This document outlines Mohammad Amin Alizadeh Khameneh's licentiate thesis on optimizing and designing geodetic networks. It introduces network quality criteria like precision, reliability, and sensitivity. It describes different orders of network design and optimization methods, including single, bi, and multi-objective models. It provides an outline of 4 papers on topics like the effect of constraints on bi-objective optimization, two-epoch optimal design of displacement monitoring networks, and optimizing a GPS monitoring network of a landslide in Lilla Edet, Sweden. The conclusion will summarize and discuss future work.

1. Introduction
Methodology
Papers
Conclusion
On Optimisation and Design of
Geodetic Networks
Licentiate Thesis in Geodesy
Mohammad Amin Alizadeh Khameneh
Royal Institute of Technology (KTH)
12 June 2015
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 1 / 31

2. Introduction
Methodology
Papers
Conclusion
Outline
1 Introduction
Network Quality Criteria
Network Optimal Design
2 Methodology
Methods
Models
3 Papers
Paper I
Paper II
Paper III
Paper IV
4 Conclusion
Round-up
Future Works
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 2 / 31

3. Introduction
Methodology
Papers
Conclusion
Network Quality Criteria
Network Optimal Design
Outline
1 Introduction
Network Quality Criteria
Network Optimal Design
2 Methodology
Methods
Models
3 Papers
Paper I
Paper II
Paper III
Paper IV
4 Conclusion
Round-up
Future Works
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 3 / 31

4. Introduction
Methodology
Papers
Conclusion
Network Quality Criteria
Network Optimal Design
Introduction
Need for geodetic networks in urban management,
engineering projects, hydrography, geo-hazard
assessment , aerial photogrammetry, ...
Deformation monitoring
Crustal movements, ground subsidence
Deformation of man-made structures: water power
dams, underground tunnels, bridges, high buildings, ...
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 4 / 31

5. Introduction
Methodology
Papers
Conclusion
Network Quality Criteria
Network Optimal Design
Establishment of a Geodetic Network:
Network Design
Where the network points should be located?
How the network should be measured?
Network quality
Execution: designed network to reality
Network Analysis
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 5 / 31

6. Introduction
Methodology
Papers
Conclusion
Network Quality Criteria
Network Optimal Design
Precision
Reliability
Economy
Sensitivity
(in case of deformation monitoring)
Optimal design leads to:
Avoiding unnecessary observations
Saving a considerable amount of time and effort
Identifying and eliminating gross errors
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 6 / 31

7. Introduction
Methodology
Papers
Conclusion
Network Quality Criteria
Network Optimal Design
Zero-Order Design (ZOD)
optimum reference datum
First-Order Design (FOD)
optimum locations for the stations
Second-Order Design (SOD)
which observations with what precision and reliability
THird-Order Design (THOD)
how to improve the existing network
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 7 / 31

8. Introduction
Methodology
Papers
Conclusion
Methods
Models
Outline
1 Introduction
Network Quality Criteria
Network Optimal Design
2 Methodology
Methods
Models
3 Papers
Paper I
Paper II
Paper III
Paper IV
4 Conclusion
Round-up
Future Works
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 8 / 31

9. Introduction
Methodology
Papers
Conclusion
Methods
Models
Methodology
Since the last few decades, the network design approaches
have evolved from the intuition/empirical to analytical
methods.
Trial and Error Method
Analytical Method
minimise/maximise some Object Function (OF) that
describes precision, reliability and cost by a scalar
value.
Criterion matrix as an ideal variance covariance
matrix, which should be best approximated by the
actual covariance matrix of estimated parameters.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 9 / 31

10. Introduction
Methodology
Papers
Conclusion
Methods
Models
Single-Objective Optimisation Model (SOOM)
minimising or maximising any of the objective functions for:
Precision
Cx − Cs = minimum
Reliability
r = maximum
Cost
P = minimum
Bi-Objective Optimisation Model (BOOM)
A pair combination of any of these criteria
Multi-Objective Optimisation Model (MOOM)
All the quality requirements are considered in the OF
Sensitivity in a Network:
The capability of a network to detect displacements or
deformation parameters of a certain magnitude
λi = ˆdT
i C−1
di
ˆdi ∼ χ2
1−α (df )
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 10 / 31

11. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Outline
1 Introduction
Network Quality Criteria
Network Optimal Design
2 Methodology
Methods
Models
3 Papers
Paper I
Paper II
Paper III
Paper IV
4 Conclusion
Round-up
Future Works
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 11 / 31

12. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Paper I Acta Geodaetica et Geophysica, 2014, Published
title
The Effect of Constraints on Bi-Objective Optimisation of
Geodetic Networks
objectives of the study
Contradiction of the controlling constraints in a SOOM,
which may lead to an infeasibility in the optimisation pro-
cess causes a problem in these models.
A BOOM of precision and reliability can solve the problem,
but how important is using the controlling constraints?
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 12 / 31

13. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Objective Function (OF) for BOOM of Precision and
Reliability
Hw − u
vec (Cs)
+
R11w − (rm − r00)
rm
→ min
subject to
DT
0 w = 0
A00w ≤ b00
By applying L2-norm to the above OF, the BOOM is converted
to a quadratic programming model and by solving that, one can
get the optimal values.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 13 / 31

14. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
The BOOM of precision and
reliability can optimise the
network properly even with-
out controlling constraints.
Unconstrained BOOM is
more economical in practi-
cal considerations as more
observables are removed
from the plan, while the
accuracy and reliability of
the network almost meet
the network requirements.
Precision of the net points: 3mm, reliability of the observations: ≥ 0.4
(a) Unconstrained (b) Constrained to Precision
(c) Constrained to Reliability (d) Constrained to Precision and
Reliability
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 14 / 31

15. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Although the standard er-
rors of the net points after
unconstrained BOOM are
a bit larger than the con-
strained results, the uncon-
strained model can success-
fully fulfil the precision and
reliability requirements.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 15 / 31

16. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Paper II Boletim de Ciˆencias Geod´esicas, 2015, Accepted
title
Two-Epoch Optimal Design of Displacement Monitoring
Networks
objective of the study
To design an optimal displacement monitoring network in
two epochs by estimating the variances of the observations
rather than their weights.
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17. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
One-Epoch Optimisation
Cx = σ2
0 AT
PA + EET −1
− E ET
EET
E
−1
ET
The main idea of the one-epoch optimisation is to change the configuration and determine the
weight of observations by fitting the following mathematical model:
Hw = u
, where
H = vec ∂C∆ˆx
∂x1
− ∂C
2∂x1
vec ∂C∆ˆx
∂y1
− ∂C
2∂y1
· · ·
vec ∂C∆ˆx
∂xm
− ∂C
2∂xm
vec ∂C∆ˆx
∂ym
− ∂C
2∂ym
vec ∂C∆ˆx
∂p1
· · · vec ∂C∆ˆx
∂pn
,with C
2
as a criterion matrix, and
w = (∆x1 ∆y1 · · · ∆xm ∆ym ∆p1 ∆pn)T
as an improvement vector for net points position and observation weights, and
u = vec
C
2
− vec (C∆ˆx)
In order to derive w, the following optimization model should be solved:
Hw − u 2 → min
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18. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Two-Epoch Optimisation
Using Gauss-Helmert model instead of Gauss-Markov, gives this ability to consider all
observations of two epochs:
A∆x + B
ε1
ε2
= w = B
L1
L2
with B = −In In
C∆ˆx = AT
K−1
A + DDT
− E ET
DDT
E
−1
ET
where K = BQBT
and
Q = diag Q1 Q2
The expansion of C∆ˆx can be presented in a matrix form as:
H w − u
where



H = vec ∂C∆ˆx
∂x1
− ∂C
∂x1
vec ∂C∆ˆx
∂y1
− ∂C
∂y1
· · · vec ∂C∆ˆx
∂xm
− ∂C
∂xm
vec ∂C∆ˆx
∂ym
− ∂C
∂ym
vec ∂C∆ˆx
∂q1
1
· · · vec ∂C∆ˆx
∂q1
n
vec ∂C∆ˆx
∂q2
1
· · · vec ∂C∆ˆx
∂q2
n
w = (∆x1 ∆y1 · · · ∆xm ∆ym ∆q1
1 · · · ∆q1
n ∆q2
1 · · · ∆q2
n)
T
u = vec (C) − vec (C∆ˆx)
An optimisation model can be formulated as H w − u 2 → min subject to physical
constraints.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 18 / 31

19. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Comparing the two methods, we
have similar accuracies of dis-
placements
The same configuration and posi-
tion changes of the points in both
approaches
Based on the two-epoch optimisa-
tion procedure, less observations
are needed in each epoch. It can
be concluded as a more economi-
cal solution
(e) One-Epoch Optimisation
(f) Two-Epoch Optimisation (Epoch 1)
(g) Two-Epoch Optimisation (Epoch 2)
(h) Observation weights
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 19 / 31

20. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Paper III Journal of Geodetic Science, 2015, Accepted
title
Optimisation of Lilla Edet Landslide GPS Monitoring
Network
objective of the study
To implement different optimisation models in a real case
study and design an optimal network. This network is sup-
posed to be sensitive in detecting possible displacements.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 20 / 31

21. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Study Area
Lilla Edet village
Landslide and
subduction along
G¨ota river
35 GPS stations
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22. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Basic equation for measured GPS baselines:



∆xpq
∆ypq
∆zpq


 − ε =



xq − xp
yq − yp
zq − zp


 − ε =



1 −1 0 0 0 0
0 0 1 −1 0 0
0 0 0 0 1 −1













xq
xp
yq
yp
zq
zp










and Pi = σ2
0



σ2
∆xi
0 0
0 σ2
∆yi
0
0 0 σ2
∆zi



−1
The statistical test to figure out if the displacements can be detected or not: λk = ˆdT
k C−1
xk
ˆdk ∼ 2χ2
0.95 (3) ,
λk = ˆdT
k C−1
xk
ˆdk ∼ 2χ2
0.95 (3) → H0 is rejected if λk > 2χ2
0.95 (3)
Criterion matrix based on the sensitivity of the network in detecting the displacements:
Cs =






σ2
s1
I3 0 0 0
0 σ2
s2
I3 0 0
0 0
... 0
0 0 0 σ2
sk
I3






, k = 1, 2, ..., m with σ2
sk
=
ˆdT
k
ˆdk
2χ2
0.95(3)
, k = 1, 2, · · · , m
SOOM of Precision: Cs − Cx 2 = min
we try to minimise the linearised form of the variance matrix as: Hw − u 2 = min , where



H = vec ∂Cx
∂P1
vec ∂Cx
∂P2
· · · vec ∂Cx
∂Pn
u = vec (Cs) − vec (Cx)
w = ∆P1 ∆P2 · · · ∆Pn
T
SOOM of Reliability: min ( diag (R) ∞) = min diag R0
+
n
i=1
∂R
∂Pi
∆Pi
∞
= max
SOOM of Cost: P ∞ = P0
+
n
i=1
∂P
∂Pi
∆Pi
∞
= min
BOOM/MOOM:
Hw−u 2
vec(Cs) 2
+
R2w−(ro−R1) 2
ro 2
+
C2w−(co−C1) 2
co 2
→ min
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 22 / 31

23. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
(i) SOOM of reliability with precision constraint and
sensitive to detect 5 mm displacement
(j) BOOM of precision and reliability, sensitive to
detect 5 mm displacement
(k) Redundancy number (reliability) of the
observations after optimisation procedure
(l) Precision of the net points after
optimisation based on different models
(m) Results of different optimisation models
performed on the GPS network
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 23 / 31

24. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Remarks
Unconstrained SOOM of precision had no control on
reliability; precise but not reliable.
The SOOM of reliability, constrained to precision,
yielded better results (in sense of precision and
reliability).
BOOM or MOOM provided the network quality
requirements with less number of baselines (costly
efficient).
Insignificant effect of cost criterion on MOOM in GPS
networks with short baselines. BOOM can be efficient
enough.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 24 / 31

25. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
Paper IV Acta Geodaetica et Geophysica, 2015, Submitted
title
The Effect of Instrumental Precision on Optimisation of
Displacement Monitoring Networks
objective of the study
To investigate the effect of observation precision in optimisa-
tion of the Lilla Edet GPS displacement monitoring network.
It has been assumed that the precision of GPS observations
can be increased in the subsequent epochs.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 25 / 31

26. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
If we increase the weight of observations in the second epoch P2, we will acquire
a more precise network by the second observation plan, so we can write:
P2 =
1
k
P1 → Cx2 = k Cx1 with k < 1
The displacement vector: d = x2 − x1 → Cd = Cx1 + Cx2
Cd − k Cx1 = Cx1 = C0
x1
+
n
i=1
∂Cx1
∂Pi
∆Pi
We try to minimise the differences between the VC matrix of the first epoch and
a defined ideal criterion matrix:
Cs − C0
x1 2
= min
subjected to precision, reliability and physical constraints.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 26 / 31

27. Introduction
Methodology
Papers
Conclusion
Paper I
Paper II
Paper III
Paper IV
(n) Optimised observation plans for the first and second epoch,
considering k=0.5
(o) Number of removed baselines due to precision improvements.
The number of initial baselines is 245.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 27 / 31

28. Introduction
Methodology
Papers
Conclusion
Round-up
Future Works
Outline
1 Introduction
Network Quality Criteria
Network Optimal Design
2 Methodology
Methods
Models
3 Papers
Paper I
Paper II
Paper III
Paper IV
4 Conclusion
Round-up
Future Works
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 28 / 31

29. Introduction
Methodology
Papers
Conclusion
Round-up
Future Works
Conclusion
1 In Paper I: Unconstrained BOOM was also efficient.
2 In Paper II: The two-epoch method removed more ob-
servations.
3 In Paper III: The Lilla Edet GPS monitoring network
was optimised by different optimisation models.
4 In Paper IV: Significant changes in designing an obser-
vation plan of epoch-wise measurements by assuming
higher observation precision for the latter epoch.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 29 / 31

30. Introduction
Methodology
Papers
Conclusion
Round-up
Future Works
Investigating the effect of possible correlations on GPS
baseline processing.
Developing the optimisation technique to design defor-
mation monitoring networks, using Finite Element Method.
Considering a direction constraint in optimisation pro-
cedure.
Applying intelligent optimisation techniques beside the
classical methods.
Mohammad Amin Alizadeh Khameneh On Optimisation and Design of Geodetic Networks 30 / 31

31. Introduction
Methodology
Papers
Conclusion
Round-up
Future Works
Thank you for your attention
?
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