# Orthogonal Chirp-Based Ultrasonic Positioning

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## Abstract

**:**

## 1. Introduction

## 2. Ultrasonic Positioning

#### 2.1. Lateration

#### 2.2. Cross-Correlation

## 3. Description of Problem

## 4. Orthogonal Chirp Waveforms for Multiple Access Ultrasonic Positioning

## 5. Performance Evaluation of Orthogonal Chirp Waveforms

## 6. Simulation Results

## 7. Experimental Procedure

## 8. Results and Discussions

## 9. Conclusions and Future Work

## Author Contributions

## Conflicts of Interest

## Abbreviations

3D | three-dimensional |

CDMA | code division multiple access |

DSSS | direct sequence spread spectrum |

FDM | frequency-division multiplixing |

FHSS | frequency hopped spread spectrum |

FM | frequency-modulated |

MAI | multiple-access interference |

OFDM | orthogonal frequency-division multiplixing |

RMSE | root-mean-square-error |

SNR | signal-to-noise ratio |

TDM | time-division multiplixing |

TOF | time-of-flight |

UPS | ultrasonic positioning system |

US | ultrasonic |

## References

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**Figure 2.**(

**a**) 35–45 kHz/2 ms chirp in time domain with sampling frequency 1 MHz; (

**b**–

**d**) three orthogonal chirp waveforms respectively, generated from (

**a**); (

**e**) corresponding frequency spectra of the three orthogonal chirp waveforms shown in (

**b**–

**d**); and (

**f**) stem graph of the zoom plot of (

**e**).

**Figure 3.**Comparisons of auto-correlations and cross-correlations of three waveforms for the proposed method: (

**a**) waveforms 1 and 2; (

**b**) waveforms 1 and 3; and (

**c**) Waveforms 2 and 3.

**Figure 4.**Cumulative absolute location errors (from simulations) of target (receiver) obtained for the proposed, TDM and FDM techniques.

**Figure 7.**(

**a**) A test case from the experimental results that represents the positioning of transmitters and receivers; and (

**b**) zoomed version of the position of the receivers.

**Figure 8.**Cumulative absolute location errors (from experiments) of receiver obtained for the proposed, TDM and FDM techniques.

**Figure 9.**Auto-correlation width of the transmitted and received signal where the correlation width ($\mathsf{\Delta}c1$) 100 and ($\mathsf{\Delta}c2$) 167 refers 10 kHz and 6 kHz respectively according to the formula $\mathsf{\Delta}c\simeq \pm \frac{1}{{T}_{s}B}$ [15].

**Table 1.**Coordinates of the 3D rectangular room, and ideal positions of the reference points and target transducer ($\mathrm{cm}$).

x | y | z | |
---|---|---|---|

Room (top left corner) | −300 | 300 | 0 |

Room (bottom right corner) | 300 | 0 | 0 |

Reference Point 1 | −60 | 60 | 0 |

Reference Point 2 | 60 | 60 | 0 |

Reference Point 3 | 0 | 120 | 0 |

Target | −5 | 95 | 100 |

**Table 2.**Absolute location errors (from simulations and experiments) of receiver obtained for the proposed, TDM and FDM techniques in terms of 90% Error and RMSE ($\mathrm{mm}$).

Technique | Proposed | TDM | FDM |
---|---|---|---|

RMSE & 90% Error (from simulations) | 1.82 & 2.67 | 1.45 & 2.13 | 6.04 & 8.87 |

RMSE & 90% Error (from experiments) | 4.54 & 6.68 | 4.05 & 5.95 | 12.86 & 18.92 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Khyam, M.O.; Ge, S.S.; Li, X.; Pickering, M.
Orthogonal Chirp-Based Ultrasonic Positioning. *Sensors* **2017**, *17*, 976.
https://doi.org/10.3390/s17050976

**AMA Style**

Khyam MO, Ge SS, Li X, Pickering M.
Orthogonal Chirp-Based Ultrasonic Positioning. *Sensors*. 2017; 17(5):976.
https://doi.org/10.3390/s17050976

**Chicago/Turabian Style**

Khyam, Mohammad Omar, Shuzhi Sam Ge, Xinde Li, and Mark Pickering.
2017. "Orthogonal Chirp-Based Ultrasonic Positioning" *Sensors* 17, no. 5: 976.
https://doi.org/10.3390/s17050976