Accelerometer Assisted Robust Wireless Signal Positioning Based on a Hidden Markov Model Jingbin Liu, Ruizhi Chen, Ling Pei, Wei Chen, Tomi Tenhunen, Heidi Kuusniemi, Tuomo Kröger, Yuwei Chen Department of Navigation and Positioning, Finnish Geodetic Institute, MASALA, Finland
[email protected]
Abstract—Reliable and accurate indoor positioning remains nowadays as one of the greatest challenges in the area of personal navigation and location based services (LBS). This manuscript proposes the methods to improve the accuracy and robustness of indoor positioning using the signal strength measurements of the Wireless Local Area Networks (WLAN), and presents three aspects of contributions. First, the Weibull function is employed to represent the distribution of the signal strength over time. Thus, the impact of the signal strength variation on the fingerprinting database is mitigated, and the fewer samples are required for training the database. Second, the accelerometer sensor is utilized to provide the pedestrian dynamics information, which is used to improve the positioning accuracy and reliability. At last, the hidden Markov models (HMM) based particle filters are performed to compute the positioning solution through combining the signal strength measurements with the pedestrian dynamics information. Through the experimental evaluation of three scenarios, the proposed methods improve significantly the accuracy and robustness of WLAN positioning. With the affordable computational load, the positioning methods can be implemented for indoor navigation on mobile devices of mass customers without extra cost required. Key Words: WLAN Positioning, Particle Filters, Hidden Markov Model, Indoor Navigation, Pedestrian Dead Reckoning
I.
INTRODUCTION
Reliable and accurate indoor positioning remains nowadays as one of the greatest challenges in the area of personal navigation and location based services (LBS). Various handsets for personal navigation are more and more popular, including portable navigation devices (PND) and mobile phones. These handsets usually enable the location capability with an inbuilt GNSS receiver, and they perform well in GNSS friendly scenarios, e.g. the suburban, highways, etc. In GNSS degraded scenarios, e.g. the deep urban areas or indoors, however, the GNSS receivers are subject to severe performance deficiencies in accuracy and availability as the GNSS signals are degraded or blocked. Unfortunately, indoor navigation is desired with higher accuracy and reliability than outdoors from the viewpoint of LBS. So the GNSS-based handsets are not able to present an eligible capability of indoor navigation. Another approach to indoor navigation is based on wireless infrastructures, e.g. the Wireless Local Area Networks (WLAN) and Bluetooth ([1] ~ [6]). The general network infrastructures of WLAN and Bluetooth exist extensively in typical indoor environments nowadays, for example inside
office buildings and airports. The access to the wireless signals is also available in various customer handsets, e.g. the mobile phone. The positioning approach utilizes the measurements of the radio signal strength indication (RSSI) of WLAN or Bluetooth to locate the handsets, and requires almost no extra cost for indoor navigation, thus benefiting the mass customers. Positioning using the RSSI of WLAN or Bluetooth is essentially to infer the location where the signals are received according to the geographical RSSI-position dependency ([1]). The RSSI-position dependency is usually characterized using radio propagation modeling ([1], [2]) or fingerprinting-based techniques ([3]~[5]). The challenge is rendered by high temporal nonstationarity of indoor RSSI measurements, which means the RSSI values observed at same position have large variance over the time as the indoor radio propagation suffers from severe multipath fading effects due to the signal reflection, the refraction diffraction and absorption by the structure and human, etc. ([4], [6]). In the database training phase of location fingerprinting approach, a radio map is built up to characterize the probability distribution of the RSSI received from multiple APs in the geographical region. The probability is traditionally calculated with the samples using a called histogram method or a called kernel method ([3], [7]~[9]). These methods usually require a number, e.g. hundreds or thousands at least, of samples on each reference point (RP) to generate the probability distribution approximating the real. If sampling interval is enough small, the work of training database is facile to accomplish. While, due to the limit of the application programming interface (API), the sampling interval is typically 6-8 seconds on some smart phones such as NOKIA N95 we used ([10]), such that the data collection becomes much too time-consuming. Furthermore, the kernel methods choose usually Gaussian-based kernel functions as an approximation of the distribution density function (PDF) of the RSSI ([3], [8]). Some studies show, however, the RSSI is typically a non-Gaussian, left-skewed, device-dependent, and even multimodal distribution ([11], [12]). The noncoherence in the database causes system errors in positioning phase, and the Weibull function is proposed to address this issue, which is other PDF approximating method than these two existing methods. In the positioning phase, the RSSI values received from the access points (AP) are measured to estimate the location of devices largely using the methods such as nearest neighbor
([1]), probabilistic ([5]) and pattern recognition-based techniques ([3], [15]~[19]) as reviewed in [3]~[6] and [17]. These methods are essentially static positioning or single point positioning in which the location is considered as an isolated point, instead of sequential motion process. The single point positioning does not take historical positioning information into account, and just uses current epoch RSSI measurements to estimate the location. However, taking the motion dynamics of pedestrian users into account, incorporating current RSSI measurements and positioning information from past RSSI measurements can improve significantly the positioning accuracy because the motion dynamics is limited by the walking speed and the spatial coordinates of the pedestrian are correlated in time according to laws of kinematics ([6]). The incorporation of motion dynamics information with RSSI measurements is implemented through Bayesian filters to provide recursive location estimates over time ([18]). Some filters are chosen in previous works according to the nature of the motion and measurement models ([6]). The Kalman filter is applied to compute optimal minimum mean square error (MMSE) position estimates on the assumption that the motion dynamics and RSSI-position dependency follow Gauss-Markov models ([19] ~[22]). The assumption, however, is not real for the pedestrian case ([6]). In contrast to the Kalman filter, particle filter does not impose any assumptions on the motion and measurement models. In the studies of (([23] ~[25]), the particle filters are employed with the motion dynamics represented through empirical transition probabilities of a hidden Markov model (HMM) and the histogram based RSSIposition dependency. The accuracy and effectiveness of the HMM based particle filters are however limited by two aspects of factors. One is the excessive computational complexity so that it is difficult to use these filters on a mobile phone platform; the other is that the transition probabilities are calculated by empirically common motion dynamics, instead of real observations, which limits the positioning accuracy. Recently, some nonparameteric Bayesian filters, such as nonparameteric information filter ([6]), are proposed to perform the positioning estimation based on motion models. In this study, the physical distance between each pair of reference points is calculated taking the topological connectivity into account, and the matrix of the physical distances is created during the offline phase of building up the database. Thereafter, in the online positioning phase, the matrix is used to calculate the transition probability between two states with reduced computational complexity. Thus, the approach is practical on the mobile handset. Further, many modern mobiles, e.g. the NOKIA N95/N97 or the iPhone, are also assembled with an accelerometer sensor for other applications. The onboard accelerometer sensors on mobile phones offer the feasibility of utilizing the acceleration data to sense the motion dynamics of mobile phones which are carried by pedestrian users. Therefore, the sensor data can be employed to augment the WLAN positioning, which will require almost no extra charge. The simplified algorithm of pedestrian dynamics detection is introduced in this work to estimate the motion dynamics which is then fed into the particle filters to improve the accuracy and robustness of navigation solution.
This paper proposes a robust positioning solution using the RSSI measurements of WLAN signals and the accelerometer data if available. The HMM based positioning algorithm is developed, and the performance is evaluated with different options. II.
PEDESTRIAN DYNAMICS DETECTION USING THE ACCELEROMETER
When the pedestrian is walking indoors, the acceleration shows a periodic pattern responding to each step ([26]). The characteristics of the acceleration pattern are dependent on the pedestrian dynamics, e.g. the speed and the pedestrian fashion. Therefore, the accelerometer sensor is largely employed for the user context detection and pedestrian dead reckoning (PDR) ([26] ~ [28]). In this study, we collect the data using the 3-axis accelerometer sensors in the mobile of Nokia N95, and exploit the acceleration data to detect the pedestrian dynamics. The information of pedestrian dynamics is then used to assist the WLAN positioning. A simplified algorithm is developed to estimate the dynamics using the acceleration measurements. 1). Calculate the Euclidean norm of the accelerometer data a(i) from the x, y and z axes measurements for each time sample i as follows:
a(i ) = a x2 (i) + a y2 (i ) + a z2 (i )
(1)
where a x , a y , a z are the acceleration measurements related to x, y and z axes, respectively. The measurements are read through the API in the unit of g, nominally 1g = 9.8 m s 2 . 2). Define a window length, e.g. 1 second, and the variance of the measurements in each window is then calculated. 3). Two thresholds ( Tstatic , Tslowwalkin g ) of the variance are defined to recognize three types of pedestrian dynamics: static, slow walking and fast walking. If
va ≤ Tstatic , the pedestrian is static;
If
Tstatic < va ≤ Tslowwalkin g , the pedestrian is walking
slowly; Otherwise, the pedestrian is fast walking. In fact, the thresholds and the empirical speeds of slow walking and fast walking are trained in the experiments. In this study, the thresholds are selected as Tstatic = 0.008 g 2 and
Tslowwalking = 0.05 g 2 , respectively. And the slow walking is defined as the speed of 1 m/s, and the fast walking is defined as the speed of 1.5 m/s. Fig. 1 shows the example of pedestrian dynamics detection using the accelerometer data. 4). Integrate the speed of each time window to calculate the pedestrian distance during an epoch of WLAN positioning. The
estimated distance can then be used to assist WLAN positioning for improved reliability.
pdf ( x; λ , k ,θ ) =
0.4
Variance of acceleration per second
k −1
x −θ k exp − λ
(2)
where λ is the scale parameter ( λ > 0 ), k is the shape parameter ( k > 0 ), and θ is the shift parameter ( θ 3.5
(7)
θ = Mean − λ * Γ(1 + 1 k )
(8)
where Std, Mean are the standard deviation and the average of the RSSI samples. And the term ( k + 0.15) is an approximation of the expression 2 when 1 Γ(1 + 2 k ) − Γ (1 + 1 k ) 1.5 ≤ k ≤ 2.5 .
[
]
In order to evaluate the effectiveness of the parameters estimated with Eq.(6)~Eq.(8), one long-term testing is performed for about 24 hours. All of the samples then are used to estimate the parameters of the Weibull function, and the
estimated Weibull function is used to compute the probability density as the red line in Fig. 2. However, it is not practical to spend so long time collecting the data at each reference point for training the database. Therefore, every 20 continuous RSSI samples of the long-term data are taken as one group and are used to estimate the parameters of the Weibull function for the purpose of comparison with the probability density derived with all samples. The probability densities are calculated with each estimated Weibull functions, and are plotted as blue lines in Fig. 2. The results show intuitively that the probability density derived with every 20 samples is close to the probability density derived with all of samples. 0.18 0.16
0.12 0.1 0.08
0.8
0.06
0.7
0.04
0.6
0.02 0 55
60
65
70
75 RSSI
80
85
90
95
Fig.2 Probability density estimated using total samples (red line) and each 20 continuous samples (blue line cluster). The RSSI is in the unit of –dBm in this paper. In contrast, when the sampling number is limited, the histogram deviates largely from the real probability distribution as shown in Fig. 3, where the blue line is the histogram of total 20 samples, and the cyan line is the Weibull function of the RSSI probability density, the parameters of which are estimated using the same 20 samples. Weibull distribution: shape= 2.5 scale= 9.275 shift= 67 3
0.12
2.5
Occurrence
In the positioning phase, it uses the probability distribution related to each bin, instead of the probability density. Hence, it makes sense much more to have insights into the probability distribution on each bin. In order to improve the positioning robustness, it requires that the RSSI probability distribution derived with limited samples should have similar pattern with the probability distribution derived with all of plentiful samples. Fig. 4 shows the probability distribution using the Weibull function derived with all samples (red line) and each group of 20 continuous samples (blue line cluster) for the purpose of comparison. In this case, total 10760 samples can form 10741 groups, each of which consists of 20 continuous samples. Out of them, the probability distribution of most groups, except for 870 groups, have similar pattern with the distribution derived with all samples, and the rate of distorted probability distribution is 0.081.
0.1
2
0.08
1.5
0.06
1
0.04
0.5
0.02
0 50
55
60
65
70
75 RSSI
80
85
90
95
0 100
Probability distribution
Probability density
0.14
Fig.3 A typical comparison of the RSSI probability density derived with the histogram and the Weibull function (cyan line, referring to the right axis). The parameters of Weill function are estimated as k = 2.5, λ = 9.275,θ = 67 using 20 samples.
0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 BIN number
6
7
8
9
Fig.4 Probability distribution derived with the Weibull function using all samples (red line) and each group of 20 continuous samples (blue line cluster). Out of total 10741 groups, 870 groups (8.1%) of samples generate different probability distribution pattern with the distribution derived with all samples. Table 1 gives the statistic of the difference of the probability distributions using each group samples and all samples. According to the statistics values, the Weibull generated probability distribution using the 20 samples approximate effectively the probability distribution with more than 80% efficiency (3σ).
Table 1. The statistics of the difference of the probability distribution using all samples and each group of 20 continuous samples BIN number Mean NOKIA Std N95 Max IV.
1 0 0 0
2 0 0.0007 0.0137
3 -0.0219 0.0664 0.2699
4 0.0073 0.0702 0.3846
INDOOR POSITIONING SOLUTION
Based on the created database, the fingerprint approach is extensively applied to locate the device using the signal strength measurements. The Bayesian inference methods, the maximum likelihood estimation (ML) ([9], [33]) and maximum a posteriori (MAP) ([32], [33]), are typically used. These methods are essentially static positioning or single point positioning in which the location is considered as an isolated point. Hence, these methods offer the limited positioning accuracy, and encounter frequently large positioning outlier. This section proposes a robust indoor positioning solution based on the hidden Markov models (HMM) ([34] ~ [35]). A. The hidden Markov model In a regular Markov model, the state is directly visible to the observer. However, in a hidden Markov model, the state is not directly visible, but the output dependent on the state is visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states ([34]). Fig. 5 shows the general architecture of an instantiated first-order hidden Markov model, where the random variable X (t ) is the hidden state at time t, the random variable
5 0.0155 0.0746 0.2698
6 -0.0008 0.0504 0.3169
7 -0.0003 0.0084 0.1445
8 0 0.0005 0.0198
9 0 0 0.0010
The positioning is actually to find out the state sequence (locations) that is most likely to have generated the output sequence (RSSI). Therefore, the Viterbi algorithm is applied to find the solution ([35]). B. Viterbi Algorithm The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states, called the Viterbi path, that results in a sequence of observed events, especially in the context of Markov information sources, and more generally, hidden Markov models ([36]). Fig. 6 demonstrates the processing of finding the Viterbi path, where there are totally N state candidates (1, 2, ···, N) and T observation epochs o(t ), 1 ≤ t ≤ T . The a is the
(
)
ij
transition probability, which means the probability of state transition from one state (i) of previous epoch to another state (j) in current epoch. The transition probability is defined as:
aij = P (qt +1 = j | qt = i ) 1 ≤ i, j ≤ N
(9)
o(t ) is the observation at time t.
Fig. 6 The Viterbi algorithm for finding the most likely state sequence Fig. 5 The general architecture of the hidden Markov model From Fig. 5, it is clear that the conditional probability distribution of the hidden variable X (t ) at time t depends only on the value of the hidden state X (t − 1) at previous epoch t1, and the states at epoch t − 2 and before have no influence, which is called as the Markov property. The values of the observations o(t ) only depend probabilistically on the value of the hidden state X (t ) of the same epoch (both at time t).
The Viterbi algorithm is manipulated through following procedures ([37]): 1). Initialization First, two vectors
δ ,ψ
are defined and initialized using
the measurements of first epoch (o1 ) .
δ1 (i ) = π i bi (o1 ), 1 ≤ i ≤ N ψ 1 (i) = 0
(10)
= P(q1 = i ) , bi (o1 ) is the probability that the measurements (o1 ) are observed on the
where the prior probability π i
assumption that the device locates at the reference point i. 2). Recursion From second epoch later on, the vectors computed recursively. For the epoch follows:
δ ,ψ
are
(t ) , they are calculated as
δ t ( j ) = max[δ t −1 (i)aij ]b j (ot ) 1≤i≤ N
ψ t ( j ) = arg max[δ t −1 (i)aij ] 1≤i≤ N
(11)
where 2 ≤ t ≤ T, 1 ≤ j ≤ N N
∑a
ij
= 1 for all i
j =1
where T is the number of samples.
aij = Pin / M a
3). Termination When all epochs of measurements are processed recursively, the Viterbi path is found out through the backtracking. First, the recursion is terminated through determining the highest probability state of last epoch ( qT* ).
P = max[δ T (i )] *
1≤i≤ N
q = arg max[δ T (i )] * T
with higher accuracy than former methods, which are based on the constant speed consumption of the pedestrian dynamics. Fig. 7 demonstrates the process of state transition from last epoch to current epoch and the state candidates of current epoch within the cyan area. As shown in Fig. 7, the left is related to the case of the accelerometer sensor available. The state of last epoch is denoted as the triangle, and the moving distance (the “Distance” in the Fig. 7) is estimated with the acceleration measurements during the epoch interval. Then the states in the cyan ring area are considered as the state candidate of current epoch with higher probability. The central line of the ring area is the circle with the “Distance” far away from the state of last epoch, and the band width of the ring area depends on the uncertainty of the estimated moving distance. The M a states covered in the ring area are considered as the candidates of the state of current epoch with higher probability ( Pin ), and each state of them is equally probabilistically treated. Therefore, the transition probability for each of the M a candidates is given as:
(12)
1≤i≤ N
(14)
Consequently, the transition probability related to other states (k) is given as:
aik = (1 − Pin ) ( N − M a )
(15)
In this study, Pin = 0.9995 , and hence the solution may be recovered in case either the state of last epoch or the pedestrian distance is wrongly estimated. The selection of Pin depends on the trade-off between the recoverability and the smoothness of the solution.
4). Path (state sequence) backtracking For the epochs from 1 to T-1, the states are determined through the backtracking procedure as follows.
( )
qt* = ψ t +1 qt*+1 , t = T - 1, T - 2, L, 1
(13)
The computational cost of the Viterbi algorithm is proportional to the number of non-zero transitions probabilities times the sequence length. Furthermore, the physical distance between each pair of reference points is calculated taking the topological connectivity into account, and the matrix of the physical distances is created during the offline phase of building up the database. Thereafter, in the online positioning phase, the matrix is used to calculate the transition probability between two states, resulting in the reduced computational complexity. Thus, the approach is practical to be used on the mobile handset. The computation of transition probability is introduced in following subsection C. C. The transition probability The transition probability plays an important role in the solution using the Viterbi algorithm. The more precise the transition probability is, the more reliable the solution is. In this study, the accelerometer sensor is used to provide the information of the moving distance as described in section II, and the transition probability can, therefore, be calculated
Fig. 7 The state transition from last epoch to current epoch and the state candidates of current epoch (Covered in the cyan area) An alternative solution is also presented in case the accelerometer sensor is unavailable on some handsets. The right part of Fig. 7 demonstrates the situation when the accelerometer sensor is unavailable. In this case, the pedestrian distance could not be estimated using the method in the section II. Instead, the moving range is reckoned (the “Range” in the Fig. 7) with the assumption of the pedestrian dynamics, e.g. the indoor pedestrian speed is supposed as 1.2 m/s in this study. Similarly, the M u states covered in the circle area of the “Range” radius are considered as the state candidates of current epoch with higher probability ( Pin ), and each state of them is
equally probabilistically treated. The transition probability related to each state candidate is calculated using the Eq. (14) and Eq.(15) while the M a is replaced with the M u . As shown in Fig. 7, the number
M a is no more than the M u
( M a ≤ M u ). Therefore, the transition probability is refined through using the pedestrian dynamics information provided by the accelerometer sensor, and the positioning robustness is improved consequently. V.
INDOOR POSITIONING EXPERIMENTS AND RESULTS
The positioning accuracy and reliability of proposed methods are evaluated through the field experiments in the third floor of the office building of the Finnish Geodetic Institute (FGI). The building consists of two wings of about 45 meters. Fig. 8 shows the layout of the experimental field. A total of seven APs are installed in the building from first floor to third floor, and used for the positioning experiments as described below. The testing is operated using a Nokia N95 mobile phone, in which the API only allows to scan the RSS with an interval of 6~8 seconds ([10]).
In order to calculate the true position of the mobile user, the time each reference point is passed is record by the data collection application. The actual true position of each epoch is then computed through interpolation using the pedestrian dynamics information. Hence, the true position of the mobile user can be then used to calculate the positioning error. It should be pointed out that the used fingerprinting methods map discretely the positioning solutions into the reference points, which may result in extra positioning error. Therefore, the reported positioning errors related to dynamic experiments (Test #3 ~ #5) are exaggerated in some extent. Positioning error is calculated as the root mean square error ˆ (k ) . (RMSE) between the true position p(k ) and its estimate p The RMSE is computed as:
1 N 2 p(k ) − pˆ (k ) ∑ N k =1
ε=
(15)
where N is the epoch number. In this study, three typical motion scenarios are designed to evaluate the positioning accuracy and robustness of the proposed methods, including one scenario of static positioning and two scenarios of dynamic positioning. A. Static Indoor Positioning The static long-time testing is intended to evaluate the overall positioning accuracy and stability over time. In this study, two sets of overnight static testing are carried out on two days at two different reference points separately, one lasts about 20 hours (Test #1), and the other lasts about 24 hours (Test #2). Table 2 reports the experimental results related to different positioning methods (ML, MAP and HMM based method) and different database training methods. As shown in the Table 2, with the assistance of the accelerometer sensor, the proposed HMM based method offers the positioning accuracy of less than 1 meter no matter that either the Weibull function based database or the histogram based database is employed. If the acceleration data are not used, the positioning error (RMSE) increases to the triple, which is, however, still less than the error of the MAP and ML methods. The proposed Weibull function based database contributes generally to about 10% ~ 20% accuracy improvements for different positioning methods.
Fig. 8 The layout of the third floor of the office building of the Finnish Geodetic Institute As shown in Fig. 8, a total of 32 black dots represent the reference points. Out of them, two reference points situate the coffee area of each wing, and the others are situated along the corridor with a separation of 3 meters each other. During the database training phase, the measurements are collected at two opposite orientations of the corridor to mitigate the impact of the directionality on the probability distribution of the RSSI. For each reference point, a total 20 measurements are collected, thus 10 samples for each direction. Therefore, the data collection spends 2 ~ 3 minutes for each reference point.
Table 2. The comparison of static long-time positioning results of RMSE related to different positioning methods and different database training methods Weibull based database
ML MAP HMM
Test #1 4.09
Test #2 3.90
Histogram based database Test #1 5.52
Test #2 5.78
2.94
2.76
3.77
3.99
Acc
0.67
0.68
0.85
0.97
No Acc
2.26
2.23
2.41
2.46
B. Indoor/outdoor Seamless Positioning Another testing (Test #3) is carried out through combining the WLAN positioning with GPS to implement the integrated indoor/outdoor seamless positioning. When the user enters into the indoor, the GPS signals are blocked, and GPS positioning is not available any more. Thereafter, the WLAN positioning starts up with the prior information of latest GPS positioning. When the mobile user moves indoors, the proposed WLAN positioning methods compute the locations of the user. At last, GPS takes over the positioning job again when the user goes back to the outdoor.
1 0.9 0.8 Cumulative Error Probability
As shown in Fig. 10 and 11, the MAP and HMM based positioning methods are significantly affected by the biased initial positions, and the error level of starting epochs is close to the bias values. The ML method is immune to the biases as it is essentially single point positioning and unrelated with the initial position, and it hence encounters frequently large positioning error. Fortunately, the MAP and HMM based positioning methods can recover quickly from the error solution after a few of epochs. The HMM based method with the assistance of the accelerometer recovers slight slowly, while all of methods perform well without the impact of initial position after 6~7 epochs, which is demonstrated by the results in Table. 3. According to the results of positioning error RMSE, the biased initial positions affect significantly the overall positioning accuracy statistics. While the results of first 7 samples of Test #4 and #5 are removed from the statistics, the positioning errors become consistent with the result of Test #3. 35 HMM+Acc HMM(No Acc) MAP ML
30
Positioning Error (Meter)
The data of dynamic testing are only processed using the Weibull function based database in this study. Fig. 9 shows the experimental results of cumulative error probability distribution related to different positioning methods, which are consistent with the results of static cases. The HMM based method offers highest overall positioning accuracy when the accelerometer data are applied to provide the pedestrian dynamics information, where more than 90% positioning error are no more than 3 meters and maximum positioning error is smallest among all of positioning methods. Secondly, when the acceleration data are not used, the HMM based positioning method performs slightly better than the MAP method. The ML method offers the worst accuracy, and maximum positioning error reaches 18 meters.
position may render wrong positioning results for starting epochs as shown in Fig 10 and 11.
25
20
15
10
0.7 5
0.6 0.5
0
0
20
40
60 80 Epoch Number
0.4
100
120
140
0.3
0.1 0
Fig. 10 The positioning error of different positioning methods related to initial position bias of 30 meters
HMM+Acc HMM(No Acc) MAP ML
0.2
0
2
4
6
8 10 12 14 Positioning Error (Meter)
16
18
20
50 HMM+Acc HMM(No Acc) MAP ML
45
In our experimental environment, the outdoor is at the roof of the second floor, which is almost open sky condition. Therefore, GPS provides initial position of enough accuracy for the WLAN positioning. However, GPS usually encounter degraded performance at the doorway from outdoor to indoor due to the multipath. In order to evaluate the recovery capability of WLAN positioning methods from the biased prior position provided by GPS, the experiments of two simulated scenarios are operated through adding random bias of 30 and 50 meters into GPS positioning solution, referred to as Test #4 and Test #5, separately. Through adding the bias, the prior position is mapped into an error reference point as the initial point in the WLAN positioning approach. The error initial
40 Positioning Error (Meter)
Fig. 9 The cumulative error probability distribution of different positioning methods
35 30 25 20 15 10 5 0
0
20
40
60
80 100 Epoch Number
120
140
160
180
Fig. 11 The positioning error of different positioning methods related to initial position bias of 50 meters
Table 3. Indoor dynamic positioning results of RMSE related to different positioning methods and the effect of biased initial position.
5.97
Weibull based database Test #4 Test #5 Removing All Removing All first 7 first 7 samples samples 5.82 5.90 5.89 6.03
Test #3
ML MAP HMM
3.72
4.88
3.73
7.20
3.88
Acc
1.42
5.37
1.64
7.28
1.50
No Acc
2.73
5.21
2.81
7.22
2.66
[1]
[2]
[3]
[4]
[5]
[6]
VI.
CONCLUSIONS
This manuscript proposes an integrative approach to robust indoor positioning using the RSSI measurements of WLAN, and presents three aspects of contributions:
[7]
1) The Weibull function is employed to represent the distribution of the signal strength over time. Thus, the impact of the signal strength variation on the fingerprinting database is mitigated, and the fewer samples are required for training the database.
[8]
2) The accelerometer sensor is utilized to provide the pedestrian dynamics information for assisting the positioning solution, which is useful for improving the positioning accuracy and reliability.
[10] [11]
3) Through combining the RSSI measurements with the pedestrian dynamics information, the hidden Markov model based particle filters are performed to compute the positioning solution.
[12]
The proposed approach to WLAN positioning consists of an offline database training phase and an online positioning phase. The dedicated design simplifies the computation, such that the computational load of the positioning phase is affordable to the smart phone. Therefore, the methods can be implemented for indoor navigation on mobile devices of mass customers without extra cost required. Through the evaluation of five sets of experiments in three scenarios, the proposed methods improve significantly the accuracy and robustness of WLAN positioning. Generally, the Weibull function based database contributes to 10% ~ 20% accuracy improvement compared to the histogram based database. When the accelerometer sensor provides the pedestrian dynamics information available, the positioning error of the HMM based positioning method can be reduced to a half or one third of the error when the acceleration data are not used. The HMM based positioning method presents significantly higher positioning accuracy and robustness than the MAP and ML methods. In the future, the proposed approach will be further optimized, such as the measurement preprocessing and the AP selection, to improve the WLAN positioning. REFERENCES
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