# Acoustic NLOS Identification Using Acoustic Channel Characteristics for Smartphone Indoor Localization

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## Abstract

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## 1. Introduction

- An acoustic NLOS identification approach based on acoustic channel characteristics is proposed for smartphone indoor localization in the real world. This approach is suitable for the acoustic localization systems based on DOA, TOA and TDOA strategies.
- An efficient approach to estimate relative channel gain and delay based on the cross-correlation method is proposed, in order to mitigate the influence of the Doppler Effect and reduce the computational complexity.
- The differences and characteristics of acoustic relative channel gain and delay under LOS and NLOS conditions are investigated through extensive measurements in office rooms and lobby environment using COTS smartphones. Novel features are extracted from these characteristics that capture the salient properties based on time delay characteristics, waveform characteristics, Rician K-factor and frequency characteristics of relative channel gain.
- An optimal kernel function for an SVM classifier to realize acoustic NLOS identification is evaluated and chosen under the accuracy criterion, based on a data set with more than 10 thousand measurements. The best feature set of the SVM classifier for acoustic NLOS identification is investigated and proposed.

## 2. Characterization of the Acoustic Channel under LOS and NLOS Conditions

#### 2.1. The Characteristics of Room Acoustic Propagation under LOS Condition

- ${n}_{l}=\{1,0\}$. There is only one direct path between the transmitter and receiver, which is the LOS path. ${n}_{l}=1$ is the LOS condition, and 0 for the NLOS condition. ${\alpha}_{l}$ and ${\tau}_{l}$ are decreased with the increase of path length, due to the air propagation attenuation.
- The length of the reflection path is definitely longer than the LOS path. With the increase of reflection time, ${\tau}_{r}$ becomes larger and larger, while ${\alpha}_{r}$ is quickly decreased due to the acoustic absorption by air, walls and furniture. For the diffusion propagation path, the number of diffusion paths is usually very large. ${\alpha}_{d}$ and ${\tau}_{d}$ are related to the shape of the diffusion surface, absorption coefficient, and the relative position between the transmitter, receiver and diffusion surface.
- Generally speaking, the energy of signals received from the LOS path and reflection path is larger than the signals received from the diffusion path, that is ${E}_{l}\left(t\right)$, ${E}_{r}\left(t\right)$ > ${E}_{d}\left(t\right)$. However, the relationship between ${E}_{l}\left(t\right)$ and ${E}_{r}\left(t\right)$ is determined by ambient environment. It is common that the LOS signal is not the strongest, especially in large space environment.

#### 2.2. The Characteristics of Acoustic Propagation under NLOS Condition

## 3. The Relative Channel Gain and channel Delay Estimation

#### 3.1. Modelling of Received Signals

#### 3.2. Estimation Approach

## 4. Data Acquisition and Features Extraction

#### 4.1. Experiment Deployment

#### A. Obstructions

#### B. Experiment Process

#### 4.2. Features Extraction

## 5. NLOS Identification Based on SVM Classifiers

#### 5.1. The SVM Classifier and Kernel Function

#### 5.2. Cross-Validation and Evaluation Criteria

#### 5.3. Test Results and Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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RBF Kernel Function | Polynomial Kernel Function | ||||||

Feature | Precision | Accuracy | F1-Measure | Feature | Precision | Accuracy | F1-Measure |

${\tau}_{med}$ | 0.818 | 0.826 | 0.850 | ${\tau}_{med}$ | 0.832 | 0.832 | 0.850 |

${\tau}_{rms}$ | 0.749 | 0.781 | 0.824 | ${\tau}_{rms}$ | 0.776 | 0.770 | 0.795 |

k | 0.837 | 0.823 | 0.841 | k | 0.784 | 0.811 | 0.840 |

s | 0.840 | 0.828 | 0.846 | s | 0.803 | 0.821 | 0.844 |

${K}_{R}$ | 0.896 | 0.853 | 0.864 | ${K}_{R}$ | 0.895 | 0.858 | 0.873 |

${g}_{m}$ | 0.858 | 0.867 | 0.885 | ${g}_{m}$ | 0.883 | 0.858 | 0.871 |

${g}_{rms}$ | 0.850 | 0.851 | 0.870 | ${g}_{rms}$ | 0.848 | 0.837 | 0.854 |

${k}_{f}$ | 0.838 | 0.852 | 0.872 | ${k}_{f}$ | 0.813 | 0.847 | 0.871 |

${s}_{f}$ | 0.838 | 0.849 | 0.870 | ${s}_{f}$ | 0.827 | 0.846 | 0.868 |

Mean accuracy | 0.837 | Mean accuracy | 0.831 | ||||

Median accuracy | 0.849 | Median accuracy | 0.837 | ||||

Best feature | ${g}_{m}$ | Best feature | ${g}_{m}$ | ||||

Linear Kernel Function | Sigmoid Kernel Function | ||||||

Feature | Precision | Accuracy | F1-Measure | Feature | Precision | Accuracy | F1-Measure |

${\tau}_{med}$ | 0.825 | 0.826 | 0.848 | ${\tau}_{med}$ | 0.564 | 0.564 | 0.721 |

${\tau}_{rms}$ | 0.783 | 0.763 | 0.789 | ${\tau}_{rms}$ | 0.559 | 0.559 | 0.717 |

k | 0.778 | 0.800 | 0.834 | k | 0.566 | 0.566 | 0.723 |

s | 0.813 | 0.819 | 0.846 | s | 0.289 | 0.205 | 0.290 |

${K}_{R}$ | 0.876 | 0.849 | 0.862 | ${K}_{R}$ | 0.512 | 0.456 | 0.625 |

${g}_{m}$ | 0.884 | 0.861 | 0.874 | ${g}_{m}$ | 0.549 | 0.549 | 0.709 |

${g}_{rms}$ | 0.859 | 0.852 | 0.869 | ${g}_{rms}$ | 0.559 | 0.559 | 0.717 |

${k}_{f}$ | 0.810 | 0.844 | 0.870 | ${k}_{f}$ | 0.544 | 0.544 | 0.705 |

${s}_{f}$ | 0.827 | 0.847 | 0.868 | ${s}_{f}$ | 0.397 | 0.297 | 0.430 |

Mean accuracy | 0.829 | Mean accuracy | 0.478 | ||||

Median accuracy | 0.844 | Median accuracy | 0.549 | ||||

Best feature | ${g}_{m}$ | Best feature | k |

**Table 2.**The performance of three kinds of kernel functions under the accuracy criterion in ${F}^{M}$.

SVM with RBF Kernel Function | ||||

Best | Worst | Average | ||

Feature combination | Accuracy | Feature combination | Accuracy | |

${F}^{1}=\left\{{g}_{m}\right\}$ | 0.867 | ${F}^{1}=\left\{{\tau}_{rms}\right\}$ | 0.781 | 0.837 |

${F}^{2}=\{{K}_{R},{g}_{m}\}$ | 0.913 | ${F}^{2}=\{k,s\}$ | 0.841 | 0.877 |

${F}^{3}=\{k,{K}_{R},{g}_{m}\}$ | 0.975 | ${F}^{3}=\{s,{k}_{f},{s}_{f}\}$ | 0.864 | 0.931 |

${F}^{4}=\{{\tau}_{med},{\tau}_{rms},{K}_{R},{g}_{m}\}$ | 0.984 | ${F}^{4}=\{s,{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.902 | 0.967 |

${F}^{5}=\{{\tau}_{med},{\tau}_{rms},k,{g}_{m},{g}_{rms}\}$ | 0.985 | ${F}^{5}=\{k,s,{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.952 | 0.980 |

${F}^{6}=\{{\tau}_{med},{\tau}_{rms},s,{g}_{m},{g}_{rms},{s}_{f}\}$ | 0.984 | ${F}^{6}=\{k,s,{K}_{R},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.980 | 0.982 |

${F}^{7}=\{{\tau}_{rms},s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.983 | ${F}^{7}=\{{\tau}_{rms},k,s,{K}_{R},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.981 | 0.982 |

${F}^{8}=\{{\tau}_{med},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.983 | ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{s}_{f}\}$ | 0.981 | 0.982 |

${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.983 | ${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.983 | 0.983 |

Mean accuracy | 0.962 | |||

Median accuracy | 0.983 | |||

Best feature combination ${F}^{5}=\{{\tau}_{med},{\tau}_{rms},k,{g}_{m},{g}_{rms}\}$ | ||||

SVM with Polynomial Kernel Function | ||||

Best | Worst | Average | ||

Feature combination | Accuracy | Feature combination | Accuracy | |

${F}^{1}=\left\{{g}_{m}\right\}$ | 0.858 | ${F}^{1}=\left\{{\tau}_{rms}\right\}$ | 0.770 | 0.831 |

${F}^{2}=\{{K}_{R},{g}_{m}\}$ | 0.873 | ${F}^{2}=\{{\tau}_{med},{\tau}_{rms}\}$ | 0.827 | 0.853 |

${F}^{3}=\{{\tau}_{med},{K}_{R},{g}_{m}\}$ | 0.886 | ${F}^{3}=\{{\tau}_{med},{\tau}_{rms},{k}_{f}\}$ | 0.830 | 0.860 |

${F}^{4}=\{{\tau}_{med},{K}_{R},{g}_{m},{k}_{f}\}$ | 0.889 | ${F}^{4}=\{{\tau}_{med},{\tau}_{rms},k,{k}_{f}\}$ | 0.842 | 0.863 |

${F}^{5}=\{{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.890 | ${F}^{5}=\{{\tau}_{med},{\tau}_{rms},k,s,{s}_{f}\}$ | 0.843 | 0.868 |

${F}^{6}=\{{\tau}_{med},s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f}\}$ | 0.895 | ${F}^{6}=\{{\tau}_{med},{\tau}_{rms},k,{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.848 | 0.873 |

${F}^{7}=\{{\tau}_{med},{\tau}_{rms},s,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ | 0.896 | ${F}^{7}=\{{\tau}_{med},{\tau}_{rms},k,s,{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.853 | 0.880 |

${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ | 0.903 | ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.866 | 0.891 |

${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.892 | ${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.892 | 0.892 |

Mean accuracy | 0.887 | |||

Median accuracy | 0.890 | |||

Best feature combination ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ | ||||

SVM with Linear Kernel Function | ||||

Best | Worst | Average | ||

Feature combination | Accuracy | Feature combination | Accuracy | |

${F}^{1}=\left\{{g}_{m}\right\}$ | 0.861 | ${F}^{1}=\left\{{\tau}_{rms}\right\}$ | 0.763 | 0.829 |

${F}^{2}=\{{K}_{R},{g}_{m}\}$ | 0.876 | ${F}^{2}=\{{\tau}_{med},{\tau}_{rms}\}$ | 0.825 | 0.853 |

${F}^{3}=\{{\tau}_{rms},{K}_{R},{g}_{m}\}$ | 0.884 | ${F}^{3}=\{{\tau}_{med},{\tau}_{rms},k\}$ | 0.828 | 0.859 |

${F}^{4}=\{{\tau}_{med},{K}_{R},{g}_{m},{k}_{f}\}$ | 0.887 | ${F}^{4}=\{{\tau}_{med},{\tau}_{rms},k,{k}_{f}\}$ | 0.843 | 0.864 |

${F}^{5}=\{{\tau}_{med},{\tau}_{rms},{K}_{R},{g}_{m},{k}_{f}\}$ | 0.890 | ${F}^{5}=\{{\tau}_{med},{\tau}_{rms},{g}_{rms},{k}_{f}\}$ | 0.840 | 0.867 |

${F}^{6}=\{{\tau}_{med},{\tau}_{rms},s,{K}_{R},{g}_{m},{s}_{f}\}$ | 0.895 | ${F}^{6}=\{{\tau}_{med},{\tau}_{rms},k,s,{g}_{rms},{s}_{f}\}$ | 0.842 | 0.873 |

${F}^{7}=\{{\tau}_{med},{\tau}_{rms},k,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ | 0.896 | ${F}^{7}=\{{\tau}_{rms},k,s,{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.852 | 0.878 |

${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ | 0.902 | ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.863 | 0.887 |

${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.894 | ${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.894 | 0.894 |

Mean accuracy | 0.887 | |||

Median accuracy | 0.890 | |||

Best feature combination ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ |

**Table 3.**The performance of logistic regression (LR) and the linear discriminant analysis (LDA) classifier under the accuracy criterion in ${F}^{M}$.

Logistic Regression | ||||

Best | Worst | Average | ||

Feature combination | Accuracy | Feature combination | Accuracy | |

${F}^{1}=\left\{{g}_{m}\right\}$ | 0.860 | ${F}^{1}=\left\{{\tau}_{rms}\right\}$ | 0.776 | 0.830 |

${F}^{2}=\{{K}_{R},{g}_{m}\}$ | 0.882 | ${F}^{2}=\{{\tau}_{med},{\tau}_{rms}\}$ | 0.803 | 0.850 |

${F}^{3}=\{s,{K}_{R},{g}_{m}\}$ | 0.882 | ${F}^{3}=\{{\tau}_{med},{\tau}_{rms},s\}$ | 0.828 | 0.858 |

${F}^{4}=\{k,{K}_{R},{g}_{m},{g}_{rms}\}$ | 0.893 | ${F}^{4}=\{{\tau}_{rms},k,s,{s}_{f}\}$ | 0.837 | 0.862 |

${F}^{5}=\{s,{K}_{R},{g}_{m},{g}_{rms},{s}_{f}\}$ | 0.889 | ${F}^{5}=\{{\tau}_{med},{\tau}_{rms},s,{g}_{rms},{k}_{f}\}$ | 0.839 | 0.866 |

${F}^{6}=\{{\tau}_{med},{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.903 | ${F}^{6}=\{{\tau}_{rms},k,s,{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.839 | 0.874 |

${F}^{7}=\{{\tau}_{med},{\tau}_{rms},s,{K}_{R},{g}_{m},{k}_{f},{s}_{f}\}$ | 0.895 | ${F}^{7}=\{{\tau}_{med},{\tau}_{rms},k,s,{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.839 | 0.878 |

${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{s}_{f}\}$ | 0.895 | ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.877 | 0.886 |

${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.890 | ${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.890 | 0.890 |

Mean accuracy | 0.888 | |||

Median accuracy | 0.890 | |||

Best feature combination ${F}^{6}=\{{\tau}_{med},{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | ||||

LDA | ||||

Best | Worst | Average | ||

Feature combination | Accuracy | Feature combination | Accuracy | |

${F}^{1}=\left\{{K}_{R}\right\}$ | 0.848 | ${F}^{1}=\left\{{\tau}_{rms}\right\}$ | 0.760 | 0.809 |

${F}^{2}=\{{K}_{R},{g}_{m}\}$ | 0.882 | ${F}^{2}=\{{\tau}_{med},{\tau}_{rms}\}$ | 0.767 | 0.844 |

${F}^{3}=\{{\tau}_{rms},s,{K}_{R}\}$ | 0.879 | ${F}^{3}=\{{\tau}_{med},{\tau}_{rms},s\}$ | 0.829 | 0.855 |

${F}^{4}=\{{\tau}_{rms},s,{K}_{R},{k}_{f}\}$ | 0.878 | ${F}^{4}=\{{\tau}_{med},{\tau}_{rms},k,{k}_{f}\}$ | 0.834 | 0.860 |

${F}^{5}=\{{\tau}_{med},{\tau}_{rms},s,{K}_{R},{g}_{m}\}$ | 0.887 | ${F}^{5}=\{{\tau}_{med},{\tau}_{rms},k,{k}_{f},{s}_{f}\}$ | 0.836 | 0.864 |

${F}^{6}=\{{\tau}_{med},{\tau}_{rms},s,{K}_{R},{g}_{m},{g}_{rms}\}$ | 0.891 | ${F}^{6}=\{{\tau}_{med},{\tau}_{rms},k,s,{k}_{f},{s}_{f}\}$ | 0.847 | 0.867 |

${F}^{7}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{k}_{f}\}$ | 0.889 | ${F}^{7}=\{{\tau}_{med},{\tau}_{rms},s,{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.848 | 0.870 |

${F}^{8}=\{{\tau}_{med},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.885 | ${F}^{8}=\{{\tau}_{med},{\tau}_{rms},k,s,{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.855 | 0.874 |

${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.873 | ${F}^{9}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{g}_{rms},{k}_{f},{s}_{f}\}$ | 0.873 | 0.873 |

Mean accuracy | 0.879 | |||

Median accuracy | 0.882 | |||

Best feature combination ${F}^{7}=\{{\tau}_{med},{\tau}_{rms},k,s,{K}_{R},{g}_{m},{k}_{f}\}$ |

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## Share and Cite

**MDPI and ACS Style**

Zhang, L.; Huang, D.; Wang, X.; Schindelhauer, C.; Wang, Z.
Acoustic NLOS Identification Using Acoustic Channel Characteristics for Smartphone Indoor Localization. *Sensors* **2017**, *17*, 727.
https://doi.org/10.3390/s17040727

**AMA Style**

Zhang L, Huang D, Wang X, Schindelhauer C, Wang Z.
Acoustic NLOS Identification Using Acoustic Channel Characteristics for Smartphone Indoor Localization. *Sensors*. 2017; 17(4):727.
https://doi.org/10.3390/s17040727

**Chicago/Turabian Style**

Zhang, Lei, Danjie Huang, Xinheng Wang, Christian Schindelhauer, and Zhi Wang.
2017. "Acoustic NLOS Identification Using Acoustic Channel Characteristics for Smartphone Indoor Localization" *Sensors* 17, no. 4: 727.
https://doi.org/10.3390/s17040727