# A Knowledge-Based Step Length Estimation Method Based on Fuzzy Logic and Multi-Sensor Fusion Algorithms for a Pedestrian Dead Reckoning System

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. System Overview

#### 2.1. Pedestrian Navigation Scheme

#### 2.2. System Configuration and Setup

^{2}or g, the latter of which is the magnitude of the Earth’s gravitational field. The gyroscope transfers the objection rotation into physical values with the unit in deg/s. One tri-axis accelerometer and one tri-axis gyroscope are used in the developed sensor module. In this study, the accelerometer used was a KXR94-2050 accelerometer with a full-scale output range of ±2 g (19.6 m/s

^{2}), produced by Kionix, Inc. (Ithaca, NY, USA). The gyroscope used was an A3G4250D gyroscope with a full-scale output range of ±245 deg/s, produced by STMicroelectronics. The basic specifications of the two sensors used are listed directly below in Table 1.

## 3. Sensor Calibration and Multi-Sensor Fusion Algorithm

#### 3.1. Sensor Error Model and Calibration Method

**K**,

**T**, and $\overrightarrow{b}$ denote the sensor outputs, observed physical quantity, scale factor matrix, orthogonalization angles matrix, and bias vector, respectively. The details of

**K**,

**T**, and $\overrightarrow{b}$ are as follows [29]:

#### 3.2. Accelerometer Calibration

#### 3.3. Gyroscope Calibration

#### 3.4. Multi-Sensor Fusion Algorithm

## 4. Pedestrian Dead Reckoning Algorithm

#### 4.1. Step Counting

#### 4.2. Knowledge-Based SLE Algorithm Based on Fuzzy Logic

#### 4.3. Heading Estimation

## 5. Experiment Results and Discussion

#### 5.1. Step Length Estimation Experiment and Results

#### 5.2. Pedestrian Navigation Experiment and Results

#### 5.3. Results and Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**The calibration results of the total rotation measured from the gyroscope triad (the red line is the reference).

**Figure 9.**Acceleration signals in each axis and the Signal Vector Magnitude (SVM) value of the user.

Specifications | KXR94-2050 Tri-Axis Accelerometer | A3G4250D Tri-Axis Gyroscope |
---|---|---|

Measurement Range | ±2 g | ±245 deg |

Sensitivity | 660 mV/g | 8.75 mdps/digit |

Sensitivity Change over Temp | 0.01 (xy) 0.02 (z)%/°C | ±2%/°C |

Non-Linearity | 0.1% of FS | 0.2% of FS |

Cross Axis Sensitivity | 2% | - |

Noise Density | 45 $\mathsf{\mu}$g/$\sqrt{Hz}$ | 0.03 dps/$\sqrt{Hz}$ |

Axis | Scale Factor (ratio) | Bias (V) | Nonorthogonal Angle (°) | |
---|---|---|---|---|

x | 0.9968 | 0.0506 | α_{x} | −0.0207 |

y | 0.9991 | 0.0006 | α_{y} | 0.0004 |

z | 1.0025 | 0.0019 | α_{z} | −0.0505 |

Axis | Scale Factor (ratio) | Bias (V) | Nonorthogonal Angle (°) | |
---|---|---|---|---|

x | 1.0138 | 0.2920 | α_{x} | 0.0014 |

y | 0.9702 | 0.2486 | α_{y} | 0.0207 |

z | 1.0031 | 0.1029 | α_{z} | −0.0090 |

Test | Step Counting | Estimated Length (cm) | Distance (m) | ||||||
---|---|---|---|---|---|---|---|---|---|

Ref. | Estimated | FL Mean | FL Std. | 4th-r Mean | 4th-r Std. | Ref. | FL | 4th-r | |

1. Sub1-30 cm | 50 | 49 | 30.70 | 2.66 | 30.15 | 1.82 | 15.25 | 15.04 | 14.77 |

2. Sub1-30 cm | 50 | 50 | 29.30 | 2.18 | 30.50 | 3.11 | 15.25 | 14.65 | 15.24 |

3. Sub1-30 cm | 50 | 50 | 31.15 | 4.45 | 28.96 | 1.80 | 15.25 | 15.57 | 14.47 |

4. Sub1-60 cm | 50 | 50 | 60.25 | 4.05 | 60.06 | 1.84 | 30.50 | 30.12 | 30.03 |

5. Sub1-60 cm | 50 | 50 | 59.64 | 4.27 | 59.64 | 2.01 | 30.50 | 29.82 | 29.82 |

6. Sub1-60 cm | 50 | 50 | 60.91 | 4.09 | 61.57 | 2.19 | 30.50 | 30.46 | 30.79 |

7. Sub1-90 cm | 50 | 50 | 89.77 | 2.73 | 90.08 | 2.21 | 45.75 | 44.89 | 45.04 |

8. Sub1-90 cm | 50 | 49 | 91.46 | 3.27 | 87.74 | 5.65 | 45.75 | 44.81 | 42.99 |

9. Sub1-90 cm | 50 | 50 | 90.42 | 2.28 | 83.77 | 7.73 | 45.75 | 45.21 | 41.88 |

Total | 450 | 448 | 274.50 | 270.57 | 265.03 |

Test | Step Counting | Estimated Length (cm) | Distance (m) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Ref. | Est. | FL Mean | FL std. | 4th-r Mean | 4th-r Std. | Ref. | FL | Location Error | 4th-r | |

1. Sub2/170/65 | 50 | 49 | 61.55 | 4.52 | 56.77 | 4.72 | 30.50 | 30.78 | 0.39 | 28.38 |

2. Sub2/170/65 | 50 | 50 | 59.61 | 3.24 | 54.18 | 4.34 | 30.50 | 29.80 | 0.81 | 27.09 |

3. Sub3/177/80 | 50 | 50 | 63.05 | 4.06 | 55.99 | 5.13 | 30.50 | 31.53 | 0.88 | 27.99 |

4. Sub3/177/80 | 50 | 50 | 63.60 | 4.02 | 55.00 | 4.35 | 30.50 | 31.80 | 1.87 | 27.50 |

5. Sub4/162/60 | 50 | 50 | 62.96 | 5.24 | 52.62 | 5.05 | 30.50 | 31.45 | 1.49 | 26.31 |

6. Sub4/162/60 | 50 | 50 | 63.13 | 5.75 | 50.92 | 5.88 | 30.50 | 31.57 | 1.84 | 25.46 |

7. Sub5/167/50 | 50 | 50 | 64.36 | 3.81 | 50.23 | 6.16 | 30.50 | 32.18 | 1.08 | 25.12 |

8. Sub5/167/50 | 50 | 50 | 65.40 | 4.60 | 54.36 | 4.28 | 30.50 | 32.70 | 0.90 | 27.18 |

9. Sub6/170/70 | 50 | 50 | 61.74 | 6.88 | 51.48 | 4.73 | 30.50 | 30.87 | 0.27 | 25.74 |

10. Sub6/170/70 | 50 | 50 | 62.22 | 6.57 | 51.77 | 5.09 | 30.50 | 31.11 | 0.51 | 25.88 |

11. Sub7/157/48 | 50 | 50 | 61.34 | 5.08 | 52.27 | 6.64 | 30.50 | 30.67 | 0.56 | 26.14 |

12. Sub7/157/48 | 50 | 50 | 61.57 | 2.25 | 56.42 | 4.36 | 30.50 | 30.78 | 0.55 | 28.21 |

13. Sub8/160/56 | 50 | 50 | 64.89 | 5.38 | 58.83 | 5.10 | 30.50 | 32.45 | 1.94 | 29.42 |

14. Sub8/160/56 | 50 | 50 | 63.86 | 4.71 | 56.16 | 5.15 | 30.50 | 31.93 | 1.85 | 28.08 |

15. Sub9/163/70 | 50 | 50 | 68.48 | 4.60 | 65.76 | 1.76 | 30.50 | 34.24 | 2.37 | 32.88 |

16. Sub9/163/70 | 50 | 50 | 67.71 | 4.88 | 66.29 | 3.06 | 30.50 | 33.85 | 2.75 | 33.15 |

17. Sub10/168/53 | 50 | 50 | 64.68 | 4.83 | 55.03 | 4.78 | 30.50 | 32.34 | 1.42 | 27.51 |

18. Sub10/168/53 | 50 | 50 | 65.28 | 5.27 | 54.94 | 5.91 | 30.50 | 32.64 | 0.61 | 27.47 |

Total | 900 | 899 | 549.00 | 572.69 | 499.51 |

Test | Step Counting | Estimated Length (cm) | Distance (m) | |||||
---|---|---|---|---|---|---|---|---|

Ref. | Est. | FL Mean | FL SD | Ref. | FL | Error (%) | S-E | |

1. Sub2-60 cm | 192 | 192 | 60.53 | 2.20 | 116.51 | 116.22 | 0.24 | 0.72 |

2. Sub2-60 cm | 192 | 191 | 60.27 | 2.30 | 116.51 | 115.12 | 1.19 | 0.73 |

3. Sub1-free | 179 | 179 | 65.16 | 2.42 | 116.51 | 116.64 | 0.11 | 1.27 |

4. Sub1-free | 168 | 169 | 69.39 | 3.16 | 116.51 | 117.27 | 0.65 | 2.22 |

Total | 731 | 731 | 466.04 | 465.25 | 4.94 |

Test | Step Counting | Estimated Length (cm) | Distance (m) | Heading Error (deg) | |||||
---|---|---|---|---|---|---|---|---|---|

Ref. | Est. | FL Mean | FL SD | Ref. | FL | Error (%) | S-E | ||

1. Sub1-free | 556 | 556 | 69.59 | 1.80 | 385.2 | 386.93 | 0.45 | 5.80 | 0.90 |

2. Sub1-free | 542 | 541 | 71.17 | 2.28 | 385.2 | 385.01 | 0.05 | 1.49 | 3.60 |

3. Sub1-free | 541 | 541 | 70.59 | 2.17 | 385.2 | 378.35 | 1.78 | 5.03 | 1.95 |

4. Sub1-free | 542 | 541 | 70.91 | 1.92 | 385.2 | 383.60 | 0.41 | 4.76 | 4.27 |

5. Sub1-free | 553 | 553 | 70.70 | 2.33 | 385.2 | 390.96 | 1.50 | 10.15 | 4.07 |

6. Sub1-free | 557 | 557 | 70.34 | 1.98 | 385.2 | 391.82 | 1.72 | 5.71 | 1.46 |

Total | 3291 | 3289 | 2311.2 | 2316.7 | 31.75 |

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## Share and Cite

**MDPI and ACS Style**

Lai, Y.-C.; Chang, C.-C.; Tsai, C.-M.; Huang, S.-C.; Chiang, K.-W.
A Knowledge-Based Step Length Estimation Method Based on Fuzzy Logic and Multi-Sensor Fusion Algorithms for a Pedestrian Dead Reckoning System. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 70.
https://doi.org/10.3390/ijgi5050070

**AMA Style**

Lai Y-C, Chang C-C, Tsai C-M, Huang S-C, Chiang K-W.
A Knowledge-Based Step Length Estimation Method Based on Fuzzy Logic and Multi-Sensor Fusion Algorithms for a Pedestrian Dead Reckoning System. *ISPRS International Journal of Geo-Information*. 2016; 5(5):70.
https://doi.org/10.3390/ijgi5050070

**Chicago/Turabian Style**

Lai, Ying-Chih, Chin-Chia Chang, Chia-Ming Tsai, Shih-Ching Huang, and Kai-Wei Chiang.
2016. "A Knowledge-Based Step Length Estimation Method Based on Fuzzy Logic and Multi-Sensor Fusion Algorithms for a Pedestrian Dead Reckoning System" *ISPRS International Journal of Geo-Information* 5, no. 5: 70.
https://doi.org/10.3390/ijgi5050070