# Performance Improvement of Time-Differenced Carrier Phase Measurement-Based Integrated GPS/INS Considering Noise Correlation

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## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Time-Differenced Carrier Phase (TDCP) Measurements

#### 2.2. TDCP-Based Global Positioning System/Inertial Navigation System (GPS/INS).

## 3. Simulation and Experimental Results

#### 3.1. Preliminary Test

#### 3.2. Simulation

#### 3.2.1. Simulation Environment

#### 3.2.2. Simulation Results

#### 3.2.3. Monte Carlo Simulation Results

#### 3.3. Experiment

#### 3.3.1. Experimental Environment

#### 3.3.2. Experimental Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Difference between global positioning system (GPS) (1 Hz) and inertial navigation system (INS) (3 Hz) data output.

**Figure 8.**Horizontal results of the (

**a**) inertial measurement unit (IMU) sensor specification case, (

**b**) 2.5× case, and (

**c**) 5× case.

**Figure 10.**Horizontal results obtained from the (

**a**) conventional and (

**b**) delayed state filter Monte Carlo simulations.

**Figure 13.**Horizontal results of the (

**a**) IMU sensor specification case, (

**b**) 2.5× case, and (

**c**) 5× case.

Conventional Filter (Modified H) | Delayed State Filter (Modified H, R, and C) | |
---|---|---|

Filter Configuration | $\begin{array}{l}{{H}^{\prime}}_{k+1}=H+J{\mathsf{\Phi}}_{i+99,i}^{-1}\delta {x}_{i+100}\\ {{R}^{\prime}}_{k+1}=R\\ {C}_{k+1}=0\end{array}$ | $\begin{array}{l}{{H}^{\prime}}_{k+1}=H+J{\mathsf{\Phi}}_{i+99,i}^{-1}\delta {x}_{i+100}\\ {{R}^{\prime}}_{k+1}=R+{\displaystyle \sum _{j=0}^{99}J{\mathsf{\Phi}}_{i+j,i}^{-1}Q{\left({\mathsf{\Phi}}_{i+j,i}^{-1}\right)}^{T}{J}^{T}}\\ {C}_{k+1}=-{\displaystyle \sum _{j=0}^{99}{\mathsf{\Phi}}_{i+99,i}{\mathsf{\Phi}}_{i+j,i}^{-1}Q{\left({\mathsf{\Phi}}_{i+j,i}^{-1}\right)}^{T}{J}^{T}}\end{array}$ |

Noise (σ) | Accelerometer (m/s^{2}) | Gyroscope (°/s) | ||||
---|---|---|---|---|---|---|

x-axis | y-axis | z-axis | x-axis | y-axis | z-axis | |

Engine Off (Stop) | 0.0118 | 0.0111 | 0.0119 | 0.0547 | 0.0502 | 0.0448 |

Engine On (Stop) | 0.1095 | 0.1203 | 0.0433 | 0.2659 | 0.2633 | 0.0562 |

Meter | IMU Sensor Case | 2.5× Case | 5× Case | |||
---|---|---|---|---|---|---|

3σ | Accuracy | 3σ | Accuracy | 3σ | Accuracy | |

Conventional Filter | 0.469 m | 0.168 m | 0.779 m | 0.214 m | 1.410 m | 0.274 m |

Delayed State Filter | 0.384 m | 0.138 m | 0.390 m | 0.139 m | 0.412 m | 0.123 m |

Time (s) | Conventional Filter | Delayed State Filter |

$8.2\times {10}^{-5}$ | $10.6\times {10}^{-5}$ |

Meter | Conventional Filter | Delayed State Filter | ||
---|---|---|---|---|

3σ | Accuracy (RMS ^{1}) | 3σ | Accuracy (RMS ^{1}) | |

Horizontal | 1.411 m | 0.255 m | 0.417 m | 0.142 m |

**Root mean square (RMS).**

^{1}Meter | IMU Sensor Case | 2.5× Case | 5× Case | |||
---|---|---|---|---|---|---|

3σ | Accuracy | 3σ | Accuracy | 3σ | Accuracy | |

Conventional Filter | 0.691 m | 0.485 m | 0.925 m | 0.486 m | 1.486 m | 0.486 m |

Delayed State Filter | 0.636 m | 0.449 m | 0.638 m | 0.442 m | 0.642 m | 0.439 m |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, J.; Kim, Y.; Song, J.; Kim, D.; Park, M.; Kee, C.
Performance Improvement of Time-Differenced Carrier Phase Measurement-Based Integrated GPS/INS Considering Noise Correlation. *Sensors* **2019**, *19*, 3084.
https://doi.org/10.3390/s19143084

**AMA Style**

Kim J, Kim Y, Song J, Kim D, Park M, Kee C.
Performance Improvement of Time-Differenced Carrier Phase Measurement-Based Integrated GPS/INS Considering Noise Correlation. *Sensors*. 2019; 19(14):3084.
https://doi.org/10.3390/s19143084

**Chicago/Turabian Style**

Kim, Jungbeom, Younsil Kim, Junesol Song, Donguk Kim, Minhuck Park, and Changdon Kee.
2019. "Performance Improvement of Time-Differenced Carrier Phase Measurement-Based Integrated GPS/INS Considering Noise Correlation" *Sensors* 19, no. 14: 3084.
https://doi.org/10.3390/s19143084