Strength of drift noise (γ)

Algorithms

ε
_{
M
}

ε
_{
S
}

ε
_{
F
}


 
Mean

STD

Mean

STD

Mean

STD

2.0

LS

6.32

2.59

0.43

0.08

28.32

10.61


TLS

19.57

179.54

0.50

0.12

111.66

949.78


CTLS

5.81

3.10

0.47

0.10

28.62

17.56

1.0

LS

4.46

1.51

0.39

0.05

21.21

6.61


TLS

4.83

2.15

0.43

0.08

26.42

14.98


CTLS

3.17

1.24

0.41

0.06

16.08

7.20

0.1

LS

3.68

1.05

0.38

0.02

17.93

4.34


TLS

3.58

1.27

0.40

0.05

19.90

8.33


CTLS

2.18

0.68

0.38

0.02

11.16

2.91

0.05

LS

3.68

1.04

0.38

0.02

17.92

4.10


TLS

3.63

1.35

0.40

0.06

19.88

8.16


CTLS

2.18

0.69

0.38

0.02

11.14

2.93

 The table shows the error comparisons in terms of the mean and the standard deviation (STD) for different strengths of drift noise for each method based on 1000 MonteCarlo simulations. The number of measurements per experiment is fixed at 21. All conditions are the same as the ones for Table 1 with only the drift noise being added. ε_{
M
}is the sum of two tems, i.e (1/N_{1}) Σ α_{
i j
} and (l/N_{2}) Σ β_{
i j
}, where β_{
i j
}and β_{
i j
}are the relative magnitude errors in the nonzero and zero elements of the true Jacobian, respectively, and N_{1} and N_{2} are the number of nonzero and zero elements in the true Jacobian, respectively. ε_{
S
}is given by (1/n^{2}) Σ sign(\widehat{f}_{
i j
})  sign(f_{
i j
}), i.e. the average sign differences, where \widehat{f}_{
i j
}and f_{
i j
}are the (ith row, jth column) element of the estimated and the true Jacobian, respectively. ε_{
F
}is the Frobenius norm of the difference between the estimated and the true Jacobian, i.e. \widehat{F}  F_{
F
}.