# Performance Enhancement of Indoor Pedestrian Positioning with Two-Order Bayesian Estimation Based on EKF and PF

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## Abstract

**:**

## 1. Introduction

## 2. Algorithm Fundamentals

#### 2.1. Inertial Navigation System

#### 2.2. Zero-Velocity Update

#### 2.3. Particle Filter

#### 2.4. Wi-Fi Propagation Model

## 3. Fusion Algorithm

#### 3.1. First-Order Data Fusion

#### 3.1.1. Quaternion Update

#### 3.1.2. Pedestrian Inertial Navigation Solution

#### 3.1.3. EKF Implantation

#### 3.2. Second-Order Data Fusion

## 4. Experimental Evaluation

#### 4.1. Text Bed Setup

#### 4.2. Filter Parameter Initialization

#### 4.3. Experimental Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Pedestrian movement model; (

**b**) the schematic of the particle filter for data fusion. IMU: Inertial Measurement Unit. AP: Access Point.

**Figure 6.**(

**a**) The trajectories of Wi-Fi positioning based on the propagation model; (

**b**) The trajectories of pedestrian positioning of the inertial navigation system (INS) based on EKF (INS+EKF), Pedestrian Dead Reckoning (PDR)-only, proposed algorithm and ground truth.

Initial Position | ${[0,0,0]}^{T}$ |

Initial Velocity | ${\left[0,0,0\right]}^{T}$ |

Initial Attitude | $rol{l}_{0}=\mathrm{arctan}\left(\frac{{\mathrm{a}}_{y}^{sensor}}{{\mathrm{a}}_{z}^{sensor}}\right)$, $pitc{h}_{0}=\mathrm{arctan}\left(\frac{{a}_{x}^{sensor}}{g}\right)$, $ya{w}_{0}=0$ |

The System Noise Covariance Matrix | $Q$ is a 9-dimensional square matrix, all elements are zero, except that the diagonal elements are $\left[\begin{array}{ccc}\begin{array}{ccc}\begin{array}{ccc}{\sigma}_{ax}^{2}& {\sigma}_{ay}^{2}& {\sigma}_{az}^{2}\end{array}& {\sigma}_{gx}^{2}& {\sigma}_{gy}^{2}\end{array}& {\sigma}_{gz}^{2}& \begin{array}{cc}\begin{array}{cc}0& 0\end{array}& 0\end{array}\end{array}\right]$ |

The Measurer Noise Covariance Matrix | $R$ is a 3-dimensional zero-square matrix |

The Error Covariance Matrix | ${P}_{0}$ is a 9-dimensional zero-square matrix |

Inertial Step Length | ${s}_{0}=0$ |

Inertial Yaw | 0 |

Particle Number | 500 |

Initial Position | ${[{x}_{wifi\_propagation},{y}_{wifi\_propagation}]}^{T}$ |

Initial Particle Weight | 1/500 |

Algorithm | Error (m) | |||
---|---|---|---|---|

Maximum | Minimum | Mean | RMS | |

INS+EKF | 7.21 | 0.02 | 2.86 | 3.88 |

PDR-only | 11.59 | 0.02 | 3.04 | 5.73 |

Proposed algorithm | 4.83 | 0.01 | 1.85 | 2.19 |

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**MDPI and ACS Style**

Jiang, T.; Yang, X.; Cui, X.
Performance Enhancement of Indoor Pedestrian Positioning with Two-Order Bayesian Estimation Based on EKF and PF. *Symmetry* **2017**, *9*, 91.
https://doi.org/10.3390/sym9060091

**AMA Style**

Jiang T, Yang X, Cui X.
Performance Enhancement of Indoor Pedestrian Positioning with Two-Order Bayesian Estimation Based on EKF and PF. *Symmetry*. 2017; 9(6):91.
https://doi.org/10.3390/sym9060091

**Chicago/Turabian Style**

Jiang, Tao, Xianfeng Yang, and Xufei Cui.
2017. "Performance Enhancement of Indoor Pedestrian Positioning with Two-Order Bayesian Estimation Based on EKF and PF" *Symmetry* 9, no. 6: 91.
https://doi.org/10.3390/sym9060091