Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments
Abstract
:1. Introduction
2. Proposed Location-Aggregation Method
2.1. Error-Distribution Fitting
2.2. GPS
2.3. WLAN
2.4. BLE Beacons
2.5. Location Aggregation
Algorithm 1 Pseudocode of the localization-aggregation method |
Input: Points indicated by used methods with timestamps: GPS ; , WLAN , , BLE , , distributions of errors of GPS (), WLAN () and (), present timestamp t Output: Coordinates of the optimum with value of function (Equation (10)) Calculate range of calculations:
|
3. Aggregation-Accuracy Analysis
3.1. Movement Model
3.2. Simulation Model
- a mobile node moves according to the Gauss–Markov mobility model with parameters: , , ;
- position of the mobile node changes every 5 ms;
- there exist three localization systems: GPS, WLAN, and BLE beacons; as mentioned before, and they give information about localization every 1000 ms, 100 ms, and 300 ms, respectively;
- for successive methods, errors to the actual position are added according to the corresponding distribution error (for instance, GPS errors are pseudorandom values from gamma distribution with shape parameter and scale parameter );
- a position of the mobile node is calculated every 250 ms.
4. Results and Discussion
4.1. Aggregation of WLAN, GPS, and BLE Localization
4.2. Aggregation of Only WLAN and GPS
4.3. Adaptation to Different Positioning System Error Characteristics
5. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
References
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Distribution | Root-Mean-Squared Error (RMSE) Values | Parameters |
---|---|---|
Gamma | 0.01636 | |
Weibull | 0.01710 | |
Normal | 0.03513 | |
Cauchy | 0.05591 | |
Exponential | 0.11877 |
Description | Average Error (m) | Relative Error | Standard Deviation |
---|---|---|---|
Grid method | 0.94242 | 100.00% | 0.51959 |
Local Search | 0.94883 | 100.68% | 0.51900 |
Arithmetic mean | 1.07947 | 114.54% | 0.59607 |
GPS | 1.49522 | 158.66% | 0.87496 |
WLAN | 1.50353 | 159.54% | 1.12203 |
BLE beacons | 2.90712 | 308.47% | 1.18136 |
Description | Average Error (m) | Relative Error | Standard Deviation |
---|---|---|---|
Grid method | 0.95197 | 100.00% | 0.53865 |
Local Search | 0.96055 | 100.90% | 0.52843 |
Arithmetic mean | 1.01307 | 106.42% | 0.62801 |
GPS | 1.49814 | 157.37% | 0.87623 |
WLAN | 1.50363 | 157.95% | 1.12050 |
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Książek, K.; Grochla, K. Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments. Sensors 2019, 19, 1694. https://doi.org/10.3390/s19071694
Książek K, Grochla K. Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments. Sensors. 2019; 19(7):1694. https://doi.org/10.3390/s19071694
Chicago/Turabian StyleKsiążek, Kamil, and Krzysztof Grochla. 2019. "Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments" Sensors 19, no. 7: 1694. https://doi.org/10.3390/s19071694
APA StyleKsiążek, K., & Grochla, K. (2019). Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments. Sensors, 19(7), 1694. https://doi.org/10.3390/s19071694