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results.txt
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==================================================================
VI. ILLUSTRATIVE RESULTS
==================================================================
A. Cases when observability is guaranteed/impossible
------------------------------------------------------------------
Fig.4(a)
----------
O_r = [O_3^1;O_3^2;O_5^3]:
0.0011 -0.0007 0
0.0017 -0.0021 0
0.0013 -0.0008 -0.0025
rank(O_r) = 3
----------
G_2:
0.0028 0.0009 0 1.0000 1.0000
0.0029 0.0002 0 1.0000 2.0000
0.0029 -0.0006 0 1.0000 3.0000
0.0027 -0.0012 0 1.0000 4.0000
-0.0002 -0.0028 -0.0008 1.0000 21.0000
rank(G_2) = 5
----------
rank(F) = 38, with column number of 38
----------
rank(J_G) = 275, with column number of 275
------------------------------------------------------------------
Fig.4(b)
----------
O_r = [O_3^1;O_3^2;O_5^3]:
0 -0.0013 0
0.0002 -0.0013 -0.0001
-0.0004 -0.0004 -0.0006
rank(O_r) = 3
----------
G_2:
-0.0012 -0.0008 0.0025 1.0000 1.0000
-0.0011 -0.0015 0.0023 1.0000 2.0000
-0.0007 -0.0020 0.0021 1.0000 3.0000
-0.0002 -0.0023 0.0018 1.0000 4.0000
0.0003 -0.0024 0.0016 1.0000 5.0000
rank(G_2) = 5
----------
rank(F) = 38, with column number of 38
----------
rank(J_G) = 182, with column number of 182
------------------------------------------------------------------
Fig.5(a)
----------
O_r = [O_3^1;O_3^2;O_5^3]:
0.0011 -0.0007 0
0.0016 -0.0026 0
0.0026 0 -0.0029
rank(O_r) = 3
----------
G_2:
0.0028 0.0009 0 1.0000 1.0000
0.0029 0 0 1.0000 2.0000
0.0029 0 0 1.0000 3.0000
0.0029 0 0 1.0000 4.0000
-0.0029 0 0 1.0000 6.0000
rank(G_2) = 4
----------
rank(F) = 34, with column number of 38
----------
rank(J_G) = 67, with column number of 71
------------------------------------------------------------------
Fig.5(c)
----------
O_r = [O_3^1;O_3^2;O_5^3]:
-0.0007 -0.0019 0
-0.0004 -0.0016 0
-0.0003 0 -0.0013
rank(O_r) = 3
----------
G_2:
-0.0029 0 0 1.0000 9.0000
-0.0029 0 0 1.0000 10.0000
-0.0029 0 0 1.0000 11.0000
-0.0029 -0.0003 0 1.0000 12.0000
-0.0029 -0.0003 -0.0003 1.0000 13.0000
rank(G_2) = 4
----------
rank(F) = 36, with column number of 38
----------
rank(J_G) = 72, with column number of 74
==================================================================
B. Cases with only time offsets or clock drifts
------------------------------------------------------------------
Fig.5(c) with only time offset
----------
O_r = [O_3^1;O_3^2;O_5^3]:
-0.0007 -0.0019 0
-0.0004 -0.0016 0
-0.0003 0 -0.0013
rank(O_r) = 3
----------
G_2:
-0.0029 0 0 1.0000
-0.0029 0 0 1.0000
-0.0029 -0.0003 0 1.0000
-0.0029 -0.0003 -0.0003 1.0000
rank(G_2) = 3
----------
rank(F) = 29, with column number of 31
----------
rank(J_G) = 65, with column number of 67
------------------------------------------------------------------
Fig.5(c) with only clock drift
----------
O_r = [O_3^1;O_3^2;O_5^3]:
-0.0007 -0.0019 0
-0.0004 -0.0016 0
-0.0003 0 -0.0013
rank(O_r) = 3
----------
G_2:
-0.0029 0 0 10.0000
-0.0029 0 0 11.0000
-0.0029 -0.0003 0 12.0000
-0.0029 -0.0003 -0.0003 13.0000
rank(G_2) = 4
----------
rank(F) = 31, with column number of 31
----------
rank(J_G) = 67, with column number of 67
------------------------------------------------------------------
Fig.5(b) with only clock drift
----------
O_r = [O_3^1;O_3^2;O_5^3]:
-0.0007 -0.0019 0
-0.0004 -0.0016 0
-0.0003 0 -0.0013
rank(O_r) = 3
----------
G_2:
-0.0029 0 0 9.0000
-0.0029 0 0 10.0000
-0.0029 0 0 11.0000
-0.0029 -0.0003 0 12.0000
rank(G_2) = 3
----------
rank(F) = 27, with column number of 31
----------
rank(J_G) = 60, with column number of 64
==================================================================
C. Impact of eigenvalues of FIM on observability and convergence
of the system
Check plotting of Fig.6(b) below.
==================================================================
VII. EXPERIMENTAL RESULTS
------------------------------------------------------------------
Fig.8(a)
----------
O_r = [O_3^1;O_3^4;O_5^50]:
-0.0009 -0.0005 0
-0.0010 -0.0006 0
-0.0001 -0.0004 -0.0015
rank(O_r) = 3
----------
G_2:
0.0015 0.0026 0 1.0000 1.0000
0.0015 0.0026 0 1.0000 2.0000
-0.0018 -0.0023 0 1.0000 30.0000
0.0012 -0.0027 0 1.0000 50.0000
0.0028 -0.0008 0 1.0000 70.0000
rank(G_2) = 4
----------
rank(F) = 24, with column number of 28
----------
rank(J_G) = 312, with column number of 316
------------------------------------------------------------------
Fig.8(b)
----------
This step will take a while (up to 1 min), please be patient ...
O_r = [O_3^1;O_3^4;O_5^50]:
-0.0009 -0.0005 0
-0.0010 -0.0006 0
-0.0001 -0.0004 -0.0015
rank(O_r) = 3
----------
G_2:
0.0015 0.0026 0 1.0000 1.0000
-0.0018 -0.0023 0 1.0000 30.0000
0.0012 -0.0027 0 1.0000 50.0000
0.0028 -0.0008 0 1.0000 70.0000
0.0007 0.0001 -0.0029 1.0000 130.0000
rank(G_2) = 5
----------
rank(F) = 28, with column number of 28
----------
rank(J_G) = 715, with column number of 715
==================================================================
Plotting figures in Fig.4, Fig.6 and Fig.8
------------------------------------------------------------------
Plot Fig.4(a) in Fig. 1.
------------------------------------------------------------------
Plot Fig.4(b) in Fig. 2.
------------------------------------------------------------------
Plot Fig.6(a) in Fig. 3.
------------------------------------------------------------------
Plot Fig.6(b) in Fig. 4.
------------------------------------------------------------------
Plot Fig.8(b) in Fig. 5.
==================================================================
Finish
==================================================================
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