# Scale Factor Calibration for a Rotating Accelerometer Gravity Gradiometer

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## Abstract

**:**

## 1. Introduction

^{TM}Airborne Gravity Gradiometer (AGG), with a noise performance of 3.3 E achieved in a 0.18 Hz bandwidth and it came into service after a two-year flight test [7,8]. Moreover, Lockheed Martin upgraded the system from a marine Full Tensor Gradiometer to an air Full Tensor Gradiometer named Air-FTG

^{TM}, with noise power densities of 7–8 E

^{2}·km in a Cassna C208 and 5–6 E

^{2}·km in a Basler BT-67. Since 2014, it has flown a two million kilometer test-line, and has shown lots of advantages and excellent success in navigation and commercial applications [9,10]. Starting from the 1990s, rapid progress has been made in atomic interference, superconducting, and other technologies. Atomic interferometer gravity gradiometers (such as Stanford AI), superconducting gravity gradiometers (such as VK1), and other gravity gradiometers based on late-model technologies have come into public sight [11,12,13].

^{−3}E/h [14,15,16]. However, the scale factor calibration had not been reported and the output unit of RAGG was directed to E. Hofmeyer et al., who focused on the intrinsic noise of the RAGGs and proved an achievable sensitivity below 3 E/√Hz for stationary measurements using the eight-accelerometer gravity gradiometer and the performance has been improved through optimization in the gradiometer measurement [17,18,19]. Although the sensitivity has been tested and calculated by E/√Hz instead of V/√Hz, the scale factor calibration of RAGG has still not been released. Cai et al. calculated and simulated a calibration method of an RAGG using centrifugal gradients, and provided detailed procedures and mathematical formulations for calibrating scale factors and other parameters in their model [20]. However, the particular and detailed RAGG calibration method needs to be further verified in experiments.

## 2. Principle

**r**denotes the location where the potential is determined,

**r′**indicates the location of differential volume element dV, and G is the gravitational constant.

^{2}) between two mass bodies with a distance of 1 m. The RAGG employs mechanical rotation modulation and synchronous electrical demodulation to extract the gravity gradient signal as a lock-in amplifier, as shown in Figure 1. In order to measure the gravity gradient at point O, the four accelerometers are assembled onto a disc whose center is point O. The directions of the sensitive axes of the accelerometers, which the black arrows indicate, are along the tangent of the disk in a clockwise manner. Therefore, the sensitive axes of the two adjacent accelerometers are orthogonal to each other. The disk is then driven by a precision motor at a constant angular rate, $\omega $.

## 3. Experimental Results

^{−5}/°C), should be discussed. Moreover, these system errors are varied from one location to another. Finally, the processing error of each term and its contributions to the gravity gradient are shown in Table 2 and Figure 3.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**The procedure for gravity gradient data extracting. (

**a**) Power Spectrum Density (PSD) of U

_{1234}. (

**b**) PSD of U

_{1234}after band-pass filter of 0.5 Hz. (

**c**) PSD of U

_{1234}after demodulating. (

**d**) Gravity gradient signal was extracted through an averaging of 120 s.

Different Angle β | Demodulated by sin2ωt | Demodulated by cos2ωt |
---|---|---|

$\beta =0$ | ||

$\beta =\pi /4$ | ||

$\beta =\pi /2$ |

System Error Terms | Processing Error | System Error Terms | Processing Error |
---|---|---|---|

Height of cylinder | ±2 mm | Positioning along rail | ±5 mm |

Diameter of cylinder | ±2 mm | Temperature fluctuation | ±1 °C |

Density of Lead | δρ/ρ ~ 1% | Central line misalignment | ±5 mm |

Different Toward-Away Directions | Demodulated by sin2ωt | Demodulated by cos2ωt |
---|---|---|

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## Share and Cite

**MDPI and ACS Style**

Deng, Z.; Hu, C.; Huang, X.; Wu, W.; Hu, F.; Liu, H.; Tu, L.
Scale Factor Calibration for a Rotating Accelerometer Gravity Gradiometer. *Sensors* **2018**, *18*, 4386.
https://doi.org/10.3390/s18124386

**AMA Style**

Deng Z, Hu C, Huang X, Wu W, Hu F, Liu H, Tu L.
Scale Factor Calibration for a Rotating Accelerometer Gravity Gradiometer. *Sensors*. 2018; 18(12):4386.
https://doi.org/10.3390/s18124386

**Chicago/Turabian Style**

Deng, Zhongguang, Chenyuan Hu, Xiangqing Huang, Wenjie Wu, Fangjing Hu, Huafeng Liu, and Liangcheng Tu.
2018. "Scale Factor Calibration for a Rotating Accelerometer Gravity Gradiometer" *Sensors* 18, no. 12: 4386.
https://doi.org/10.3390/s18124386