# Cost-Effective Fitting Model for Indoor Positioning Systems Based on Bluetooth Low Energy

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## Abstract

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## 1. Introduction

- Its relatively low unit cost, as the signaling device, and bases its positioning method on the planar model equation in order to save labor and time costs.
- A model that more closely matches the signal strength of the reference points in the environment can be established to replace the original planar model.
- The advantages of collecting less signal strength data from reference points is retained in order to control the equipment cost and manpower/time expenses for establishment of the comparison database, while improving the positioning accuracy of the planar model.

## 2. Related Works

#### 2.1. Received Signal Strength-Based Methods

#### 2.2. Other Positioning Systems

## 3. System Architecture and Proposed Method

#### 3.1. System Architecture

#### 3.2. Experimental Environment

#### 3.3. Research Method

#### 3.3.1. Model Production

**Step 1**. Data Collection and Collation

**Step 2**. MATLAB Fitting Model Tools

**Step 3**. Custom Equation

#### 3.3.2. Fitting Model and Equation Generation

#### 3.3.3. Equation Solutions and Positioning Determinations

## 4. Evaluation Results and Analysis

#### 4.1. Results Produced by the Models and Their Comparison

#### 4.2. Signal Pattern Comparison

#### 4.3. Comparison and Analysis of Both Methods

#### 4.4. Model Optimization

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**RADAR Positioning Technology Flowchart [2].

**Figure 2.**Graph of Relationship between Signal Intensity and Distance [6].

**Figure 8.**Input of Reference Point Data into MATLAB [17].

**Table 1.**Comparisons of characteristics in various positioning technologies [16].

Wireless Position System | Localization Technique | Range | Accuracy |
---|---|---|---|

DOLPHIN (RF with Ultrasonic) | ToA, trilateration | Indoor | 2 cm |

RFID/INS | RSS/INS | Indoor | 2 m |

UWB | TDoA/ToA, trilateration | 15 m | 10 cm |

RFID/FPM | RSS/INS | Indoor | 1.7 m |

Land Marc | RSS, triangulation | 50 m | 1~2 m |

GPS | ToA, trilateration | Global | 1~5 m |

Radar | RSS, triangulation | Indoor | Indoor |

Cricket | ToA, trilateration | 10 m | 2 cm |

Active Bats | ToA, trilateration | 50 m | 9 cm |

Active Badge | ToA, trilateration | 5 m | 7 cm |

COMPASS | RSS, triangulation | 15 m | 1.65 m |

WhereNet (RF) | RSS, triangulation | 20 m | 2~3 m |

LiFS | Fingerprinting database | Indoor | 9 m |

Bluetooth | RSSI fingerprinting/RSSI theoretical propagation model | Indoor | 2~5 m |

Base Station | Fitting Model Equation |
---|---|

A | $s=f\left(x,y\right)=-0.01175{x}^{2}-0.01268{y}^{2}-77.02$ |

B | $s=f\left(x,y\right)=-0.007802{x}^{2}+0.009089{y}^{2}-79.91$ |

C | $s=f\left(x,y\right)=0.01176{x}^{2}+0.009245{y}^{2}-80.9$ |

D | $s=f\left(x,y\right)=0.008952{x}^{2}+0.00218{y}^{2}-81.45$ |

**Table 3.**Individual Fitting Model Equations for the Same Base Station Using Data Collected from Different Directions.

Direction Faced | Fitting Model Equation |
---|---|

East | $s=f\left(x,y\right)=-0.01175{x}^{2}-0.01268{y}^{2}-77.02$ |

West | $s=f\left(x,y\right)=-0.01139{x}^{2}-0.01305{y}^{2}-73.97$ |

South | $s=f\left(x,y\right)=-0.01411{x}^{2}-0.009248{y}^{2}-75.84$ |

North | $s=f\left(x,y\right)=-0.0114{x}^{2}-0.03213{y}^{2}-70.71$ |

**Table 4.**Models and Equations Generated from the Four Directions in the Experimental Environment for Base Station A.

Planar Model and Equation | Fitting Model and Equation | |
---|---|---|

East | $s=-0.3888x-0.1935y-74.29$ | $s=-0.01175{x}^{2}-0.01268{y}^{2}-77.02$ |

West | $s=-0.3418x-0.1775y-71.94$ | $s=-0.01139{x}^{2}-0.01305{y}^{2}-73.97$ |

South | $s=-0.4371x-0.1187y-73.36$ | $s=-0.01411{x}^{2}-0.009248{y}^{2}-75.84$ |

North | $s=-0.3678x-0.4942y-67.44$ | $s=-0.0114{x}^{2}-0.03213{y}^{2}-70.71$ |

**Table 5.**Models and Equations Generated from the Four Directions in the Experimental Environment for Base Station B.

Planar Model and Equation | Fitting Model and Equation | |
---|---|---|

East | $s=-0.2374x+0.1595y-79.18$ | $s=-0.007802{x}^{2}+0.009089{y}^{2}-79.91$ |

West | $s=-0.3475x+0.002143y-73.26$ | $s=-0.01062{x}^{2}+0{y}^{2}-75.23$ |

South | $s=-0.5678x+0.1538y-70.02$ | $s=-0.01772{x}^{2}+0.006322{y}^{2}-72.54$ |

North | $s=-0.367x+0.5903y-76.58$ | $s=-0.01102{x}^{2}+0.03956{y}^{2}-77.38$ |

**Table 6.**Models and Equations Generated from the Four Directions in the Experimental Environment for Base Station C.

Planar Model and Equation | Fitting Model and Equation | |
---|---|---|

East | $s=0.3368x+0.1355y-82.74$ | $s=0.01176{x}^{2}+0.009245{y}^{2}-80.9$ |

West | $s=0.3664x-0.1108y-84.79$ | $s=0.01197{x}^{2}-0.007782{y}^{2}-83.13$ |

South | $s=0.3602x-0.3704y-79.25$ | $s=0.01272{x}^{2}-0.02044{y}^{2}-78.81$ |

North | $s=0.4804x+0.04798y-82.61$ | $s=0.01668{x}^{2}-0.0004788{y}^{2}-80.03$ |

**Table 7.**Models and Equations Generated from the Four Directions in the Experimental Environment for Base Station D.

Planar Model and Equation | Fitting Model and Equation | |
---|---|---|

East | $s=0.2999x+0.05238y-83.44$ | $s=0.008952{x}^{2}+0.00218{y}^{2}-81.45$ |

West | $s=0.4071x+0.3622y-88.17$ | $s=0.01393{x}^{2}+0.02336{y}^{2}-85.34$ |

South | $s=0.361x+0.3386y-82.61$ | $s=0.01382{x}^{2}+0.02518{y}^{2}-80.69$ |

North | $s=0.3209x+0.1229y-85.41$ | $s=0.01058{x}^{2}+0.01095{y}^{2}-83.69$ |

Method | Original | Area | Optimal |
---|---|---|---|

Signal Pattern Matching | 7.77 | 6.63 | 3.56 |

Planar Model | 14.15 | 8.15 | 4.34 |

Fitting Model | 9.7 | 7.82 | 4.02 |

Environment | Original | Area | Optimal |
---|---|---|---|

Basketball Court (large environment) | 31% | 4% | 7% |

Method (No. Reference Points, Spacing) | Original | Area |
---|---|---|

Planar Model (120, 2 m) | 14.15 | 8.15 |

Planar Model (32, 4 m) | 13.15 | 7.88 |

Planar Model (8, 8 m) | 13.12 | 7.11 |

Fitting Model (120, 2 m) | 9.7 | 7.82 |

Fitting Model (32, 4 m) | 9.5 | 7.4 |

Fitting Model (8, 8 m) | 11.15 | 6.66 |

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**MDPI and ACS Style**

Yeh, S.-C.; Wang, C.-H.; Hsieh, C.-H.; Chiou, Y.-S.; Cheng, T.-P. Cost-Effective Fitting Model for Indoor Positioning Systems Based on Bluetooth Low Energy. *Sensors* **2022**, *22*, 6007.
https://doi.org/10.3390/s22166007

**AMA Style**

Yeh S-C, Wang C-H, Hsieh C-H, Chiou Y-S, Cheng T-P. Cost-Effective Fitting Model for Indoor Positioning Systems Based on Bluetooth Low Energy. *Sensors*. 2022; 22(16):6007.
https://doi.org/10.3390/s22166007

**Chicago/Turabian Style**

Yeh, Sheng-Cheng, Chia-Hui Wang, Chaur-Heh Hsieh, Yih-Shyh Chiou, and Tsung-Pao Cheng. 2022. "Cost-Effective Fitting Model for Indoor Positioning Systems Based on Bluetooth Low Energy" *Sensors* 22, no. 16: 6007.
https://doi.org/10.3390/s22166007