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Stereophotogrammetry for 2-D building deformation monitoring using Kalman Filter

J. O. Odumosu
J. O. Odumosu
, 
O. O. Adeleke
O. O. Adeleke
, 
V. C. Nnam
V. C. Nnam
, 
O. J. Avoseh
O. J. Avoseh
 and 
O. A. Ogundeji
O. A. Ogundeji
   | Aug 07, 2020
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Article Category: Original Article
Published Online: Aug 07, 2020
Page range: 1 - 7
Received: Mar 08, 2020
Accepted: Jun 26, 2020
DOI: https://doi.org/10.2478/rgg-2020-0006
Keywords
© 2020 J. O. Odumosu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Study area location
Study area location

Figure 2

Description of traverse from known stations to selected GCPs
Description of traverse from known stations to selected GCPs

Figure 3

Illustrative view of data acquisition
Illustrative view of data acquisition

Figure 4

Detected movements at PCP “A”–“D”
Detected movements at PCP “A”–“D”

Results of space resection and ground measurement in the first epoch given in metres

Point Ground Measurement Photo Generated Residuals
Easting Height Easting Height Easting Height
A 220115.351 235.907 220115.111 236.033 0.240 −0.126
B 220079.639 236.513 220079.622 236.454 0.017 0.059
C 220018.515 236.567 220018.542 236.552 −0.027 0.015
D 219989.901 236.071 219989.825 236.067 0.076 0.004

Results of space resection and ground measurement in the second epoch given in metres

Point Ground Measurement Photo Generated Residuals
Easting Height Easting Height Easting Height
A 220115.351 235.907 220115.863 235.960 −0.512 −0.053
B 220079.639 236.513 220079.655 236.513 −0.016 0.000
C 220018.515 236.567 220018.832 236.780 −0.317 −0.213
D 219989.901 236.071 219989.195 236.373 0.706 −0.302

Parameters of Polynomial Transformation

Easting Coordinate Height Coordinate
Parameter Value Parameter Value
C0 220124.628 D0 243.094
C1 −0.04 D1 −0.000251
C2 −0.07 D2 −0.016352
C3 0.00008206 D3 0.00000012

Results of Kalman filter analysis

Initial State Vector Next State Vector Final State Vector
X 220115.111 220115.863 220116.199
Z 236.033 235.96 236.084
Vx 0.0000001984 0.0000004233 0.0000011648
Vz 0.0000001042 0.0000000438 0.0000010805
X2 220079.622 220079.655 220079.123
Z2 236.454 236.513 236.743
Vx 0.0000000141 0.0000000132 0.0000033623
Vz 0.0000000488 0.000000000000 0.000001315311
X3 220018.542 220018.832 220017.728
Z3 236.552 236.78 236.214
Vx 0.0000000223 0.0000002621 0.0000071106
Vz 0.0000000124 0.0000001761 0.0000011012
X4 219989.825 219989.195 219990.067
Z4 236.067 236.373 236.079
Vx 0.0000000628 0.0000005837 0.0000004696
Vz 0.0000000033 0.0000002497 0.0000009152

Detected horizontal and vertical motions at the epochs

A B C D
Epoch 1 Vx [m/epoch] 1.984e-7 1.41e-8 2.23e-8 6.28e-8
Vz [m/epoch] 1.042e-7 4.88e-8 1.24e-8 3.3e-9
Remarks Stable Stable Stable Stable
Epoch 2 Vx [m/epoch] 4.233e-7 1.32e-8 2.621e-7 5.837e-7
Vz [m/epoch] 4.38e-8 0 1.761e-7 2.497e-7
Remarks Ins. Mov. Stable Ins. Mov. Ins. Mov.
Epoch 3 Vx [m/epoch] 1.1648e-6 3.3623e-6 7.1106e-6 4.696e-7
Vz [m/epoch] 1.0805e-6 1.3153e-6 1.1012e-6 9.152e-7
Remarks Ins. Mov. Ins. Mov. Ins. Mov. Ins. Mov.

Accuracy of initial traverse for determination of the coordinates of GCPs

Parameter Obtained Remarks
Misclosure in Easting 0.005 m Acceptable
Misclosure in Northing −0.045 m Acceptable
Linear Accuracy 1:3000 Acceptable

Results of space resection and ground measurement in the third epoch given in metres

Point Ground Measurement Photo Generated Residuals
Easting Height Easting Height Easting Height
A 220115.351 235.907 220115.199 236.084 −0.152 0.177
B 220079.639 236.513 220079.123 236.743 −0.516 0.23
C 220018.515 236.567 220017.728 236.214 −0.787 −0.353
D 219989.901 236.071 219990.067 236.079 0.166 0.008

Materials used for the study

Material Data Type Collection method Accuracy
Coordinates of Ground control points (GCPs) Primary data Field survey 1:3000
Coordinates of photo control points (PCPs) Primary data Overlapping photographs ±0.0001 m
Digital camera Primary data Perspective projection —

Observed and photo-generated coordinates for all three observation epochs

Point Ground Measurement Photo Generated Epoch 1 Photo Generated Epoch 2 Photo Generated Epoch 3
Easting [m] Height [m] Easting [m] Height [m] Easting [m] Height [m] Easting [m] Height [m]
A 220115.351 235.907 220115.111 236.033 220115.863 235.960 220115.199 236.084
B 220079.639 236.513 220079.622 236.454 220079.655 236.513 220079.123 236.743
C 220018.515 236.567 220018.542 236.552 220018.832 236.780 220017.728 236.214
D 219989.901 236.071 219989.825 236.067 219989.195 236.373 219990.067 236.079
eISSN:
2391-8152
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Computer Sciences, other, Geosciences, Geodesy, Cartography and Photogrammetry
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