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Utilization of a Non-Linear Error Function in a Positioning Algorithm for Distance Measurement Systems Designed for Indoor Environments^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Positioning Based on Distance Measurements

## 3. Selected Known Positioning Algorithms

## 4. The Proposed Positioning Algorithm for Distance Measurement Systems

## 5. SALOn Radio Localization System

## 6. Research Results

## 7. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example of an error distribution of real distance measurements realized in an indoor environment [21].

**Figure 3.**The scheme of the Automatic Person Localization System (SALOn) structure [3].

**Figure 4.**The relationship between the value of parameter $A$ and the accuracy, precision, and mean number of iterations when all devices were deployed inside an inhabited single-family house; $B$ = 10.

**Figure 5.**The relationship between the value of parameter $B$ and the accuracy, precision, and mean number of iterations when all devices were deployed inside an inhabited single-family house; $A$ = 1.1.

**Figure 6.**Comparative analysis of performance of (

**a**) the new algorithm, (

**b**) the Chan algorithm, (

**c**) the Foy algorithm, and (

**d**) the cumulative distribution functions of position errors when all devices were deployed inside an inhabited single-family house.

**Figure 7.**Comparative analysis of the performance of (

**a**) the new algorithm, (

**b**) the Chan algorithm, (

**c**) the Foy algorithm, and (

**d**) the cumulative distribution functions of position errors when all devices were deployed within one corridor, with assurance of good geometry.

**Figure 8.**Comparative analysis of the performance of (

**a**) the new algorithm, (

**b**) the Chan algorithm, (

**c**) the Foy algorithm, and (

**d**) the cumulative distribution functions of position errors when all devices were deployed within one corridor with poor geometry.

**Figure 9.**Comparative analysis of the performance of (

**a**) the new algorithm, (

**b**) the Chan algorithm, (

**c**) the Foy algorithm, and (

**d**) the cumulative distribution functions of position errors when PIMs were placed on the first floor of an un-inhabited single-family house and reference nodes (RNs) were deployed outside it.

**Table 1.**Results of comparative analysis when all devices where deployed inside an inhabited single-family house.

Analyzed Parameters | New Algorithm | Chan Algorithm | Foy Algorithm |
---|---|---|---|

RMSE accuracy (m) | 2.04 | 8.92 | 2.97 |

RMSE precision (m) | 0.78 | 6.35 | 1.18 |

Loss probability | 0 | 5.9 × 10^{−4} | 0 |

**Table 2.**Results of comparative analysis when all devices were deployed within one corridor, with assurance of good geometry.

Analyzed Parameters | New Algorithm | Chan Algorithm | Foy Algorithm |
---|---|---|---|

RMSE accuracy (m) | 2.42 | 12.36 | 5.50 |

RMSE precision (m) | 1.83 | 11.09 | 4.49 |

Loss probability | 0 | 0.0030 | 0.0026 |

**Table 3.**Results of comparative analysis when all devices were deployed within one corridor with poor geometry.

Analyzed Parameters | New Algorithm | Chan Algorithm | Foy Algorithm |
---|---|---|---|

RMSE accuracy (m) | 2.85 | 12.81 | 10.38 |

RMSE precision (m) | 2.73 | 11.57 | 8.44 |

Loss probability | 0 | 0.0022 | 0.0071 |

**Table 4.**Results of comparative analysis when PIMs were placed on the first floor of un-inhabited single-family house and RNs were deployed outside it.

Analyzed Parameters | New Algorithm | Chan Algorithm | Foy Algorithm |
---|---|---|---|

RMSE accuracy (m) | 3.04 | 9.70 | 4.05 |

RMSE precision (m) | 1.80 | 6.25 | 2.41 |

Loss probability | 0 | 0.00184 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Czapiewska, A. Utilization of a Non-Linear Error Function in a Positioning Algorithm for Distance Measurement Systems Designed for Indoor Environments. *J. Sens. Actuator Netw.* **2019**, *8*, 21.
https://doi.org/10.3390/jsan8020021

**AMA Style**

Czapiewska A. Utilization of a Non-Linear Error Function in a Positioning Algorithm for Distance Measurement Systems Designed for Indoor Environments. *Journal of Sensor and Actuator Networks*. 2019; 8(2):21.
https://doi.org/10.3390/jsan8020021

**Chicago/Turabian Style**

Czapiewska, Agnieszka. 2019. "Utilization of a Non-Linear Error Function in a Positioning Algorithm for Distance Measurement Systems Designed for Indoor Environments" *Journal of Sensor and Actuator Networks* 8, no. 2: 21.
https://doi.org/10.3390/jsan8020021