Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments
Abstract
:1. Introduction
2. Proposed LocationAggregation Method
2.1. ErrorDistribution Fitting
2.2. GPS
2.3. WLAN
2.4. BLE Beacons
2.5. Location Aggregation
Algorithm 1 Pseudocode of the localizationaggregation method 
Input: Points indicated by used methods with timestamps: GPS $\{({x}_{GPS}^{1},{y}_{GPS}^{1}),\dots ,({x}_{GPS}^{{n}_{1}},{y}_{GPS}^{{n}_{1}})\}$; $\{{t}_{GPS}^{1},\dots ,{t}_{GPS}^{{n}_{1}}\}$, WLAN $\{({x}_{WLAN}^{1},{y}_{WLAN}^{1}),\dots ,({x}_{WLAN}^{{n}_{2}},{y}_{WLAN}^{{n}_{2}})\}$, $\{{t}_{WLAN}^{1},\dots ,{t}_{WLAN}^{{n}_{2}}\}$, BLE $\{({x}_{BLE}^{1},{y}_{BLE}^{1}),\dots ,({x}_{BLE}^{{n}_{3}},{y}_{BLE}^{{n}_{3}})\}$, $\{{t}_{BLE}^{1},\dots ,{t}_{BLE}^{{n}_{3}}\}$, distributions of errors of GPS (${f}_{GPS}$), WLAN (${f}_{WLAN}$) and (${f}_{BLE}$), present timestamp t Output: Coordinates of the optimum with value of function $\mathrm{\Phi}(x,y)$ (Equation (10)) Calculate range of calculations:

3. AggregationAccuracy Analysis
3.1. Movement Model
3.2. Simulation Model
 a mobile node moves according to the Gauss–Markov mobility model with parameters: $\beta =0.9$, $\overline{v}=3\frac{m}{s}$, $\overline{\phi}=\frac{\pi}{2}$;
 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 $2.33$ and scale parameter $0.37$);
 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
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Distribution  RootMeanSquared Error (RMSE) Values  Parameters 

Gamma  0.01636  $\mathrm{shape}=2.331727,\phantom{\rule{3.33333pt}{0ex}}\mathrm{scale}=0.370786$ 
Weibull  0.01710  $\mathrm{scale}=0.910326,\phantom{\rule{3.33333pt}{0ex}}\mathrm{scale}=1.68668$ 
Normal  0.03513  $\mathrm{mean}=0.654757,\phantom{\rule{3.33333pt}{0ex}}\mathrm{std}.\mathrm{deviation}=0.479675$ 
Cauchy  0.05591  $\mathrm{location}=0.618981,\phantom{\rule{3.33333pt}{0ex}}\mathrm{scale}=0.362026$ 
Exponential  0.11877  $\mathrm{rate}=0.749887$ 
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