#
Systematic Performance Evaluation of a Novel Optimized Differential Localization Method for Capsule Endoscopes^{ †}

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Fundamentals of Static Magnetic Localization

#### 2.1. Magnetic Dipole Model

#### 2.2. Soft Magnetic Distortion

## 3. Methods

#### 3.1. Localization Setup

#### 3.2. Simulation Setup

^{®}5.4. The simulation model of the localization setup described in Section 3.1 is depicted in Figure 4.

#### Absolute Magnetic Localization Method

#### 3.3. Differential Localization Method

#### 3.4. Experimental Validation of the Differential Method

#### 3.5. Position and Orientation Errors

#### 3.6. Differential Localization Method for Ideal Conditions

#### 3.7. Systematic Evaluation of the Non-Idealities of the Proposed Localization System

#### 3.7.1. Evaluation of Sensor Displacement

#### 3.7.2. Evaluation of Sensor Misalignment

#### 3.7.3. Evaluation of RMS-Noise of Magnetic Sensors

#### 3.7.4. Evaluation of the Ferromagnetic Material in the Proximity of the System

_{r}= 4000 was considered in the COMSOL simulations (Figure 9).

_{r}= 4000. The dimensions and orientation were chosen as described in Section 3.4. The measured components of the geomagnetic flux density were applied in the simulations.

#### 3.8. Evaluating All Considered Non-Idealities Simultaneously

#### 3.9. Evaluation of Rotation of the Localization System under Non-Ideal Conditions

## 4. Results

#### 4.1. Experimental Validation of the Differential Geomagnetic Compensation Method

#### 4.2. Reference Results under Ideal Conditions

#### 4.3. Results for Systematic Evaluation of Non-Idealities of the Localization System

#### 4.3.1. Results for Sensor Displacement

#### 4.3.2. Results for Sensor Misalignment

#### 4.3.3. Results for the RMS-Noise of Sensors

#### 4.3.4. Results for Ferromagnetic Material in the Proximity of the System

#### 4.3.5. Results for the Combination of all Considered Non-Idealities and the Variation of the Magnet Length on the Localization System

#### 4.3.6. Results for the Rotation of the System under Non-Ideal Conditions

## 5. Discussion

#### Comparison of State-of-the-Art Localization Methods for Capsule Endoscopes

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

GIT | Gastrointestinal tract |

IMU | Inertial measurement unit |

RF | Radio-frequency |

RMS | Root-mean-square |

RSS | Received signal strength |

STD | Standard deviation |

TOA | Time of arrival |

WCE | Wireless capsule endoscopy |

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**Figure 2.**Comparison of the magnetic flux density B for undistorted (

**left**) and soft-iron distorted (

**right**). A ferromagnetic material (black rectangle) is placed within B.

**Figure 3.**Localization scenario of a permanent magnet with the proposed localization system and the reference coordinate system.

**Figure 4.**Proposed simulation setup in COMSOL Multiphysics

^{®}5.4. The 12 sensors and the magnet are highlighted in blue. Moreover, the spherical computational domain is shown.

**Figure 5.**A representative sensor ring with 4 mounted sensors. The normal vector ${S}_{\mathrm{n}}$ for each sensor is depicted. The coordinate systems of sensors corresponding to a pair (Sensor 1 and Sensor 2) are shown in blue.

**Figure 6.**Measurement setup of a representative sensor pair. Sensors 1 and 2 are approximately equally orientated.

**Figure 7.**Block-diagram of various non-idealities influencing the proposed differential localization setup.

**Figure 8.**A representative sensor and its reference coordinate system (blue). The sensor is rotated around the three angles of roll, yaw, and pitch.

**Figure 9.**Iron cylinder in the proximity of the sensor array. The cylinder is z-orientated, whereas the displacement of the cylinder is in the y-direction.

**Figure 10.**Mean position and orientation errors for different maximal random displacement and misalignment of sensors. The y-axis is in log-scale.

**Figure 11.**Absolute magnetic flux density B depending on the distance from the magnet. The measured magnetic flux density and its standard deviation (STD) are compared with the simulated one from COMSOL. Moreover, the assumed RMS-noise is depicted.

**Figure 12.**Position and orientation errors for different distances from the localization system to an iron cylinder.

**Figure 13.**Comparison of localization performance under non-ideal conditions with performance under ideal conditions [26] for different applied magnet sizes.

**Figure 14.**Comparison of the absolute method and differential method by applying displacement, misalignment, and RMS-noise for rotations of the system around the $-x$-, $-y$- and $-z$-axes and for different sizes of magnets.

**Table 1.**Comparison of the three measured values at the two LSM303D. the absolute difference between the corresponding measured components is given.

${\mathit{B}}_{\mathit{x}}$ (µT) | ${\mathit{B}}_{\mathit{y}}$ (µT) | ${\mathit{B}}_{\mathit{z}}$ (µT) | |
---|---|---|---|

Reference measurement | |||

Sensor 1 | −5.2 | −19.5 | −43.8 |

Sensor 2 | −6.3 | −19.8 | −43.4 |

Difference | 1.1 | 0.3 | 0.4 |

x-Displacement of Sensor 2 + 5 mm | |||

Sensor 1 | −5.2 | −19.5 | −43.8 |

Sensor 2 displaced | −6.5 | −19.2 | −43.5 |

Difference | 1.3 | 0.3 | 0.3 |

Rotation around the z-axis of Sensor 2 + 5° | |||

Sensor 1 | −5.2 | −19.5 | −43.8 |

Sensor 2 rotated | −8.1 | −19.0 | −43.5 |

Difference | 2.9 | 0.5 | 0.3 |

Heating element approximately 50 cm next to Sensor 2 | |||

Sensor 1 | −8.7 | −18.3 | −42.7 |

Sensor 2 | −7.2 | −15.6 | −37.4 |

Difference | 1.5 | 2.7 | 5.3 |

**Table 2.**Position ${P}_{\mathrm{err}}$ and orientation ${O}_{\mathrm{err}}$ errors and their mean value and standard deviation (STD) for the differential method for the four different orientations of the magnet under ideal conditions [32].

Orientation of the Magnet: | P_{err} in mm | O_{err} in ° |
---|---|---|

$(1,\phantom{\rule{4.pt}{0ex}}0,\phantom{\rule{4.pt}{0ex}}{0)}^{\u22ba}$ | 0.01 | 0.07 |

$(0,\phantom{\rule{4.pt}{0ex}}1,\phantom{\rule{4.pt}{0ex}}{0)}^{\u22ba}$ | 0.05 | 0.07 |

$(0,\phantom{\rule{4.pt}{0ex}}0,\phantom{\rule{4.pt}{0ex}}{1)}^{\u22ba}$ | 0.03 | 0.01 |

$\frac{1}{\sqrt{3}}(1,\phantom{\rule{4.pt}{0ex}}1,\phantom{\rule{4.pt}{0ex}}{1)}^{\u22ba}$ | 0.14 | 0.06 |

Mean value and STD | 0.05 ± 0.05 | 0.05 ± 0.02 |

Orientation of the Magnet: | P_{err} in mm | O_{err} in ° |
---|---|---|

$(1,\phantom{\rule{4.pt}{0ex}}0,\phantom{\rule{4.pt}{0ex}}{0)}^{\u22ba}$ | 0.67 | 0.42 |

$(0,\phantom{\rule{4.pt}{0ex}}1,\phantom{\rule{4.pt}{0ex}}{0)}^{\u22ba}$ | 0.61 | 0.34 |

$(0,\phantom{\rule{4.pt}{0ex}}0,\phantom{\rule{4.pt}{0ex}}{1)}^{\u22ba}$ | 0.75 | 0.04 |

$\frac{1}{\sqrt{3}}(1,\phantom{\rule{4.pt}{0ex}}1,\phantom{\rule{4.pt}{0ex}}{1)}^{\u22ba}$ | 1.36 | 0.45 |

Mean value and STD | 0.85 ± 0.30 | 0.31 ± 0.16 |

**Table 4.**Position ${P}_{\mathrm{err}}$ and orientation ${O}_{\mathrm{err}}$ errors and their mean value and standard deviation (STD) for the differential method for the four different orientations of the magnet. A heating element at a distance of 50 cm was placed next to the setup.

Orientation of the Magnet: | P_{err} in mm | O_{err} in ° |
---|---|---|

$(1,\phantom{\rule{4.pt}{0ex}}0,\phantom{\rule{4.pt}{0ex}}{0)}^{\u22ba}$ | 0.4 | 0.4 |

$(0,\phantom{\rule{4.pt}{0ex}}1,\phantom{\rule{4.pt}{0ex}}{0)}^{\u22ba}$ | 0.2 | 0.03 |

$(0,\phantom{\rule{4.pt}{0ex}}0,\phantom{\rule{4.pt}{0ex}}{1)}^{\u22ba}$ | 0.4 | 0.3 |

$\frac{1}{\sqrt{3}}(1,\phantom{\rule{4.pt}{0ex}}1,\phantom{\rule{4.pt}{0ex}}{1)}^{\u22ba}$ | 0.5 | 0.3 |

Mean value and STD | 0.38 ± 0.11 | 0.26 ± 0.13 |

**Table 5.**Comparison of state-of-the-art localization methods for capsule endoscopes. For the proposed differential method, non-ideal conditions, rotation of the entire system, and a magnet of length 10 mm were applied.

Method: | Year | P_{err} (mm) | O_{err} (°) |
---|---|---|---|

Static Magnetic: | |||

Proposed differential method (simulations) [26] | 2020 | 2 | 1 |

Shao et al. [35] | 2019 | 10 | 12 |

Dai et al. [25] | 2019 | 5 | 6 |

Shimizu et al. [18] | 2020 | 10 | 5 |

Quasi-static Magnetic: | |||

Islam et al. [15] | 2018 | 3 | - |

Yang et al. [19] | 2020 | 2 | 0.2 |

RF-based: | |||

Barbi et al. [36] | 2019 | 10 | - |

Geng et al. [13] (simulations) | 2015 | <10 | - |

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**MDPI and ACS Style**

Zeising, S.; Ararat, K.; Thalmayer, A.; Anzai, D.; Fischer, G.; Kirchner, J. Systematic Performance Evaluation of a Novel Optimized Differential Localization Method for Capsule Endoscopes. *Sensors* **2021**, *21*, 3180.
https://doi.org/10.3390/s21093180

**AMA Style**

Zeising S, Ararat K, Thalmayer A, Anzai D, Fischer G, Kirchner J. Systematic Performance Evaluation of a Novel Optimized Differential Localization Method for Capsule Endoscopes. *Sensors*. 2021; 21(9):3180.
https://doi.org/10.3390/s21093180

**Chicago/Turabian Style**

Zeising, Samuel, Kivanc Ararat, Angelika Thalmayer, Daisuke Anzai, Georg Fischer, and Jens Kirchner. 2021. "Systematic Performance Evaluation of a Novel Optimized Differential Localization Method for Capsule Endoscopes" *Sensors* 21, no. 9: 3180.
https://doi.org/10.3390/s21093180