WLAN-Based Local Positioning using Distorted ...

WLAN-Based Local Positioning using Distorted Template Harish Reddy, M.Girish Chandra, Harihara S.G, P. Balamuralidhar, Jaydip Sen, Deepika Arora Embedded Systems Research Group, Tata Consultancy Services, 96, EPIP Industrial Estate, Whitefield Road, Bangalore, INDIA. {h.reddy, m.gchandra, harihara.g, balamurali.p, jaydip.sen, deepika.a}@tcs.com

Abstract— Local positioning, particularly in indoor environments, poses challenges that are not faced by global and terrestrial positioning systems. Many a times, it is cost effective to build these localization schemes on the existing wireless local area networks (WLANs). In that direction, a time-of-arrival (TOA) estimation based on the “distorted template”[1], which is obtained by convolving the clean template with the channel estimate, was proposed in our earlier work. In this paper, the scheme is further examined for different channel estimation techniques. Towards the direction of designing a complete system, the differential time difference of arrival (DTDOA) synchronization scheme is analyzed and based on the analysis, guidelines for positioning the access points is also provided. Keywords- local positioning; time-of-arrival; channel estimation; differential time difference of arrival;

I.

INTRODUCTION

Technologies which allow us to automatically locate people or objects (positioning), or to check that another person or object is close-by (proximity detection) can enable many new applications. Often the applications are only relevant to a confined local area and thus local positioning is important. A wide variety of technologies are available to deploy local positioning systems-like optical, ultrasound, radio frequency (RF) [2]. In recent times, wireless network systems (with their ability to support mobility) are widely deployed to provide different services. It has been recognized that the location awareness is a cornerstone for future wireless network systems and also to provide context awareness for Ubiquitous Computing [2]. Thus, RF based indoor location built on the existing wireless infrastructures can provide cost-effective implementations. Indoor positioning requires high accuracy positioning (better than one meter) in harsh multipath environments and it is also required to track fast-moving objects or people [2]. Solutions based on Global Positioning System (GPS) or terrestrial cellular systems do not provide the required

accuracy. There is a possibility to arrive at localization systems based on IEEE 802.11a/b/g WLANs. The systems can be based on received signal strength indication (RSSI), fingerprinting or/and time measurements. A good number of ideas and proposals are available in the existing literature and the area is still quite active as there are possibilities to come out with better solutions for the systems. In our research on local positioning, TOA or Time Difference of Arrival (TDOA) is chosen as the basis as they avoid having an elaborate database of empirical measurements or simulated signal strengths. Furthermore, the task of imitating or manipulating TOA/TDOA on the scale of a few tens or hundreds of nanoseconds is substantially harder and thus brings an inherent security [2]. The report [3] succinctly captures our research efforts. The ultimate goal of our research is to design and implement an improved and cost-effective local positioning system. It is well known that the time measurements between the unknown position of mobile terminal (MT) and the fixed positions access points (APs) or base stations (BSs) are converted to distance measurements and these are used in the process of multilateration to evaluate the position coordinates. In TOA, we require the knowledge of transmitting time of MT (through time stamping, say) and synchronization of the clocks of MT and the BSs. It is possible to omit the start time measurement by introducing an additional BS at a known position and measuring the TDOA at the receivers of a signal transmitted by the MT. In TDOA we still need synchronization between the receivers, which can be further eliminated by using DTDOA [4], [5], [6]. In designing a time-based localization system, it is necessary to consider three main issues [3]: (1) Base-station geometry and synchronization issues (2) Time of arrival estimation (3) Algorithm for multilateration. In our previous paper [1], we concentrated on the TOA estimation relevant to IEEE 802.11a WLAN and proposed a novel method, referred as “distorted template” (a carry over from the “dirty template” concept of [7]). The technique utilizes the estimated channel to distort the template of the long training symbols (LTS) of the IEEE 802.11a frame (see [8], [9] for the frame structure), before carrying out the correlation. As shown in [1], the technique provides considerable improvement over the conventional correlation-based technique.

Since channel estimation is involved in the distorted template method, it is of interest to examine this issue under different conditions like additive white Gaussian noise (AWGN), dominant line-of-sight (DLOS), etc. Apart from providing results in this direction, this paper extends the analysis of DTDOA provided in [4], [5], [6]. The paper is organized as follows: in Part II, the distorted template method is briefly captured. Part III provides good amount of simulation results related TOA estimation, including those relevant to using interpolation to evaluate high-resolution correlation. Part IV deals with the issues related to DTDOA; couple of comments on implementing it in the IEEE 802.11x WLAN systems are also given. Conclusions are given in Part V. II.

DISTORTED TEMPLATE METHOD OF TIME-OFARRIVAL ESTIMATION

Once the base-station geometry and synchronization issues are decided upon, the time of arrival estimation is to be done very accurately, as even one nanosecond error translates into a distance error of 30 cm. In indoor scenarios, multipath and non line-of-sight (NLOS) conditions pose real challenge in the time estimation. This is particularly prevalent in narrow band systems as discussed in [2], where it is brought out that accuracy well inside the coverage area is dominated by multipath. In [1], we have proposed the distorted template based time estimation (Figure 8) with the emphasis on using the existing WLAN infrastructure. Though the method is tailored for IEEE 802.11g transmission modes, it can be utilized in various other communication systems where there is a known sequence (such as training or preamble sequence) in the transmit frame. Similar to [1] we restrict our attention to IEEE 802.11a set up in this paper; some results related to IEEE 802.11b systems are available in [3]. In the distorted template method, an initial estimate of TOA (coarse timing synchronization) is carried out using the short training symbols (STSs). See [8], [9] for necessary details regarding the IEEE 802.11a frame structure. Then, LTS are used for the next stage of computations. The advantage with LTS is that we can take care of frequency offset by correcting it through the estimated value of offset. Further, with LTS, the channel estimation available during that period can be utilized for getting an estimate of the distorted version of the LTS (distorted template); utilizing this can lead to better correlation. Since we cannot be certain about the start of the channel impulse response (CIR), we hypothesize different candidate impulse responses of the same length, each of them include the maximum estimated path. These candidates (corresponding to different hypothesis) are convolved with the clean LTS template to obtain corresponding distorted template. This distorted template is then correlated with the received signal. The template that results in the largest correlation peak is assumed to be the true hypothesis. The position of the

maximum path in the chosen hypothesis is used as an indication of the offset between the initial time of arrival estimate and the true estimate. This offset is subtracted from the initial time of arrival estimation to obtain the refined estimate. Elaborate simulation studies carried out suggested that the proposed scheme exhibits an improvement over the conventional correlation technique for an indoor office channel scenario (see [1] and [3]). III.

SOME TOA-RELATED RESULTS AND DISCUSSION

In our simulations, an 802.11a packet is transmitted which consists of the STS, LTS and the signal field. The data portion is not transmitted as it does not affect the TOA estimation performance. Since IEEE 802.11a systems can be deployed in a wide range of environments, such as offices, industrial buildings, exhibition halls or home environments, different channel models are specified for different environments (see [10],[11]). These channel models are named as A, B, C, D and E and each has specific power delay profile; model A corresponds to typical office environment with NLOS condition. For simulation, channels are modeled with tapped delay lines, where each tap suffers independent Rayleigh or Rician fading with a mean corresponding to an exponentially decaying average delay profile [10]. The intricacies of channel simulation as elaborated in Chapter 14 of [12] are taken into consideration. Further, to simulate a more realistic situation, we also introduced subsampling offset in the received signal. This was achieved by oversampling the transmitted signal by a factor of 100, after which a random number between 1-to-100 was chosen as the signal starting point. The oversampled signal is downsampled (by a factor of 100) starting from the chosen point. In all cases, we have also used simulated frame synchronization, again to consider realistic operation. In the distorted template method outlined earlier, the channel estimation was based on the traditional Fast Fourier Transform (FFT). We have examined channel estimation techniques based on the Least Mean Square (LMS) adaptive algorithm [13], and Minimum Mean Square Error (MMSE) given in [14]. The TOA performance with different channel estimation techniques are compared in Figures 1, 3 and 4. The performance is given in terms of the percentage of times the error is less than a specified value, in other words, we use the cumulative distribution function (CDF). The figures are based on 10 4 simulations and a signal-to-noise ratio (SNR) of 10 dB. Similar performance is also observed for different SNRs like 15 dB and 20 dB. While comparing the results, we have also considered three additional cases: (1) Performance when there is perfect channel information (PCI) available to the receiver (2) An heuristic method referred to as x-corr1 in the figures. The idea behind this scheme is the observation that because of multipath, especially in an indoor environment, the estimated TOA is more often than not is delayed from the true TOA. Therefore, if we take this into account the performance should improve compared to correlation. If distorted template is to function as expected it should be perform better than this heuristic scheme, hence this scheme can be used to validate the

performance of distorted template scheme and (3) Virtual Multipath (VM) given in [15]. In Figure 1, the CDFs of the distorted template scheme with different channel estimation are compared with each other and correlation method in typical indoor environment (channel A). The corresponding histogram is given in Figure 2. From the figures it is clear that all the estimation schemes perform better than correlation method. We can also note that the performance of distorted template using PCI is better than the other channel estimation schemes as expected. Also, the CDF

concentrated around zero, as a result the mean error of the TOA estimate is closer to zero compared to correlation which has a positive bias. This is especially useful when multiple TOA measurements are performed (the relevant results are already presented in [1]). Figure 3 shows the CDFs of the TOA error in an environment with DLOS condition. For the DLOS case the channel taps were generated using the model for indoor environment and the channel tap values of the first tap and the maximum tap were swapped. In the DLOS case, we notice that the performance of the LMS and FFT is still similar, whereas the performance of MMSE is inferior to all but the heuristic method. From Figures 1and 3 it is clear that distorted template based scheme provides consistent results in the both indoor and DLOS conditions. In other words, in conditions where both DLOS and NLOS conditions occur in the same environment because of movement of people and objects distorted template will give consistent TOA estimation.

Figure 1. CDF Comparison in Indoor Office Channel

Figure 3. CDF Comparison in DLOS Condition

Figure 2. Histogram Comparison in Indoor Office Channel

of LMS and FFT based distorted template is similar, so are for the MMSE and PCI. The reason that MMSE and PCI are similar in this case is because the channel values used in obtaining the covariance matrix required in MMSE method matches well with the channel seen during the simulation. If the channel values are different during the computation of the covariance matrix and simulation we expect the channel estimation to be inaccurate and hence the performance of distorted template using MMSE to be inferior. Also from Figure 2, we can see that the estimates of distorted template is

Figure 4. CDF Comparison in AWGN Channel

We compare the performance of the above schemes in AWGN channel. The idea behind simulating in AWGN is to understand the best possible TOA estimation that can be

achieved. The comparison is shown in Figure 4; the results obtained by the correlation and PCI overlap, whereas the performances of LMS and FFT schemes are the worst. This is because channel estimates obtained are not an impulse but it has some energy in the taps other than the LOS path. However, it is clear from the results that if the channel estimates are improved we will see results similar to correlation for the case of AWGN. As far as the comparison with the VM method is concerned, the performance of the distorted template is superior to VM. Also, the performance of VM is only comparable to the heuristic based scheme. It is well known that higher sampling or high-resolution correlation is a useful thing to adopt for time estimation. The latter can be implemented by interpolating the correlated signal (correlation is between the received signal and the template). The interpolation can also be implemented using the FFT as suggested in [16]. In our simulations, the interpolation was performed in MATLAB using the “interp1” function. Figures 5and 6 shows the CDF of TOA estimate using interpolation for the conventional correlation in AWGN and indoor office environment respectively.

Figure 6. CDF and TOA Estimation in Indoor Office Channel with Different Oversampling Factors

IV. A MATHEMATICAL LOOK AT DTDOA CONSIDERING SAMPLING AND MULTIPATH ERRORS As mentioned earlier, time measurements are carried out between the MT and the fixed BSs. The positions of BSs need to be carefully selected (issue related to base-station geometry), which is brought out in this section. Another important issue in the localization system is that of synchronization and we have adopted DTDOA for synchronization.

Figure 5. CDF and TOA Estimation in AWGN with Different Oversampling Factors

Interpolation will help in approximating the continuous correlated signal with greater resolution.As a result if the correlation peak corresponds to the true TOA as in the case of AWGN, TOA estimate is improved. However, in a multipath channel the peak of the continuous correlated signal does not correspond to the true TOA. Moreover it is biased depending on the channel taps. In other words, if the multipath taps are such that the second path has equal or higher magnitude than the first path the peak of the continuous correlated signal is delayed or moved further from the true peak. This results in an estimate worse than the correlation at a lower sampling rate. As a result, the resolution of TOA estimate in multipath channels does not increase by this simple high-resolution correlation.

In the DTDOA scheme proposed in [4], [5], [6], there are two kinds of base stations: a master base station (MBS) and three or more slave base stations (SBS). The MBS initiates and coordinates the localization process. Every BS has a link (wired or wireless for communication purpose and not for synchronization) to a host-PC, which collects all the measured time stamps and performs additional calculations/processing to estimate the position. In [5], a mathematical analysis is provided for the system. In certain applications, it is more suitable if MT initiates the localization procedure. In this paper, we provide the necessary mathematical equations for the MT initiated synchronization. This is depicted in Figure 7. Additionally, we extend the analysis provided in [5] by incorporating errors introduced due to finite sampling intervals and multipath. After establishing the network with all involved components including the MT, let the MT initiate the measurement procedure by transmitting the echo-request command at time t start . This signal arrives after the individual propagation delay τ MZ i at the ith BS at the time

t1Z i = t start + τ

i offset

t1Z i (Phase 1):

+ τ MZi + ς MZi + γ MZi

Since the clocks of the BSs are not synchronized,

(1)

τ

i offset

represents an individual unknown offset of the clock in each BS; ς MZ i and γ MZ i are the errors due to finite sampling interval and multipath between the MT and the ith BS

respectively. Afterwards, the MBS (station Z 0 ) transmits the echo-response signal with a certain internal delay τ F and this

t 2 Z i (Phase 2):

signal arrives at the ith BS at the time

i t 2 Z i = t start + τ offset + τ MZ 0 + ς MZ 0 + γ MZ 0

(2)

+ τ F + τ Z0Zi + ς Z0Zi + γ Z0Zi

τZ Z

introducing additional individual propagation delays

0 i

between the MBS and BSs together with individual errors. The time difference ∆t i between receiving the echo-request and the echo-response at the time measuring stations Z i are:

∆ti = t2 Z i − t1Z i = τ MZ 0 + ς MZ 0 + γ MZ 0 + τ F + τ Z 0 Z i

(3)

+ ς Z 0 Z i + γ Z 0 Z i − τ MZ i − ς MZ i − γ MZ i

assured between MT and BSs. This can be achieved for instance by placing the BSs close to the ceiling. Thus, it is clear that with an appropriate positioning of the BS we can significantly reduce the errors that occur due to additional transmissions required for synchronization. The DTDOA scheme can be implemented for locating the special purpose tags in the case of 802.11x based systems by using request to send (RTS) for echo-request and clear to send (CTS) for echo-response. Another option is to use packets with zero byte Medium Access Control (MAC) payloads as the echo-request and the corresponding acknowledgement as the echo-response. For data transmitting stations like laptops and personal digital assistants the data packets and the corresponding acknowledgments transmitted between the station and the access point can be used for estimating the TDOA. Additional details are available in [3].

The difference of the arrival times ∆t ij at time measuring

V. CONCLUSIONS

stations Z i and Z j can be calculated as:

∆t ij = ∆t i − ∆t j = τ Z 0 Z i + ς Z 0 Z i + γ Z 0 Z i − τ MZ i − ς MZ i

(4)

− γ MZ j − τ Z 0 Z j − ς Z 0 Z j − γ Z 0 Z j + τ MZ j + ς MZ j + γ MZ j

The path differences ∆d ij from the mobile to the two measurement stations are given by

(

∆d ij = c ⋅ τ MZi − τ MZ j

)

(5)

and

τ MZ − τ MZ = −∆t ij + (τ Z Z − τ Z Z ) + {ς Z Z + γ Z Z − i

0 i

j

0

0 i

j

0 i

(6)

ς MZ − γ MZ − ς Z Z − γ Z Z + ς MZ + γ MZ } i

0

i

0

j

j

j

From the analysis it is to be noted that

j

τZ Z

0 i

and

τZ Z 0

j

are

known by prior measurement and the scheme does not require τ F , Eqn.6,

ςZ Z

0 i

i t start and τ offset [5].

and

γZ Z

0 i

Going further, suppose in

τ MZ − τ MZ = −∆t ij + (τ Z Z − τ Z Z ) + {ς MZ + γ MZ 0

j

REFERENCES

can be neglected in all BSs. This is

possible by placing the BSs so that the LOS is assured between MBS and SBSs and hence error terms corresponding to multipath can be neglected. Further, the error terms corresponding to the sampling interval can be reduced significantly or eliminated if the distance between the MBS and each of the SBS is such that the time taken by the signal to propagate between these stations is very close to an integer multiple of the sampling interval. Then, i

The extensive simulation study of the distorted template scheme with subsampling offset in the received signal suggests that the scheme performs consistently better than the conventional correlation scheme both in NLOS and DLOS conditions. The improvement in DLOS is less compared to the case of NLOS condition. The study with different channel estimations, including the perfect channel information, suggests that with subsampling offset, multipath poses the limit in the performance. As a further research, it may be useful to examine the equalization of the channel when there is subsampling offset to achieve performance close to AWGN case. Towards the design of the complete localization system, DTDOA is a useful synchronization scheme to adopt and this can be realized on the existing WLAN schemes. The positioning of base stations or access points is important to reduce synchronization errors.

0

i

j

j

j

(7)

[1]

[2]

[3]

[4]

− ς MZi − γ MZi } which shows synchronization error is given by

ε sync = {ς MZ + γ MZ − ς MZ − γ MZ } j

j

i

i

(8)

From Eqn.8 it is clear that that the synchronization errors introduced depends on the BSs relative positions. The error terms corresponding to multipath can be eliminated or reduced to a large extent if the BSs are placed in such that LOS is

[5]

[6]

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Figure 7. DTDOA Scheme. Candidate Selection (Hypothesis)

r(n)

Initial TOA Estimation

CIR Estimator

Candidate IR

LTS Clean Template

Correlator and Maximum Selection

Hypothesis Selection and Offset Estimation

For Correcting Initial TOA Estimation

Figure 8. Block Diagram of the Distroted Template TOA Scheme.