# A Narrow-Down Approach Based on Machine Learning for Indoor Localization

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## Abstract

**:**

## 1. Introduction

- This study proposes a narrow-down approach (NDA), which comprises the coarse and accurate positioning phases.
- The contribution is to select specific reference points (RPs) to train the classification algorithm, while the key considerations are to reduce the offline storage as we do not use all the RPs for training, and the chosen training points for the classifier are distant enough to share minimum RSSI characteristics. This strategy increases classification accuracy.
- We also propose a three-step source domain refinement (SDR) scheme to reduce the computational complexity of training data and enhance the classification accuracy at the same time.
- A very lightweight DNN-based multivariate regression (DNN-MVR) model, trained independently on each sub-cluster, is presented. The proposed methods are evaluated on a public dataset to show their reliability and robustness.

## 2. Related Work

## 3. System Design

#### 3.1. Area Division and Overlapping

#### 3.2. Training Data Selection

#### 3.3. Source Domain Refinement (SDR)

#### 3.3.1. Data Averaging Technique

#### 3.3.2. Outlier Removal Scheme

#### 3.3.3. Stable AP’s Weight Enhancement

- 1.
- We define a detection vector ${d}_{a}^{l}=[{d}_{a}^{l,1},{d}_{a}^{l,2},\dots ,{d}_{a}^{l,{N}_{a}}]$, where ${d}_{a}^{l,n}\in \{0,1\}$, is the detection indicator for the ${l}^{th}$ AP of ${n}^{th}$ sample in the sub-area “a”. When the value of a particular RSSI feature is above a threshold, $T{h}_{a}$, the corresponding AP is detected, and the value of ${d}_{a}^{l,n}$ would be considered as 1 or otherwise, 0. The detection vector ${d}_{a}^{l}$ is calculated for each AP in each sub-area.
- 2.
- For the current sub-area “a”, the sum ${S}_{a}^{l}$ for the ${l}^{th}$ AP’s detection indicators ${d}_{a}^{l,n}$ can be calculated as:$${S}_{a}^{l}=\sum _{n=1}^{{N}_{a}}{d}_{a}^{l,n}$$And the distinction vector ${K}_{a}\in {R}^{(L\times 1)}$ can be written as, ${K}_{a}=[{S}_{a}^{1},{S}_{a}^{2},\dots ,{S}_{a}^{L}]$, which we can normalize by dividing the whole vector ${K}_{a}$ by the maximum entry in the vector ${K}_{a}$:$${G}_{a}=\frac{{K}_{a}}{max\left({K}_{a}\right)}$$
- 3.
- Sort ${G}_{a}$ in descending order, where each entry is the stability indicator of the corresponding AP in sub-area “a”. Now, select those APs whose stability indicator is greater than a threshold $T{h}_{a}^{\prime}$ and add a small bias ${b}_{a}$ into the RSSI measurements of the selected APs. Remember that the values of $T{h}_{a}^{\prime}$ and ${b}_{a}$ are arbitrary.

#### 3.4. Sub-Clustering Algorithms

#### 3.4.1. Support Vector Machine (SVM)

#### 3.4.2. Random Forest (RF) Classifier

#### 3.4.3. Multi-Variate Regression-Based DNN Algorithm

## 4. Experiment Evaluations

#### 4.1. Experimental Setup

#### 4.2. Data Description

#### 4.3. Evaluation Metrics

#### 4.4. Experiment Results

#### 4.4.1. Classification Performance

#### 4.4.2. Regression Performance

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Library environment; photo taken from [30]; dataset available at the Zenodo repository under the open-source MIT license (https://doi.org/10.3390/data3010003, accessed on 15 February 2023).

Classifier | Training Time | Response Time | |
---|---|---|---|

Unprocessed Data | Refined Data | ||

SVM | 0.15 | 0.01 | 0.0009 |

RF | 9.7 | 4.7 | 0.0019 |

Floor | Sub-Area | Offline Samples | Online Samples | Training Time (s) |
---|---|---|---|---|

3 | 1 | 1800 | 9000 | 45.7 |

3 | 2 | 1800 | 9000 | 33.4 |

3 | 3 | 1800 | 9000 | 42.1 |

3 | 4 | 1800 | 9000 | 20.15 |

5 | 1 | 1800 | 9000 | 23.6 |

5 | 2 | 1800 | 9000 | 59.2 |

5 | 3 | 1800 | 9000 | 37.3 |

5 | 4 | 1800 | 9000 | 66.27 |

Total/Average | 8 | 14,400 | 72,000 | 327.72 |

Floor 3 | |||||
---|---|---|---|---|---|

Sub-Area | AED (m) | 25th Percentile (m) | 50th Percentile (m) | 75th Percentile (m)
| 95th Percentile (m) |

1 | 2.02 | 1.2500 | 1.9000 | 2.6500 | 3.7900 |

2 | 2.316 | 1.51 | 2.20 | 2.93 | 4.0 |

3 | 1.94 | 1.21 | 1.862 | 2.577 | 3.6073 |

4 | 2.34 | 1.4000 | 2.1900 | 3.0200 | 4.2700 |

Floor 5 | |||||

1 | 1.99 | 1.1500 | 1.8460 | 2.5900 | 3.4780 |

2 | 2.38 | 1.4320 | 2.2000 | 3.0800 | 4.3500 |

3 | 1.79 | 1.0000 | 1.6000 | 2.2500 | 3.1100 |

4 | 1.95 | 1.1000 | 1.7300 | 2.3400 | 3.2800 |

**Table 4.**Positioning error measures (in meters) and average response time (in milliseconds) for different methods.

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**MDPI and ACS Style**

Umair, S.M.A.; Arslan, T.
A Narrow-Down Approach Based on Machine Learning for Indoor Localization. *Algorithms* **2023**, *16*, 529.
https://doi.org/10.3390/a16110529

**AMA Style**

Umair SMA, Arslan T.
A Narrow-Down Approach Based on Machine Learning for Indoor Localization. *Algorithms*. 2023; 16(11):529.
https://doi.org/10.3390/a16110529

**Chicago/Turabian Style**

Umair, Sahibzada Muhammad Ahmad, and Tughrul Arslan.
2023. "A Narrow-Down Approach Based on Machine Learning for Indoor Localization" *Algorithms* 16, no. 11: 529.
https://doi.org/10.3390/a16110529