# Geo-Positioning Accuracy Using Multiple-Satellite Images: IKONOS, QuickBird, and KOMPSAT-2 Stereo Images

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Data and Sensor Model

IKONOS | QuickBird | KOMPSAT-2 | ||||
---|---|---|---|---|---|---|

Scene-1 | Scene-2 | Scene-1 | Scene-2 | Scene-1 | Scene-2 | |

Date of acquisition | 7 February 2002 | 7 February 2002 | 16 January 2005 | 16 January 2005 | 10 May 2007 | 6 May 2008 |

Azimuth angle | 338.1° | 234.9° | 199.5° | 5.2° | 79.7° | 256.7° |

Elevation angle | 66.5° | 68.4° | 59.5° | 58.7° | 58.2° | 74.1° |

Convergence angle | 35.00° | 61.27° | 47.68° | |||

BIE angle | 75.53° | 85.74° | 89.34° | |||

GSD (column/row) | 0.90 m/0.96 m | 0.92 m/0.90 m | 0.71 m/0.79 m | 0.71 m/0.83 m | 1.30 m/1.10 m | 1.04 m/1.01 m |

## 3. Test Cases for the Use of Multiple-Satellite Images

**Figure 3.**Test cases for comparison between single-satellite stereo and dual-satellite integration. (

**a**) single-satellite stereo, (

**b**) dual-satellite stereo.

**Figure 4.**Test cases for comparison before and after the integration of higher resolution single image. (

**a**) single-satellite stereo, (

**b**) single-satellite stereo + higher resolution single image.

**Figure 5.**Test cases for comparison before and after the integration of higher resolution stereo image. (

**a**) single-satellite stereo, (

**b**) single-satellite stereo + higher resolution stereo image.

## 4. Experimental Results

Convergence Angle | BIE Angle | Horizontal Accuracy | Vertical Accuracy | |
---|---|---|---|---|

KOMPSAT-2 stereo | 47.7° | 89.3° | 2.15 m | 1.75 m |

IKONOS stereo | 35.0° | 75.5° | 1.53 m | 0.86 m |

QuickBird stereo | 61.3° | 85.7° | 1.15 m | 0.63 m |

Image 1 | Image 2 | Convergence Angle | BIE Angle | Horizontal Accuracy | Vertical Accuracy |
---|---|---|---|---|---|

K2-s1 | IK-s1 | 42.5° | 71.7° | 1.65 m | 2.74 m |

K2-s1 | IK-s2 | 52.0° | 83.9° | 1.78 m | 2.39 m |

K2-s2 | IK-s1 | 26.1° | 74.8° | 1.86 m | 2.87 m |

K2-s2 | IK-s2 | 8.90° | 71.6° | 3.87 m | 12.10 m |

K2-s1 | QB-s1 | 53.2° | 73.2° | 1.88 m | 1.65 m |

K2-s1 | QB-s2 | 25.3° | 69.4° | 1.83 m | 2.80 m |

K2-s2 | QB-s1 | 36.9° | 64.0° | 2.12 m | 2.71 m |

K2-s2 | QB-s2 | 39.1° | 75.7° | 1.51 m | 2.02 m |

IK-s1 | QB-s1 | 50.4° | 79.8° | 1.39 m | 1.07 m |

IK-s1 | QB-s2 | 14.5° | 63.2° | 2.80 m | 3.59 m |

IK-s2 | QB-s1 | 17.6° | 65.1° | 1.95 m | 2.86 m |

IK-s2 | QB-s2 | 47.8° | 78.2° | 1.30 m | 1.54 m |

Integration of Three Images (Single-Satellite Stereo + Higher Resolution Single Image) | |||||||||||||||||||

1 | 2 | 3 | Convergence Angle | BIE Angle | Horizontal Accuracy | Vertical Accuracy | |||||||||||||

1-2 | 1-3 | 2-3 | 1-2 | 1-3 | 2-3 | ||||||||||||||

K2-s1 | K2-s2 | IK-s1 | 47.7° | 42.5° | 26.1° | 89.3° | 71.7° | 74.8° | 1.66 m | 1.65 m | |||||||||

K2-s1 | K2-s2 | IK-s2 | 47.7° | 52.0° | 8.9° | 89.3° | 83.9° | 71.6° | 1.72 m | 2.37 m | |||||||||

K2-s1 | K2-s2 | QB-s1 | 47.7° | 53.2° | 36.9° | 89.3° | 73.1° | 64.0° | 1.56 m | 1.60 m | |||||||||

K2-s1 | K2-s2 | QB-s2 | 47.7° | 25.3° | 39.1° | 89.3° | 69.4° | 75.7° | 1.43 m | 1.27 m | |||||||||

IK-s1 | IK-s2 | QB-s1 | 35.0° | 50.4° | 17.6° | 75.5° | 79.8° | 65.1° | 1.31 m | 0.70 m | |||||||||

IK-s1 | IK-s2 | QB-s2 | 35.0° | 14.5° | 47.8° | 75.5° | 63.2° | 78.2° | 1.65 m | 0.89 m | |||||||||

Integration of Four or More Images (Single-Satellite Stereo + Higher Resolution Stereo Image) | |||||||||||||||||||

1 | 2 | 3 | 4 | Convergence Angle | BIE Angle | Horizontal Accuracy | Vertical Accuracy | ||||||||||||

1-2 | 1-3 | 1-4 | 1-2 | 1-3 | 1-4 | ||||||||||||||

2-3 | 2-4 | 3-4 | 2-3 | 2-4 | 3-4 | ||||||||||||||

K2-s1 | K2-s2 | IK-s1 | IK-s2 | 47.7° | 42.5° | 52.0° | 89.3° | 71.7° | 83.9° | 1.62 m | 1.45 m | ||||||||

26.1° | 8.90° | 35.0° | 74.8° | 71.6° | 75.5° | ||||||||||||||

K2-s1 | K2-s2 | QB-s1 | QB-s2 | 47.7° | 53.2° | 25.3° | 89.3° | 73.2° | 69.4° | 1.37 m | 0.92 m | ||||||||

36.9° | 39.1° | 61.3° | 64.0° | 75.7° | 85.7° | ||||||||||||||

IK-s1 | IK-s2 | QB-s1 | QB-s2 | 35.0° | 50.4° | 14.5° | 75.5° | 79.8° | 63.2° | 1.21 m | 0.65 m | ||||||||

17.6° | 47.8° | 61.3° | 65.1° | 78.2° | 85.7° | ||||||||||||||

Integration of All Images (Three Stereo Pairs) | |||||||||||||||||||

Convergence Angle | BIE Angle | Horizontal Accuracy | Vertical Accuracy | ||||||||||||||||

K2stereo + IKstereo + QBstereo | - | - | 1.35 m | 0.68 m |

## 5. Discussion

_{S}, estimated using two rays. In the left panel, if the two rays have no errors (the error-free scenario is represented by dashed lines), the two rays will intersect exactly at the true ground point G

_{T}. However, the rays generally have individual pointing errors (represented in the middle panel as $\overrightarrow{{\mathrm{G}}_{\mathrm{T}}{\mathrm{G}}_{\mathrm{1}}}$ and $\overrightarrow{{\mathrm{G}}_{\mathrm{T}}{\mathrm{G}}_{\mathrm{2}}}$) that generate horizontal and vertical errors in object space. G

_{1}and G

_{2}are the intersection points of the two rays of scene-1 and scene-2, respectively, with the horizontal plane containing G

_{T}. The individual pointing errors were previously represented to describe the horizontal and vertical errors [13] but their relationship was not discussed. Here, we discuss how the pointing errors relate to horizontal and vertical accuracy as shown in Figure 6.

**Figure 7.**Pointing error vectors and their subtracting vectors for single-satellite stereo and dual-satellite stereo (five ICPs). (

**a**) KOMPSAT-2/IKONOS, (

**b**) KOMPSAT-2/QuickBird, (

**c**) IKONOS/QuickBird.

**Table 5.**Similarity of pointing error patterns for single-satellite stereo and dual-satellite stereo (18 ICPs).

Image 1 | Image 2 | Correlation | $\left|\overrightarrow{{G}_{T}{G}_{1}}-\overrightarrow{{G}_{T}{G}_{2}}\right|$ | |
---|---|---|---|---|

Single-satellite stereo pairs | K2-s1 | K2-s2 | 0.651 | 1.26 m |

IK-s1 | IK-s2 | 0.810 | 0.69 m | |

QB-s1 | QB-s2 | 0.760 | 0.83 m | |

Dual-satellite integrations | K2-s1 | IK-s1 | 0.256 | 1.92 m |

K2-s1 | IK-s2 | 0.213 | 2.11 m | |

K2-s2 | IK-s1 | 0.292 | 1.75 m | |

K2-s2 | IK-s2 | 0.310 | 1.69 m | |

K2-s1 | QB-s1 | 0.233 | 2.25 m | |

K2-s1 | QB-s2 | 0.320 | 2.16 m | |

K2-s2 | QB-s1 | 0.342 | 1.83 m | |

K2-s2 | QB-s2 | 0.370 | 1.91 m | |

IK-s1 | QB-s1 | 0.351 | 1.63 m | |

IK-s1 | QB-s2 | 0.392 | 1.57 m | |

IK-s2 | QB-s1 | 0.311 | 1.81 m | |

IK-s2 | QB-s2 | 0.345 | 1.60 m |

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Fraser, C.S.; Hanley, H.B.; Yamakawa, T. Three-dimensional geopositioning accuracy of IKONOS imagery. Photogramm. Rec.
**2002**, 17, 465–480. [Google Scholar] [CrossRef] - Grodecki, J.; Dial, G. Block adjustment of high-resolution satellite images described by rational polynomials. Photogramm. Eng. Remote Sens.
**2003**, 69, 59–68. [Google Scholar] - Noguchi, M.; Fraser, C.S.; Nakamura, T.; Shimono, T.; Oki, S. Accuracy assessment of QuickBird stereo imagery. Photogram. Rec.
**2004**, 19, 128–137. [Google Scholar] [CrossRef] - Tong, X.; Liu, S.; Weng, Q. Bias-corrected rational polynomial coefficients for high accuracy geo-positioning of QuickBird stereo imagery. ISPRS J. Photogramm. Remote Sens.
**2010**, 65, 218–226. [Google Scholar] [CrossRef] - Büyüksalih, G.; Koçak, G.; Topan, H.; Oruç, M.; Marangoz, A. Spot revisited: Accuracy assessment, DEM generation and validation from stereo SPOT-5 HRG images. Photogram. Rec.
**2005**, 20, 130–146. [Google Scholar] - Chen, L.; Teo, T.; Liu, C. The geometrical comparisons of RSM and RFM for FORMOSAT-2 satellite images. Photogramm. Eng. Remote Sens.
**2006**, 72, 573–580. [Google Scholar] - Fraser, C.S.; Ravanbakhsh, M. Georeferencing accuracy of GeoEye-1 imagery. Photogramm. Eng. Remote Sens.
**2009**, 75, 634–640. [Google Scholar] - Dolloff, J.; Settergren, R. An assessment of WorldView-1 positional accuracy based on fifty contiguous stereo pairs of imagery. Photogramm. Eng. Remote Sens.
**2010**, 76, 935–943. [Google Scholar] [CrossRef] - Aguilar, M.A.; Aguilar, F.J.; del Mar Saldana, M. Geopositioning accuracy assessment of GeoEye-1 panchromatic and multispectral imagery. Photogramm. Eng. Remote Sens.
**2012**, 78, 247–258. [Google Scholar] [CrossRef] - Aguilar, M.A.; Saldana, M.M.; Aguilar, F.J. Assessing geometric accuracy of the orthorectification process from GeoEye-1 and WorldView-2 panchromatic images. Int. J. Appl. Earth Obs. Geoinf.
**2013**, 21, 427–435. [Google Scholar] [CrossRef] - Li, R.; Zhou, F.; Niu, X.; Di, K. Integration of Ikonos and QuickBird imagery for geopositioning accuracy analysis. Photogramm. Eng. Remote Sens.
**2007**, 73, 1067–1074. [Google Scholar] - Li, A.K.Y.; Batchvarova, T. Topographic mapping and terrain modeling from multi-sensor satellite imagery. In Proceedings of the ISPRS Congress of the International Society for Photogrammetry and Remote Sensing ISPRS Annals, Beijing, China, 3–11 July 2008; Volume 37, pp. 809–814.
- Jeong, J.; Kim, T. Analysis of dual-sensor stereo geometry and its positioning accuracy. Photogramm. Eng. Remote Sens.
**2014**, 80, 653–662. [Google Scholar] [CrossRef] - Li, R.; Niu, X.; Liu, C.; Wu, B.; Deshapnde, S. Impact of imaging geometry on 3D geopositioning accuracy of Stereo Ikonos imagery. Photogramm. Eng. Remote Sens.
**2009**, 75, 1119–1126. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Jeong, J.; Yang, C.; Kim, T.
Geo-Positioning Accuracy Using Multiple-Satellite Images: IKONOS, QuickBird, and KOMPSAT-2 Stereo Images. *Remote Sens.* **2015**, *7*, 4549-4564.
https://doi.org/10.3390/rs70404549

**AMA Style**

Jeong J, Yang C, Kim T.
Geo-Positioning Accuracy Using Multiple-Satellite Images: IKONOS, QuickBird, and KOMPSAT-2 Stereo Images. *Remote Sensing*. 2015; 7(4):4549-4564.
https://doi.org/10.3390/rs70404549

**Chicago/Turabian Style**

Jeong, Jaehoon, Chansu Yang, and Taejung Kim.
2015. "Geo-Positioning Accuracy Using Multiple-Satellite Images: IKONOS, QuickBird, and KOMPSAT-2 Stereo Images" *Remote Sensing* 7, no. 4: 4549-4564.
https://doi.org/10.3390/rs70404549