Indoor Locationing and Tracking
4. Bandwidth Concatenation
4.5 Experiment Results
In addition to the two large desks, the indoor space is filled with other furniture including chairs and computers, which are not shown inFigure 4.7for brevity.
4.5.1.2 Configurations
Two USRPs are used to obtain the CFRs with bandwidth configured asW =10 MHz.
The two USRPs coordinate with each other to perform synchronous frequency hopping using the mechanism discussed in Section 4.4. The step size of frequency hopping is fixed at f = 8.28 MHz.1 The minimum number of CFRs per channel is set as Mmin=10.
4.5.1.3 Details of Measurement
One USRP is placed on the grid points on a measurement platform in the small room as shown in Figure 4.7.The center of the USRP is aligned with the grid point. The distance between two adjacent grid points is 5 cm. The other USRP is placed on the table of the larger room. CFRs fromL =75 different grid points are measured within an area of 70 cm×20 cm. For each measurement, the two USRPs sweep the frequency band from 4.9 to 5.9 GHz, leading to a total ofD =124 times of frequency hopping with a step size of 8.28 MHz. The effective bandwidthWeis thus 1 GHz. For each of the 75 locations, we formulateM=10 location fingerprints.
4.5.2 Metrics for Performance Evaluation
For theM=10 fingerprints collected at each location, we store the firstM1=5 CFRs into the fingerprint database in the offline phase, and consider the otherM2=5 finger- prints as samples collected in the online phase. Denoting themth location fingerprint formulated at location as Gm[], we calculate the TRRS matrix Rwith the (i,j)th entry ofRgiven byγ[Gm[],Gn[]], wherem=Mod(i,M1)+1, = i−Mm1−1+1, n = Mod(j,M2)+1, and = j−Mn−1
2 +1. Here,Modis the modulus operator,i is termed as the training index, andj is termed as the testing index.
We define the entries ofRcalculated from CFRs obtained at the same locations as thediagonal entriesand those calculated using CFRs obtained from different locations as the off-diagonal entries. We demonstrate the histograms and cumulative density functions for the diagonal and off-diagonal entries.
Based onR, we evaluate the localization performances using the metrics of the true- positive rate, denoted asPTP, and the false-positive rate, denoted asPFP.PTPis defined as the probability that the IPS localizes the device to its correct location, while PFP captures the probability that the IPS localizes the device to a wrong location, or fails to localize the device.
In the performance evaluation, the CFR sifting parameterτis set as 0.8.
1 Considering the null subcarriers at both edges of the Wi-Fi channel spectrum, we adjust the frequency hopping step size such that the entire spectrum can be covered without spectrum holes. Notice that the presented IPS does not require the measured frequency band to be contiguous.
4.5 Experiment Results 81
4.5.3 Performance Evaluation
4.5.3.1 TRRS Matrix under DifferentWe
Figure 4.8demonstratesRwithWe ∈[10,40,120,1,000] MHz. We observe that when We = 10 MHz, there exists many large off-diagonal entries inR, indicating severe ambiguities among different locations. When the total bandwidth We increases, the ambiguities among different locations are significantly eliminated, while the TRRSs within the same location are almost unchanged.
4.5.3.2 Distribution of Diagonal and Off-Diagonal Entries under DifferentWe
Figure 4.9visualizes the distribution of the diagonal and off-diagonal entries ofRwith differentWe∈[10,40,120,1,000] MHz using histograms. Statistics of the diagonal and off-diagonal entries are shown as well. As we can see, the TRRS values at the same locations are identical with different We, implying high stationarity of the presented IPS. On the other hand, the off-diagonal entries are more suppressed and approach a Gaussian-like distribution whenWeincreases. We also observe an enlarged gap between the diagonal and off-diagonal entries whenWeincreases, indicating a better separability among different locations. The increase ofWe also reduces the variations of diagonal and off-diagonal entries, as shown by the decreasing standard deviations. Moreover,
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(c) We= 120 MHz (d) We= 1,000 MHz (b) We= 40 MHz
Figure 4.8 TRRS matrix under differentWe.
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 20 40 60 80 100
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 1 2 3 4 5
Diagonal Avg 0.981 Std 0.113 Med 0.999 Max 1.000 Min 0.153
Off-diagonal Avg 0.666 Std 0.205 Med 0.701 Max 0.992 Min 0.000
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 20 40 60 80 100
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 1 2 3 4 5
Diagonal Avg 0.982 Std 0.061 Med 0.997 Max 1.000 Min 0.517
Off-diagonal Avg 0.426 Std 0.168 Med 0.427 Max 0.907 Min 0.000
(a)We=10 MHz (b)We=40 MHz
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 20 40 60 80 100
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 2 4 6 8
Diagonal Avg 0.981 Std 0.045 Med 0.997 Max 1.000 Min 0.721
Off-diagonal Avg 0.364 Std 0.112 Med 0.364 Max 0.721 Min 0.008
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Percent (%)
0 20 40 60
TRRS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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0 5 10 15 20
Diagonal Avg 0.987 Std 0.012 Med 0.992 Max 0.998 Min 0.915
Off-diagonal Avg 0.346 Std 0.042 Med 0.345 Max 0.533 Min 0.195
(c)We=120 MHz (d)We=1000 MHz
Figure 4.9 Histogram of diagonal and off-diagonal entries under differentWe.
a large We removes the outliers in the diagonal entries: when We = 10 MHz, the minimum value of diagonal entries is 0.153, while the minimum value increases to 0.915 whenWe = 1,000 MHz. Thus, a largeWe improves the robustness of the IPS against outliers.
4.5.3.3 Cumulative Density Functions of Diagonal and Off-Diagonal Entries under DifferentWe
In Figure 4.10,we demonstrate the cumulative density functions of diagonal and off- diagonal entries with We ∈ [10,20,40,80,120,300,500,1,000] MHz. As can be seen from the figure, a large We reduces the spread of both the diagonal and off-diagonal entries, which agrees with the results shown inFigure 4.9.
4.5.3.4 Mean and Standard Deviation Performances under DifferentWe
Figure 4.11depicts the impact ofWeon the mean and standard deviation performances for both diagonal and off-diagonal entries. The upper and lower bars indicate the±σ bounds with respect to the average, where σ stands for the standard deviation. We conclude that a largeWe improves the distinction among different locations, but also reduces the variation of the TRRS at the same locations as well as among different locations. In other words, a large We makes the IPS performance more stable and predictable.
4.5 Experiment Results 83
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
TRRS 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CDF
Diag., Eff. BW = 10 MHz Diag., Eff. BW = 20 MHz Diag., Eff. BW = 40 MHz Diag., Eff. BW = 80 MHz Diag., Eff. BW = 120 MHz Diag., Eff. BW = 300 MHz Diag., Eff. BW = 500 MHz Diag., Eff. BW = 1,000 MHz Off-diag., Eff. BW = 10 MHz Off-diag., Eff. BW = 20 MHz Off-diag., Eff. BW = 40 MHz Off-diag., Eff. BW = 80 MHz Off-diag., Eff. BW = 120 MHz Off-diag., Eff. BW = 300 MHz Off-diag., Eff. BW = 500 MHz Off-diag., Eff. BW = 1,000 MHz
Figure 4.10 Cumulative density functions of diagonal and off-diagonal entries of the TRRS matrix under differentWe.
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TRRS
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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Figure 4.11 Mean and standard deviation of the diagonal and off-diagonal entries of the TRRS matrix under differentWe.
4.5.3.5 ThresholdSettings under DifferentWe
Figure 4.12depicts the smallest thresholdunderWe =[20,60,100, . . . ,1,000] MHz to achieve (i) PTP = 100% andPFP = 0% and (ii)PTP ≥ 95% andPFP ≤ 5%.
We observe a decreasing in when We is larger, which can be justified by the fact that the gap between the diagonal and off-diagonal entries enlarges whenWebecomes larger. When We = 20 MHz, the IPS fails to achievePTP = 100% and PFP = 0%.
Effective bandwidth
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
100% true-positive rate, 0% false-positive rate
At least 95% true-positive rate, at most 5% false-positive rate
Figure 4.12 Thresholdunder differentWeto achieve (i)PTP=100% andPFP=0% and (ii) PTP≥95% andPFP≤5%.
Figure 4.12also implies that we can achieve a perfect 5 cm localization ifis chosen appropriately.
Based on the experiment results, we conclude that a largeWe is imperative for the robustness, stability, and performance of the presented IPS. By formulating the location fingerprint that concatenates multiple channels, the presented IPS achieves a perfect centimeter localization accuracy in an NLOS environment with one pair of single- antenna Wi-Fi devices.