# Integrated WiFi/PDR/Smartphone Using an Adaptive System Noise Extended Kalman Filter Algorithm for Indoor Localization

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## Abstract

**:**

## 1. Introduction

## 2. The Wireless Positioning Technology Based on Field Strength

#### 2.1. The Feature Extraction Integrating the Distance and Signal Information

_{1}, b

_{2}, ..., b

_{n}} comprises all APs within the fingerprint positioning area, where all artificially planned RPs also compose Collection L = {l

_{1}, l

_{2}, ..., l

_{m}}. The element l

_{i}(1 ≤ i ≤ m) in Collection L consists of two pieces of data, one of which is represented by G

_{i}= (x

_{i}, y

_{i}), which is the geographic coordinate of this point, and the other indicated by V

_{i}= (v

_{i.}

_{1}, v

_{i}

_{.2}, ..., v

_{i.n}), which is the signal strength vector of each AP received at the point, where v

_{i.j}(1 ≤ I ≤ m, 1 ≤ j≤ n) represents the intensity of the signal received in the spatial position associated with l

_{i}from b

_{j}.

_{i}and l

_{j}. Typically, the value of m_ij is much larger when the positions related to l

_{i}and l

_{j}are near each other, and vice versa. Because the value of m_ij can reflect the spatial distance relationship between the respective points in some degree, the introduction of variable m_ij can increase the signal distance value between long-distance points and reduce the signal distance value between the short-distance points when calculating the signal distance. The geographical distance between two sampling points is defined as

#### 2.2. Affinity Propagation Clustering

_{m*m}between m points, and the fused feature MixDis is used in this paper. The similarity matrix S

_{m*m}represents the characteristic matrix for the signal distance and the spatial distance between m APs with the calculation of every value made according to the fusion feature, MixDis(i, j) in Formula 3. Moreover, s(i, j) represents the fusion feature of the ith AP and the jth AP, also representing the fused value of the spatial distance and the signal distance between two APs. Generally, a median in S

_{m*m}is chosen as a reasonable value to represent s(k, k); namely, the median in line k of S is selected as the initial value of s(k, k). The calculation of the message transmission between two reference points then follows, which is the core of the algorithm: attraction message r(i, j) and attribution message a(i, j). Here, the attraction message r(i, j) is passed from point i to point j to indicate the reliability of point j as the cluster center of point i; the attribution message a (i, j) is passed from point j to point i to indicate the reliability of point i as the cluster center of point j.

#### (1) Attraction message r(i, j)

_{i}to respective point l

_{j}shows the attraction accumulation of l

_{j}to l

_{i}as the cluster center under the role of respective points except for l

_{i}, and the formula is as follows:

#### (2) The attribution message a(i, j).

_{j}to respective point l

_{i}shows the attraction accumulation of l

_{i}to l

_{j}as the cluster center under the role of the respective points instead of l

_{j}, and the formula is as follows:

#### (3) The self-attribution message:

_{i}is the center. Otherwise, point l

_{j’}is the center.

#### 2.3. Positioning Point Set Searching

_{i}, y

_{i}) is the coordinate of the ith nearest RP in the determined fingerprint class collection, $(\hat{x},\hat{y})$ is the positioning result, and d

_{i}is the signal domain distance between the ith nearest RP and the point to be positioned in the determined class. With respect to Equation (7), some other researchers used $1/{d}_{i}^{2}$ instead of $1/{d}_{i}$ [31]. From the perspective of computational efficiency, the usage of $1/{d}^{2}$ will further increase the impact of the signal distance on the calculation result. In other words, the ultimate positioning result will tend to such an RP that has a smaller signal distance. However, because the distance between two RPs in this paper is rather small, at 1.2 × 1.2 m

^{2}, such a correction will not significantly affect the positioning result.

## 3. PDR and Wi-Fi Fusion Algorithm

#### 3.1. Adaptive-Weighted Smoothing Filter Based on the Displacement Constraint

#### 3.2. Adaptive System Noise Filter Based on the Pedestrian’s Moving Status

## 4. Experimental Analysis

**Figure 1.**Experimental site. (

**a**) Floor scene graph of the fourth floor; (

**b**) 3D model of the experimental site.

#### 4.1. Wi-Fi Positioning Analysis

#### (1) Offline data acquisition and preprocessing

**Figure 3.**The polar coordinates diagram for statistical results of the Wi-Fi signal in the five consecutive days.

#### (2) Clustering analysis

**Table 1.**The statistics for the number of class members in the result of K-means clustering (10 times).

Times | Class 1 | Class 2 | Class 3 | Class 4 | Class 5 | Class 6 | Class 7 | Class 8 | Class 9 |
---|---|---|---|---|---|---|---|---|---|

1 | 17 | 15 | 10 | 7 | 6 | 8 | 10 | 11 | 9 |

2 | 17 | 15 | 10 | 7 | 9 | 15 | 8 | 3 | 9 |

3 | 17 | 6 | 10 | 12 | 10 | 8 | 10 | 11 | 9 |

4 | 11 | 6 | 6 | 10 | 9 | 7 | 9 | 15 | 20 |

5 | 8 | 9 | 6 | 10 | 12 | 10 | 8 | 10 | 20 |

6 | 17 | 6 | 10 | 9 | 7 | 9 | 15 | 11 | 9 |

7 | 17 | 6 | 10 | 9 | 7 | 6 | 8 | 10 | 20 |

8 | 9 | 9 | 14 | 10 | 7 | 9 | 15 | 11 | 9 |

9 | 8 | 9 | 6 | 10 | 12 | 10 | 18 | 11 | 9 |

10 | 32 | 13 | 10 | 8 | 10 | 8 | 3 | 5 | 4 |

#### (3) Analysis results of static positioning

#### (4) Triangle mesh structure of fingerprint points

Quadrilateral fingerprint database | Triangle fingerprint database | |
---|---|---|

Average error of static positioning / m | 1.50 | 1.76 |

Maximum error of static positioning / m | 2.80 | 3.52 |

Average error of dynamic positioning / m | 4.09 | 4.43 |

Maximum error of dynamic positioning / m | 19.76 | 22.4 |

#### 4.2. Fusion Analysis

**Figure 11.**Trajectory analysis for different indoor positioning methods. (

**a**) Trajectory of PDR, WIFI,REAL; (

**b**) trajectory of AEKFPDR, EKFPDR.

Wi-Fi | PDR | WEPDR | AWEPDR | |
---|---|---|---|---|

Minimum error/m | 0.36 | 5.14 | 0.28 | 0.22 |

Average error/m | 4.09 | 6.08 | 2.74 | 2.32 |

Maximum error/m | 19.35 | 6.46 | 7.96 | 5.25 |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Li, X.; Wang, J.; Liu, C.; Zhang, L.; Li, Z.
Integrated WiFi/PDR/Smartphone Using an Adaptive System Noise Extended Kalman Filter Algorithm for Indoor Localization. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 8.
https://doi.org/10.3390/ijgi5020008

**AMA Style**

Li X, Wang J, Liu C, Zhang L, Li Z.
Integrated WiFi/PDR/Smartphone Using an Adaptive System Noise Extended Kalman Filter Algorithm for Indoor Localization. *ISPRS International Journal of Geo-Information*. 2016; 5(2):8.
https://doi.org/10.3390/ijgi5020008

**Chicago/Turabian Style**

Li, Xin, Jian Wang, Chunyan Liu, Liwen Zhang, and Zhengkui Li.
2016. "Integrated WiFi/PDR/Smartphone Using an Adaptive System Noise Extended Kalman Filter Algorithm for Indoor Localization" *ISPRS International Journal of Geo-Information* 5, no. 2: 8.
https://doi.org/10.3390/ijgi5020008