Sensor Localization Using Time of Arrival Measurements in a Multi-Media and Multi-Path Application of In-Situ Wireless Soil Sensing
Abstract
:1. Introduction
- We present a framework to 3D localize wireless nodes located in multiple physical media (air and soil) that have multiple paths of communication through a lossy medium (soil).
- We extend the MLE framework for time of arrival of a single path signal to the multi-path case.
- We present our python-based implementation of the proposed localization schemes with simulation results validating our methodology.
- We further validate our localization schemes with rigorous sensitivity analyses of the location estimates with respect to errors in measurements of various soil parameters.
1.1. Related Works
2. Materials and Methods
2.1. MLE of ToA for a Single Path
2.2. Mean and Variance of Time of Arrival in Terms of Location Coordinates
2.2.1. Multi-Path Extension: Soil-to-Soil Communication
2.2.2. Multi-Media Extension: Air-to-Soil Communication
2.3. MLE-Based Localization
2.4. Software Implementation
3. Results
Sensitivity Analysis
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
MLE | Maximum Likelihood Estimation |
RSS | Received Signal Strength |
ToA | Time of Arrival |
AoA | Angle of Arrival |
UWB | Ultra Wide Band |
TDoA | Time Difference of Arrival |
WUSN | Wireless Underground Sensor Networks |
CRLB | Cramer–Rao Lower Bound |
SNR | Signal to Noise Ratio |
Appendix A. Mean Received Power in Terms of Locations
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Fractional Volume of Water | ||
---|---|---|
2.36 | 0.0966 | |
5.086 | 0.441 | |
16.410 | 2.368 | |
24.485 | 3.857 |
Parameter | Symbol | Value |
---|---|---|
Transmit power (Satellite node) | 38 dBm | |
Transmit power (Sensor node) | 10 dBm | |
Thermal noise | −110 dBm | |
Path loss factor (air) | 2 | |
Path loss factor (soil) | 2 | |
Relative permeability (soil) | 1.0084 | |
Frequency | f | 433 MHz |
Wavelength | 0.7 m | |
Bandwidth | B | 1 Hz |
Signal duration | 1 ms |
TOA | RSS | |||
---|---|---|---|---|
Moisture Content | xy | z | xy | z |
0% | ||||
10% | ||||
20% | ||||
30% |
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Sahota, H.; Kumar, R. Sensor Localization Using Time of Arrival Measurements in a Multi-Media and Multi-Path Application of In-Situ Wireless Soil Sensing. Inventions 2021, 6, 16. https://doi.org/10.3390/inventions6010016
Sahota H, Kumar R. Sensor Localization Using Time of Arrival Measurements in a Multi-Media and Multi-Path Application of In-Situ Wireless Soil Sensing. Inventions. 2021; 6(1):16. https://doi.org/10.3390/inventions6010016
Chicago/Turabian StyleSahota, Herman, and Ratnesh Kumar. 2021. "Sensor Localization Using Time of Arrival Measurements in a Multi-Media and Multi-Path Application of In-Situ Wireless Soil Sensing" Inventions 6, no. 1: 16. https://doi.org/10.3390/inventions6010016
APA StyleSahota, H., & Kumar, R. (2021). Sensor Localization Using Time of Arrival Measurements in a Multi-Media and Multi-Path Application of In-Situ Wireless Soil Sensing. Inventions, 6(1), 16. https://doi.org/10.3390/inventions6010016