(g,h).
Table 2.
MDB (minimal detectable bias) and MIB (minimal identifiable bias) for the case of hard constraints based on α′ = 0.001 and .
Fig 5.
for the case of hard constraints and for α′ = 0.001.
Cluster 1(A), Cluster 2(b), Cluster 3(c) and Cluster 4(d).
Table 3.
Local redundancy (ri), standard deviation of the LS-estimated outlier (mm) and the maximum absolute correlation (
) for each scenario of two soft constraints.
Fig 6.
and
for the measurements subject to the scenarios of two soft constraints for α′ = 0.001.
Cluster 1(a,b), Cluster 2(c,d), Cluster 3(e,f) and Cluster 4(g,h).
Fig 7.
Probability of and
for the two soft constraints and for α′ = 0.001.
Cluster 5: heights A and D.
Fig 8.
The for the measurements subject to the scenarios of two soft constraints for α′ = 0.001.
Cluster 1(a), Cluster 2(b), Cluster 3(c) and Cluster 4(d).
Fig 9.
The for the two soft constraints and for α′ = 0.001.
Cluster 5: heights A and D.
Table 4.
MDB and MIB for the case of two soft constraints based on α′ = 0.001 and .
Table 5.
Local redundancy (ri), standard deviation of the LS-estimated outlier (mm) and the maximum absolute correlation (
) for each scenario of the three soft constraints.
Fig 10.
The and
for the measurements subject to the scenarios of three soft constraints for α′ = 0.001.
Cluster 1(A,b), Cluster 2(c,d), Cluster 3(e,f) and Cluster 4(g,h).
Fig 11.
The and
for the three constraints and for α′ = 0.001.
Cluster 5(a,b) and Cluster 6(c,d).
Fig 12.
The for the measurements subject to the scenarios of the three soft constraints and for α′ = 0.001.
Cluster 1(a), Cluster 2(b), Cluster 3(c) and Cluster 4(d).
Fig 13.
The for the three constraints and for α′ = 0.001.
Cluster 6(b).
Table 6.
MDB and MIB for the case of the three soft constraints based on α′ = 0.001 and .
Fig 14.
and
for Cluster 1 subject to one hard constraint and for α′ = 0.001.
The and
for Cluster 1 subject to one hard constraint and for α′ = 0.001.
Fig 15.
The ,
,
and
for Cluster 1 subject to two and three hard constraints and for α′ = 0.001 and α′ = 0.1.
The (A),
(b),
(c) and
for Cluster 1 subject to two and three hard constraints and for α′ = 0.001 and α′ = 0.1.
Fig 16.
The for Cluster 1 subject to two soft constraints (2 s.c.) A and D for α′ = 0.001 and α′ = 0.1.
The for Cluster 1 subject to two soft constraints (2 s.c.) A and D for α′ = 0.001 and α′ = 0.1.
Fig 17.
The and
for the two soft constraints A and D (Cluster 5) with σc = 10mm and for α′ = 0.001.
The and
for the two soft constraints A and D (Cluster 5) with σc = 10mm and for α′ = 0.001.