1.4GHz. Dual ARM 11. 332 MHz. Memory. 8GB/16GB. 1GB RAM. 2GB ROM. 8GB. 128 MB RAM. Wi-Fi. 802.11 b/g/n. 802.11 b/g. OS. Android 4.0.3. (IceCream).
Performance Comparison of a Probabilistic Fingerprint-based Indoor Positioning System over Different Smartphones Igor Bisio, Fabio Lavagetto, Mario Marchese, Andrea Sciarrone Dept. of Telecommunication, Electronic, Electric Engineering and Naval Architectures DITEN Genoa, Italy {igor.bisio, fabio.lavagetto, mario.marchese, andrea.sciarrone}@unige.it Abstract — In this paper a performance comparison of a probabilistic Gaussian-Kernel fingerprint-based indoor positioning method over different smartphones, is presented. The work aims at highlighting the positioning accuracy, the robustness and the consistency of the method by testing it over two different smartphone platforms (i.e., Nokia N95 and Samsung Galaxy S II), within a given area. In more detail, three different variants of the probabilistic approach have been tested: Nearest Neighbor (NN), K-Nearest Neighbor (K-NN) and K Weighted-Nearest Neighbor (KW-NN). Numerical experiments, carried out in an area of around 80 [m2], have shown that the probabilistic fingerprint provides good position accuracy (less than 1.20 [m] of error) for both devices and also robustness when the signal strength acquisitions are reduced. Finally, the similarity of results provided by the two smartphones leads to assert that the probabilistic approach is also consistent with respect to the device employed in the experiments. Keywords—WiFi-Fingerprinting, Smartphone, Performance Comparison
I.
Indoor
Positioning,
INTRODUCTION
Location awareness is one of the key capabilities in contextaware computing and communications. Accurate, reliable, realtime positioning and indoor position-based services are often required within common applications of the so called Future Internet. In general, a positioning method enables a Mobile Device (MD, such as a smartphone) to determine its position, and to make the position of the device available for location-aware services, such as navigating, tracking or monitoring. Commercial examples range from low-accuracy methods based on cell identification to high-accuracy methods combining information acquired from the wireless networks in the MDs’ surroundings [1]. Satellite based positioning methods, such as the multilateration based on the GPS, are able to provide excellent results when there is a clear view of the sky; unfortunately, they have the great drawback of not being able to operate in closed environments or urban areas. In addition, limitations in the smartphones’ CPU main memory and RAM strongly bound the capabilities for such methods. Furthermore, as MDs and, in particular, smartphones have short lifetime due to power limitations of the related batteries. For this reason, it
is important to design the positioning method in a way that ensures that as less power as possible is consumed [3]. Many approaches are trying to deal with these problems and WiFibased localization has emerged to be one of the most promising indoor positioning solutions. Basically, in the literature two are the main approaches for WiFi indoor positioning: i) multilateration (usually called trilateration, when 3 APs are used) which is similar to the GPS-based approach and ii) fingerprinting. The first one uses the geometrical properties of triangles to estimate the position of an object of interest [4]. In the literature, some examples of this approach can be found in [5], [6] and [7]. A major deployment obstacle for such systems, however, is the high energy consumption rates of WiFi adapters in mobile devices where energy is the most valuable resource [8]. The other family of positioning approach, the fingerprinting, is based on two-step procedure [9]. In the first one, carried out off-line, we collect training data, in terms of WiFi Access Points (APs) signal strengths, for a set of given points in the area of interest, called Reference Points (RPs), in order to obtain – for each RP – position-dependent statistics called FingerPrint (FP). The second step, performed on-line which represents the positioning, is aimed at comparing an observation, a scanning of the WiFi APs signal strengths, with the stored FPs. The position estimated is one or a combination of the RPs’ coordinates whose fingerprint(s) most closely match(es) the observations. More in general, it is possible to distinguish between two FP approaches: i) Deterministic FingerPrint (D-FP) and ii) Probabilistic FingerPrint (P-FP) [10]. The former estimates the position only by considering measurements of RSSs or the average and/or the variance of these values. The latter computes the position by considering measurements as part of a random process [10], trying to exploit all the information contained within the signals acquired. In this paper we present a performance comparison of a Gaussian-kernel probabilistic fingerprint-based indoor positioning system realized with two smartphone platforms. The probabilistic fingerprint approach has been chosen since, from an energy viewpoint, it is more suited to be implemented over MDs (such as smartphones), where power consumption and energy management are crucial aspects [2]. In more detail
three are the main metrics we have evaluated: i) position accuracy, ii) the robustness and iii) the consistency. The rest of the paper is organized as follow: in Section II a general overview of indoor positioning systems is provided. Section III briefly describes the probabilistic fingerprint algorithm while Section IV describes the test-bed and the devices employed in all the experiments. Section V proposes the numerical results. Finally, the Conclusions are drawn. II.
INDOOR POSITIONING METHODS
A. Introduction The objective of a positioning method is to locate any object of interest, moving or stationary, through procedures and algorithms adapted to the technologies employed. Applications and services which exploit these methods include but are not limited to: user navigation, user guidance, and people and environments security. In all the cases in which locate an object within an area is necessary, it is mandatory to have a description of the environment, in order to consider the critical aspects that the localization process poses. The main problems that arise in developing an indoor positioning system are due to the propagation of the electromagnetic signal in presence of obstacles [11]. In particular, the errors caused by such indirect measurements are related to three aspects: •
errors due to the precision and sensitivity of system that measures the signals;
•
errors due to conversion of these measures in geometric characteristics;
•
errors due to the algorithm itself, in terms of accuracy and precision;
B. Performance Metrics In the literature, many are the parameters that allow to determinate the quality of indoor positioning methods [10]. Among them we have selected the ones reported below: •
Accuracy: it is the most important performance metric. It measures the degree of correspondence between the estimated position and the real one thought the average mean error.
•
Robustness: it is the ability of the positioning method to estimate the MD position even if some data are missing, reduced or incomplete.
•
Consistency: it represents the capability of the approach to compute the MD position in different working conditions (such as by using different MDs).
This technique can be considered as composed of two steps: •
training phase (off-line);
•
positioning phase (on-line);
The goal of the training phase is to obtain a database, called RadioMap (RM), necessary for storing the FPs and for computing the MD position. The RM consists essentially in a matrix in which the FPs and the coordinates of the RPs in which the FP has been computed are stored. The method which computes the RM is summarized in the pseudo code reported in Fig. 1:
Fig. 1: The pseudo code used to create the RadioMap
During the on-line phase, the MD acquires one or more values of the Radio Signal Strength (RSS) from each AP and computes the observation vector of the point in which the MD is situated, by simply averaging the RSS values of each AP. This observation vector represents the on-line FP of the point and is denoted with o . The vector o is then compared, using an appropriate matching algorithm, with the others fingerprints stored inside the RM. In practice, for each RP we compute the following quantity
p(l | Ƞ) =
THE PROBABILISTIC FINGERPRITING ALGORITHM
This category of algorithms for positioning includes all those methods which provide an estimate of the MD position through the analysis of one or more distinctive characteristics. The probabilistic approach models the location fingerprint with conditional probability and utilizes the Bayesian inference concept to estimate the MD position [10].
(1)
where l represents an index representing an RP, which is defined also by its coordinates referred to a fixed Cartesian reference system of the area of interest. In order to compute the quantity p(⋅ | ⋅) , we used the Gaussian probability kernel which has been used in other works (see [12], [13] and [14]). After the computation of p(l | o) , it is possible to estimate the MD’s position using different strategies. Among them, the Nearest Neighbour (NN) is the simplest and chooses, as MD position, the RP i which has the highest probability. Another simple method is the K-NN, K ≥ 2 which provides the position coordinates as average of the coordinates of the K RPs with the highest probability. Finally, the KW-NN (K Weighted Nearest Neighbour, K ≥ 2 ) computes the weighted average rather than the simple one. For our work, we use the values of p(l | o) as the average weights. IV.
III.
p(o | l ) p(l ) p (o)
ENVIROMENT SETUP
A. Test-Bed Description The test-bed area used in all the experiments is the Laboratory of Digital Signal Processing (DSPLab), which is an area of approximately 80 [m2], inside the Department of Telecommunication, Electronic, Electric Engineering and Naval Architectures (DITEN) of the University of Genoa, Italy.
It is worth noticing that all the tests have been performed within the laboratory which is not an ideal area but a real environment: it presents walls, windows, desks, a whiteboard, computers and people.
•
For the realization of the test-bed, we have used the IEEE 802.11g WiFi network infrastructure, already present in the laboratory. We have deployed up to 5 APs at approximately 3 [m] from the ground. Four of them are in the corners of the laboratory, while the last one is located in the middle as, reported in Fig. 2.
A. The impact of the APs number The three variants (NN, K-NN and KW-NN) have been tested by gradually increasing the AP’s number. Firstly we used only three APs, then we incremented their number to four (one in each corner) and finally we introduced also the fifth AP, in the middle of the area (Fig. 2). For each of the three configurations, an RM composed of 156 RP has been adopted. In order to build the FPs we have averaged, for each RP, 120 RSS values acquiring a value every second. Considering that the environment used for the experiments is not ideal, there could be RPs in which the online positioning shows higher accuracy. For this reason, for sake of fairness, we have used for all the experiments, the same 30 RPs in which compute the MD position and then average the results.
•
the robustness of the method, by varying the amount of data used during the positioning phase; the consistency of the method, by employing two different devices for the experiments.
Fig. 2: The Test-Bed area employed for experiments Fig. 3: Histogram of the average positioning error and variance for all the considered variants, for the Android Samsung Galaxy S II.
B. Employed Devices The two devices employed in this work are 2 off-the-shelf smartphones: Samsung Galaxy S II and Nokia N95. Table 1 reports their most important technical features. TABLE 1:Technical features of the three devices employed in this work.
CPU Memory Wi-Fi OS
V.
Galaxy S II Exynos 4210 1.4GHz 8GB/16GB 1GB RAM 2GB ROM 802.11 b/g/n Android 4.0.3 (IceCream).
Nokia N95 Dual ARM 11 332 MHz
The figure above shows the average positioning error and variance for the Android device Samsung Galaxy S II. From the histogram reported in Fig. 3 it is possible to see a decrement of the positioning error as the APs’ number increases. Furthermore, the accuracy of the positioning process improves passing from the NN variant to the K-NN and the WK-NN. Analogous consideration can be done for the histogram reported in Fig. 4, relative to the Nokia N95.
8GB 128 MB RAM 802.11 b/g Symbian OS 9.2 S60 rel. 3.1
NUMERICAL RESULTS
In order to evaluate the performance in computing the MD position, we have performed some experiments, detailed in the following sub-sections. The main objectives of the tests are to evaluate the three performance metrics introduced in Section II.B. Consequently we have tried to evaluate: •
the accuracy of the proposed algorithms, in terms of average error and variance;
Fig. 4: Histogram of the average positioning error and variance for all the considered variants, for the Nokia N95.
B. The impact of the number of on-line acquisitions Another set of results we have obtained are related to the impact, in terms of positioning accuracy, of the number of online RSS acquisitions. Obliviously, on one hand, using a reduced number of online RSS acquisitions, will lead to a
faster positioning computation, since less time is needed to acquire the RSS values, but the positioning accuracy will be degraded. In the same way the employment of more RSS values will provide a longer on-line positioning phase but higher position accuracy.
TABLE 2: The impact of the number of online acquisitions for some of the proposed methods for the Android Galaxy S II. All the results are expressed in [m]. Acquisitions NN 2NN 4NN 2WNN 4WNN Error
Var
Error
Var
Error
Var
Error
Var
Error
Var
1
2.71
2.31
2.65
2.81
2.81
2.85
2.35
2.43
2.43
2.11
5
2.63
2.49
2.58
2.62
2.70
2.62
2.25
2.23
2.19
2.05
10
2.03
2.72
1.98
2.70
2.05
2.71
2.15
2.31
1.87
1.68
24
1.97
2.49
1.85
2.59
2.63
1.63
2.07
1.48
1.21
60
1.89
2.63
1.65
2.45
1.71
2.53
1.57
1.67
1.27
1.15
100
1.91
2.23
1.86
2.64
1.75
2.22
1.55
1.27
1.11
1.05
120
1.95
2.15
1.72
2.21
1.73
2.07
1.25
1.19
1.05
0.97
1.83
TABLE 3: The impact of the number of online acquisitions for some of the proposed methods for the Nokia N95. All the results are expressed in [m]. Acquisitions NN 2NN 4NN 2WNN 4WNN Error
Var
Error
Var
Error
Var
Error
Var
Error
Var
1
3.25
2.41
3.21
2.76
3.01
2.87
2.86
2.33
2.70
2.32
5
3.10
2.24
3.12
2.40
2.85
2.51
2.38
2.09
2.28
1.31
10
2.75
2.12
3.06
2.35
2.56
2.64
2.15
1.95
2.01
1.44
24
2.80
1.74
2.57
1.82
1.98
2.06
1.51
1.68
1.48
1.10
60
2.94
1.65
2.36
1.70
1.86
1.86
1.40
1.28
1.31
1.03
100
2.69
1.84
2.12
1.62
1.65
1.75
1.29
1.08
1.16
0.66
120
2.21
2.03
1.83
1.48
1.70
1.68
1.12
0.97
1.12
0.63
All the results gathered in Table 2 and Table 3 were obtained by computing the MD position in 30 different RPs. Obviously, for sake of fairness, the 30 RPs chosen are exactly the same for each positioning method. The first intuitive result that is possible to see from the two tables above, is that the method’s positioning accuracy improves as the number of RSS on-line acquisitions increases, for each device. Considering the case of the Android-based device, the NN method provides an error equal to 2.71[m] when the position is computed with only one RSS acquisition, while it becomes 1.95 [m] if 120 RSS acquisition are performed, with an improvement equal to 28%. For what concern the K-NN method with K = 2 , the error ranges from 2.65 [m] when only one RRS acquisition is used to 1.72 [m] with 120 RSS acquisitions (with an improvement of 35%) while for the case of K = 4 the error varies from 2.85 [m] (one acquisition) to 2.07 [m] (improvement equals to 27%) with 120 RSS acquisitions. The weighted methods provide the best accuracy: when one acquisition is employed the method shows an error equal to 2.35 [m] and 2.45 [m] for the case of K = 2 and K = 4 , respectively. When 120 RSS values are used the position
error lowers to 1.19 [m] (with K = 2 ) and 1.05 [m] (with K = 4 ) with an improvement equals to 49% and .57%, respectively. The improvement of the positioning accuracy with the number of acquisitions is motivated by the fact that, sensing a larger number RSS values, brings more robust information about the power irradiated from each AP and acquired by the MD in each RP. Another important result is the improvement of the MD position by using the K-NN and the KW-NN methods with respect to the NN one. For example if 120 online acquisitions are used, the NN method provides a positioning error and a variance close to 2 [m] and 3 [m], respectively. Using the K-NN (with K = 2 and K = 4 ) the errors lower to 1.72 [m] and 1.73 [m], respectively (almost 12% less). The improvement for the variance is even greater: 2.71 [m] (for K = 2 ) and 2.07[m] (for K = 4 ). If the KW-NN method is employed the positioning error is the lowest: 1.25 [m] (almost 36% less than NN) and 1.05 [m] (46% less than NN) for the case K = 2 and K = 4 , respectively. The same considerations hold for the variance: 1.19[m] and 0.97[m] which indicates a more precise positioning.
Analogous consideration can be made for the Nokia N95. The NN method performed worst with a positioning error from 3.25 [m] with only one RSS acquisition, to 2.21 [m] with 120 RSS acquisitions. The K-NN variants provide better results with error from 3.21 [m] and 3.01 [m] with only one acquisition (for K = 2 and K = 4 ) to 1.83 [m] and 1.33 [m], with an average error improvement close to 50%). Again, the KW-NN methods perform better: the error ranges from 2.86 [m] and 2.70 [m] to 1.12 [m] for K = 2 and K = 4 with an average improvement of 55%. In the same way the K-NN and the WK-NN methods perform better with respect to the NN one. If 120 RSS acquisition are used the positioning error and the variance are, respectively 2.21 [m] and 2.03 [m]. If the K-NN method is employed the error lowers to 1.83 (improvement of 17%) with a variance equals to 1.48 [m] for the case of K = 2 . Finally, if the Weighted method is used the error ranges from 2.86 [m] (variance equal to 2.33 [m]) to 1.12 [m] with a variance of 0.97 [m], again for the case of K = 2 . The related improvement is close to 60%. Analogous considerations can be made for the K = 4 K-NN and WK-NN cases. In addition, as reported in the next sub-section, usually small values of K yield the best results. This indicates that using only the NN variant is not enough (some of the useful information has been ignored), but too many nearest neighbors could decrease the accuracy of the estimator, since some of them could be too far from the estimated points. The weighted K-NN variant slightly improves the accuracy of estimation. Last considerations that arise from the comparison of the two tables are related to the algorithm robustness and consistency. When the amount of data is significant (i.e., more than 10 RSS acquisitions) the performances of the method, independently from the device, are quite robust. This can be well-understood if the cases of 60 and 120 RSS acquisitions are compared: independently of the variants considered, doubling the RSS acquisitions only lead to an average improvement of 7%. Finally, comparing the performances of the two devices, it is possible to assert that the probabilistic fingerprint, in particular the weighted variant, also shows good consistency. Passing from an old device (as Nokia N 95) to a more recent one (as Samsung Android Galaxy S II) does not cause a significant position error variation. The differences exhibited by the two smartphones for the same method are obviously linked to the diverse hardware employed by the MDs. C. The impact of the number of neighbours The second set of result we have realized is related to evaluate the impact of the number of neighbors used in the positioning process. In more detail, the MD position has been estimated for 156 times, in the same 30 RPs employed in the former experiment, and then averaged. For each positioning, the number of neighbors used is incremented until all of them have been involved in the experiment. Obliviously, due to the nature of the test, the algorithm NN is excluded, since it never uses more than one neighbor.
In addition, this experiment was tested only on the weighted method. This is motivated by the fact that the performance of the K-NN will degrade as the number of neighbors increase noticeably. Indeed, this method simply averages all the RPs which have been chosen as the nearest. For this reason, increasing the neighbors’ number until they reach the totality of the RPs, will only lead the method to compute the same position (the average value of all the RPs), independently of the RSS values sensed by the MD. TABLE 4: Impact of the Neighbors number with 60 RSS acquisitions. Neighbors Number Samsung Galaxy S II Nokia N 95 Error
Var
Error
Var
1
1.89
3.63
2.94
2.65
5
1.37
2.51
1.55
1.30
10
1.44
2.43
1.57
1.32
50
1.51
2.45
1.49
1.34
100
1.49
2.44
1.53
1.33
156
1.50
2.45
1.44
1.35
TABLE 5: Impact of the Neighbors number with 120 RSS acquisitions. Neighbors Number Samsung Galaxy S II Nokia N 95 Error
Var
Error
Var
1
1.95
2.96
2.21
2.03
5
1.22
1.20
1.49
0.91
10
1.19
1.05
1.17
0.89
50
1.21
1.09
1.19
0.88
100
1.23
1.05
1.16
0.89
156
1.19
1.06
1.17
0.91
Table 4 and Table 5 collect the data related to the impact of the neighbors’ number, for the two considered smartphones with 60 and 120 RSS acquisitions, respectively. From both tables it is possible to see that, when few neighbors are considered, the Android device performs better in term of positioning error. In particular, when 5 or less neighbors are employed, Galaxy S II provides an error always lower than the Nokia N 95. When the number of neighbors reaches 156, the two devices error tends to be very close (1.50 [m] and 1.44 [m] for the Galaxy S II and the N95 the for 60 RSS acquisitions case, and 1.19 [m] and 1.17 [m] for the 120 acquisition one). On the contrary, the variance results are lower for the Nokia device. Table 4 shows that when only one neighbor is used the N95 yields a variance equal to 2.65 [m] against 3.63 [m] for the Galaxy S II; when 156 neighbors are used the Nokia device has a variance of 1.35 [m] while Android one provides almost 2.50 [m]. When the Table 5 is considered, analogous considerations can be made: the behaviors of two devices are the same of the former table. Since in Table 5 120 RSS values were used, the values for the positioning errors and
the related variance are slightly lower with respect to Table 4. Summarizing the data reported in these two tables, it is possible to assert that a neighbors’ number equal to 5 is sufficient to ensure a good positioning accuracy in the considered area Similarly to the former experiment the method shows a good robustness with respect to the neighbors employed. This affirmation is motivated by considering the cases when at least 10 neighbors are used: independently of the device, the positioning error do not shows significant improvements. Finally, analogous considerations can be made for what concerns the consistency case. Moving from Nokia N95 to Android Samsung Galaxy S II does not causes great differences in terms of positioning error.
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D. Time Interval between Succesive RSSs Acquisitions In this last subsection the performances of the two devices are compared. For this test, the time interval between successive RSS acquisitions has been varied. The result of the experiment is summarized in Table 6. Again, all the values are reported in [m]. TABLE 6: Performances comparisons of the two devices. Acquisitions Samsung Galaxy S II Nokia N95 (Time interval [s]) Error Var Error Var 2.63 3.15 2.7 2.32 1 2.62 3.33 2.28 1.31 2 (5) 2.45 3.56 2.01 1.44 10 (1) 1.91 3.21 1.48 1.1 12 (5) 1.87 3.19 1.38 1.03 60 (1) 1.64 2.48 1.23 0.66 24 (5) 1.61 2.33 1.25 0.63 120 (1)
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CONCLUSIONS
In this paper a performance comparison of a probabilistic fingerprint-based indoor positioning method over two different smartphone platforms has been presented. This method has been chosen since, from an energy viewpoint, it is more suited to be implemented over Mobile Devices (such as smartphones), where power consumption and energy management are crucial aspects. The work evaluated three metrics: i) position accuracy, ii) the method robustness and iii) the method consistency. Numerical experiments, carried out in a real environment, have shown that the probabilistic fingerprint provides good position accuracy (< 1.20 [m]) for both devices. The method also shows robustness to missing or incomplete data, since doubling the RSS on-line acquisitions (from 60 to 120) only lead to an average improvement of 7% in
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