# A New Method to Improve the Detection of Co-Seismic Ionospheric Disturbances using Sequential Measurement Combination

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Assumptions

#### 2.2. De-Noising Methods Using Forward Numerical Differentiation

#### 2.3. The Minimum Noise Derivative (MND) Method

_{ν}the standard deviation of background noise in ionospheric delay measurements.

#### 2.4. Noise Level Comparisons for FDMA, TSMA, and MND

#### 2.5. SNR and the Estimation of the Best N for CID Detection

#### 2.6. Band-Pass Filter for 1-second Interval CID Data

#### 2.7. Applications for Early Detection Cases

## 3. Results

#### 3.1. Maximum SNR Comparisons

#### 3.2. SNR Comparisons in an Early Detection Case

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Normalized MND third derivatives with different N values: 20, 100, 200 (KIMC station, PRN 15).

**Figure 3.**The location of the epicenter (red star), NGII stations (blank squares), and the IPP ground tracks for one hour from the earthquake outbreak, as observed at the KIMC station (filled square). The IPP moves toward the filled circles.

**Figure 8.**Band-passed ionospheric combination by different passbands (KIMC, prn15). Values in the right shade indicate the SNR. Refer to Figure 2 for notation.

**Figure 9.**(

**a**) The time lag that is inherent in the detection algorithms for the real-time application, and (

**b**) its schematic.

**Figure 10.**The filtering outputs of conventional (ND and BP) and proposed (FDMA, TSMA and MND) detection algorithms.

**Figure 11.**SNR comparison of the MND and the TSMA within the small-N region (shaded area) for the early detection case (ANHN station, PRN15). (

**a**) SNR of the MND and the TSMA, (

**b**) SNR improvement of the MND against the TSMA.

**Table 1.**The time-derivative equations and the noise levels of the conventional (FDMA) and the proposed (TSMA, MND) methods.

Algorithm | Time Derivative Equation | Noise Level |
---|---|---|

FDMA | ${{f}^{\prime}}_{FDMA}=\frac{-{f}_{1}+{f}_{N}}{N-1}$ | ${{\sigma}^{\prime}}_{FDMA}=\frac{\sqrt{2}}{N-1}{\sigma}_{\nu}$ |

TSMA (proposed) | ${{f}^{\prime}}_{TSMA}=\frac{-\left({f}_{i}+\dots +{f}_{i+K-1}\right)+\left({f}_{N-K}+\dots +{f}_{i+N-1}\right)}{K\left(N-K\right)}$ | ${{\sigma}^{\prime}}_{TSMA}=\frac{3\sqrt{6}}{2N\sqrt{N}}{\sigma}_{\nu}$ |

MND (proposed) | ${{f}^{\prime}}_{MND}={c}_{1}{f}_{i}+\dots +{c}_{N}{f}_{i+N-1}$ where, ${c}_{k}=\frac{-6\left(N-1\right)+12\left(k-1\right)}{\left(N-1\right)N\left(N+1\right)}\left(k=1,2,\dots ,N\right)$ | ${{\sigma}^{\prime}}_{MND}=\sqrt{\frac{12}{\left(N-1\right)N\left(N+1\right)}}{\sigma}_{\nu}$ |

Noise Reduction Method | Best N |
---|---|

MND 3rd | 100 |

FDMA 3rd | 80 |

TSMA 3rd | 108 |

**Table 3.**Average values of the SNR for 45 NGII stations, using the best N values and SNR improvements of MND from other algorithms.

Algorithm | PRN 15 | PRN 26 | PRN 27 | SNR Improvement of MND |
---|---|---|---|---|

Numerical 3rd (ND, 30-second) | 3.20 | 8.92 | 2.25 | 340.6% |

Band-pass (BP, 3–20 mHz) | 16.65 | 20.08 | 8.05 | 13.6% |

FDMA 3rd | 14.27 | 28.40 | 6.88 | 12.5% |

TSMA 3rd | 17.71 | 29.37 | 7.95 | −0.8% |

MND 3rd | 17.87 | 28.98 | 7.89 |

**Table 4.**The SNR improvement of the MND against the TSMA within the small-N region (the average values of 45 NGII stations are used for analysis).

Percentage Improvement (%) | ||
---|---|---|

PRN | Maximum | Mean |

15 | 7.4 | 3.8 |

26 | 5.9 | 2.2 |

27 | 5.9 | 2.7 |

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**MDPI and ACS Style**

Kang, S.; Song, J.; Han, D.; Kim, B.; So, H.; Kim, K.-j.; Kee, C.
A New Method to Improve the Detection of Co-Seismic Ionospheric Disturbances using Sequential Measurement Combination. *Sensors* **2019**, *19*, 2948.
https://doi.org/10.3390/s19132948

**AMA Style**

Kang S, Song J, Han D, Kim B, So H, Kim K-j, Kee C.
A New Method to Improve the Detection of Co-Seismic Ionospheric Disturbances using Sequential Measurement Combination. *Sensors*. 2019; 19(13):2948.
https://doi.org/10.3390/s19132948

**Chicago/Turabian Style**

Kang, Seonho, Junesol Song, Deokhwa Han, Bugyeom Kim, Hyoungmin So, Kap-jin Kim, and Changdon Kee.
2019. "A New Method to Improve the Detection of Co-Seismic Ionospheric Disturbances using Sequential Measurement Combination" *Sensors* 19, no. 13: 2948.
https://doi.org/10.3390/s19132948