978-1-4244-5743-4/10/$26.00 ©2010 IEEE
`
`Abstract—Due to their light weight, low power, and practically
`unlimited identification capacity, radio frequency identification
`(RFID) tags and associated devices offer distinctive advantages
`and are widely recognized for their promising potential
`in
`context-aware computing; by tagging objects with RFID tags,
`the environment can be sensed in a cost- and energy-efficient
`means. However, a prerequisite to fully realizing the potential is
`accurate localization of RFID tags, which will enable and enhance
`a wide range of applications. In this paper we show how to exploit
`the phase difference between two or more receiving antennas to
`compute accurate localization. Phase difference based localization
`has better accuracy, robustness and sensitivity when integrated
`with other measurements compared to the currently popular
`technique of localization using received signal strength. Using
`a software-defined radio setup, we show experimental results
`that support accurate localization of RFID tags and activity
`recognition based on phase difference.
`Index Terms—RFID localization, phase difference, maximum
`likelihood estimation, software-defined radio.
`
`I. INTRODUCTION
`With the integration of computing into everyday objects
`and activities, ubiquitous computing has become part of our
`day to day lives. Due to the mobility and dynamic nature
`of the communication structure as well as the physical en-
`vironment, ubiquitous computing has unique challenges and
`presents unprecedented opportunities [1], making context-
`aware computing a new paradigm. In this emerging context-
`aware computing,
`the applications adapt not only to the
`computing and communication constraints and resources, but
`also to the contextual information, such as the objects in
`the surroundings and people and activities in the vicinity,
`and even emotional and other states of the user [1]. To
`realize these potential improvements and make the context-
`aware applications cost-effective, the systems must be able to
`“sense” the environment effectively, with low energy and low
`cost [22], [21]. While traditional approaches such as vision-
`sensor and active sensor based methods are obvious choices
`for object recognition and localization [17], realization of a
`robust and cost-effective system based on these sensors has
`yet to be implemented after several decades of research.1
`Recent deployment of radio frequency identification (RFID)
`technology for efficient asset tracking and management has
`made RFID tags and associated devices widely available with
`low cost and low energy usage. For example, there are active
`
`1This does not imply that computer vision does not make any progress; on
`the contrary, computer vision has made numerous important breakthroughs.
`
`89
`IEEE RFID 2010
`
`Accurate Localization of RFID Tags Using Phase
`Difference
`
`Cory Hekimian-Williams, Brandon Grant, Xiuwen Liu, Zhenghao Zhang, and Piyush Kumar
`Department of Computer Science, Florida State University, Tallahassee, FL 32306
`{hekimian,bgrant,liux,zzhang,piyush}@cs.fsu.edu
`
`RFID tags that typically last for five to seven years with
`a compact battery as a reliable wireless signal transmitter;
`obviously passive RFID tags have practically no lifetime limit.
`Clearly RFID tags, at a coarser level, provide a cost-effective
`and energy-efficient way of solving the environment sensing
`problem. One straightforward solution is to attach one or more
`RFID tags to each object of interest in the environment. As
`RFID tags have a limited range of readability, by reading all
`the tags in the proximity, using a reader or similar device, a
`computer can approximate its environment based on the sensed
`objects. Additionally, a unique advantage of RFID technology
`over vision and other sensor based methods is that RFID tags
`do not require line of sight in order to be “seen” and thus avoid
`problems associated with occlusion. Because of the unique
`and strategic advantages of RFID tags, they have been heavily
`investigated for numerous applications (e.g. [8], [17], [3], [16],
`[9], [15]).
`While coarse-grained localization, that is, whether an object
`is present or absent in the proximity, is sufficient for many
`applications, a large number of applications will benefit from
`accurate location information of objects. For example, in a
`smart house setting, a low-cost solution of knowing precisely
`where people are and what objects are close to them will
`enable optimization of user interfaces and energy utilization
`and enhanced convenience. In addition, it is often important to
`track the motion of people/objects so that dynamic activities
`can be recognized and modeled. These applications have
`motivated numerous localization schemes and systems for
`RFID devices (see [5], [27] for recent reviews). Even though
`there are other schemes for localization such as using WiFi
`devices, WiFi devices are much larger in size and have much
`more strict power requirements, which makes RFID tags the
`most attractive choice for numerous applications.
`In this paper, to achieve a fine-grained localization, we
`exploit the phase difference of the received signals at different
`antennas. While the received signal strength can attenuate
`quickly and therefore may lead to significant estimation errors
`of the location,
`the phase difference, on the other hand,
`can be estimated much more reliably as long as the signal-
`to-noise ratio is not too small. A unique advantage of the
`proposed phase difference method is that by measuring the
`phase difference between pulses within the same burst, one
`can estimate the motion of the object, thus making it feasible
`to monitor human activities at natural speeds. For example,
`our experiments suggest that we can reliably measure phase
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`RFC - Exhibit 1019
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`90
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`difference within 0.57◦ (see Figs. 6 and 7). Another advantage
`of phase difference is that it can be combined with received-
`signal-strength-based scene analysis methods to improve the
`localization accuracy by using phase difference to estimate the
`local distance to reference tags.
`To evaluate the effectiveness of phase difference for local-
`ization, we set up a plot study system that consists of active
`RFID tags, Universal Software Radio Peripheral (USRP) as
`receivers, and a pan-tilt unit to accurately place tags for various
`controlled experiments. Note that the model and the phase
`difference estimation methods apply to passive RFID tags in
`a similar manner2; here we limit our scope to active RFID
`tags, mainly so that our experiments are easy to replicate.
`The initial results we have are encouraging even though more
`localization experiments under real-world settings need to be
`further investigated.
`The rest of the paper is organized as follows. Section II
`outlines the general localization problem and then reviews the
`related work on localization using RFID technology in the
`given framework by categorizing them based on several crite-
`ria. In Section III we describe the phase difference model and
`Section IV presents algorithms for phase difference estimation.
`Section V presents experimental results on localization and
`motion estimation and modeling. Section VI concludes the
`paper with a summary and discussion.
`
`II. RELATED WORK
`The most general setup for RFID localization can be posted
`in a statistical inference framework [6], [14]. We represent
`the region of interest as a scene that consists of K RFID
`tags (wireless signal
`transmitters), whose configuration at
`time t is given by the location in the three dimensional
`space, the orientation of the transmitter’s antenna, and the
`power level3; and N receivers, whose configuration is given
`similarly. Given a number of measurements between the tags
`and the receivers,
`the localization problem is to estimate
`the probability distribution of the location of the tags and
`receivers. Note that even though the localization algorithms
`developed for wireless ad-hoc networks and in particular,
`wireless sensor networks [14], can,
`in theory, be applied
`to localization using RFID technology, due to the unique
`characteristics of RFID technology, for example, no or very
`limited computation capabilities available on the tags,
`the
`potential large number of tags, and typical indoor operating
`environments; localization algorithms specific to RFIDs should
`be developed and studied [4].
`The existing localization methods can be categorized based
`on 1) the constraints (i.e., range-free (based on connectivity
`information) or continuous measurements (such as received
`signal strength)), 2) the temporal nature of locations of tags
`and receivers (e.g., anchor-free or with reference tags or
`receivers at fixed locations), 3) and the statistical inference
`
`2For example, we can use one RFID reader to power and initiate wireless
`communications from passive tags.
`3The power level of an active RFID tag is constant; for a passive tag, it
`can be changed by changing the power level of the reader.
`
`algorithm given the constraints. In the given setting, it is
`clear that range-free localization methods can be seen as a
`special case of using received signal strength, where only
`binary values of received signal strengths are available through
`reachability.
`Before we summarize existing methods and systems for
`localization using RFID technology, we stress the significant
`differences between the results based only on computer simu-
`lations and the results based on physical system measurements.
`While RFID tags and readers are widely available, setting
`up an experimental system is not a straightforward task, as
`capturing wireless signals is full of challenges [23]. To avoid
`difficulties associated with prototyping, simulation is often
`used in various localization studies. For example, Wang et
`al. [20] propose an active scheme and passive scheme for
`RFID localization and provide supporting evidence through
`simulation in Matlab; Zhang et al. [25] propose the use of
`direction estimation for two dimensional localization; while
`they propose to use the phase difference to estimate the
`direction of arrival but they provide only simulation results.
`Bouet and Pujolle [4] use connectivity constraints through
`detectability of tags of mobile readers. While simulation
`results can be used to verify principles and theoretical aspects
`of localization and other methods, they are not sufficient to
`evaluate RFID localization performance as the wireless signals
`are affected by many other factors. Therefore, localization
`accuracy comparison between methods based on physical
`system measurements and methods based on simulation results
`(e.g. [4]) should be interpreted carefully.
`Due to the difficulties of capturing and processing RFID
`communications, localization systems commonly rely on avail-
`able wireless measurements at
`the receivers (e.g., RFID
`readers) such as received signal strength (RSS) (e.g., [11],
`[13]).4 These RSS measurements can be binarized using some
`hardware or software threshold, resulting in binary readabil-
`ity/reachability values, which can be used as connectivity
`constraints in range-free localization systems. When the trans-
`mitting power of the transmitters can be dynamically changed,
`one can obtain a multi-level approximation of the range using
`multiple readability values [13]. This can be interpreted as an
`intermediate range representation between continuous values
`and range-free binary values. These measurements lead to
`constraints on the location and the orientation of tags as well
`as on the readers, which are then used by a statistical inference
`algorithm for localization. The localization step is often called
`the scene analysis step [5].
`As the measurements and therefore constraints are pairwise
`between transmitters and receivers, they can be used to localize
`either transmitters or receivers using known fixed receivers
`or transmitters (called anchors), or both as in anchor-free
`systems. For example, SpotON [11] is based on RSS measure-
`ments estimated from adjustable sensors and the measurements
`
`4There are other measurements that can be used to estimate the distance,
`such as time difference of arrival [18] and time of arrival; these measurements
`are rarely used in RFID technology as these measurements are difficult and
`expensive to implement.
`
`

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`91
`
`are used to estimate inter-tag distances with improved accuracy
`by calibrating radio signals to reduce the effects of hardware
`variability; as custom-built sensors used in SpotON are both
`transmitters and receivers,
`the system is more similar to
`a wireless ad-hoc network than to an RFID-based system.
`Landmarc [13] localizes RFID tags through comparing profiles
`with a number of reference tags with known locations; in
`this system nine readers with eight different power levels are
`used and a number of reference tags (i.e., tags with fixed and
`known location) are used for localization. To localize a tag, its
`estimated signal strengths from all the readers are compared
`to the corresponding measurements of reference tags. The
`estimated tag location is given by a weighted average of the k-
`nearest neighbors. The system is robust to some environmental
`factors as the reference and the unknown tags are subject to
`the same conditions; however, it is sensitive to tag orientation
`as the reference tags and the unknown tag can be oriented
`differently, specially when the tag is used to track moving ob-
`jects. VIRE [26] uses the same localization method as in [13]
`and improves the efficiency of Landmarc by introducing a
`proximity map so that only tags in the neighboring areas need
`to be compared, rather than all the tags as in [13]. Zhang et
`al. [24] improves the localization accuracy of [13] by modeling
`the noise so that dissimilarity among tags is reduced for more
`reliable nearest neighbor matching and estimation. While the K
`nearest-neighbor estimation is commonly used as the inference
`algorithm, statistical inference algorithms are also used. For
`example, Bekkali et al. [2] propose to use Kalman filtering to
`estimate locations of unknown tags based on multilateration
`to the reference tags using two mobile RFID readers. A more
`general statistical inference framework is to use the Bayesian
`network [12] to estimate the locations and even orientation of
`tags and readers.
`In this paper, we study the phase difference for accurate
`localization and motion tracking and activity recognition.
`In contrast to Zhang et al. [25], where phase difference is
`used only in simulations, our phase difference estimation is
`implemented and demonstrated using a prototype system and
`therefore our study is directly relevant to RFID applications
`that rely on localization. Our experiments show the phase
`difference can be estimated with high accuracy and can be
`used for three dimensional positioning. To the best of our
`knowledge, this is the first time that phase differences from
`RFID tags are measured reliably and are used for three
`dimensional positioning, motion estimation and tracking.
`
`III. SYSTEM SETUP AND COMMUNICATION MODEL
`In this paper, we focus on quantitative models of phase
`difference for RFID tags. The phase difference measurements
`are based on software-defined radios due to their flexibility
`in implementing various algorithms. To be more precise in
`presenting our model and algorithms, our formulation is based
`on the following setup we have. Clearly, for a different setup,
`the phase difference estimation algorithm and results should
`be similar even though changes may need to be made. As
`shown in Fig. 1, the system we have consists of RFID tags,
`
`Fig. 1. The system setup (consisting a software-defined radio (USRP), RFID
`tags, and a pan-tilt unit) we have used for accurate manipulation and placement
`of tags for controlled experiments.
`
`a software-defined radio system, and a pan-tilt unit. The
`tags we use are the M100 asset tags from RF Code5. The
`carrier frequency of the tags is 433.92 MHz with typical
`transmission range over 90 meters (sufficient to cover entirely
`typical houses and offices). The tag uses the on-off keying
`(OOK) for communication, as it is simple to implement and
`is energy efficient (to prolong battery life). To meet
`the
`energy efficiency requirement, the signals are transmitted in
`a burst only at almost regular internals6. Using a compact
`battery (Lithium CR2032, which is replaceable), a tag typically
`lasts over seven years. During each burst, a fixed number of
`pulses are transmitted at seemingly the same magnitude with
`predetermined intervals, where we suspect that the lengths of
`the intervals are used to identify the tag. Each pulse is basically
`a sine wave for a short period of time on the carrier frequency.
`To be able to implement various phase difference estima-
`tion algorithms and measure various aspects of the wireless
`communication, we have used software-defined radios for the
`experiments due to their flexibility7. The software-defined
`radios are based on the USRP from Ettus Research LLC8,
`along with software modules and packages from the GNU
`software-defined ratio project9. We have used two RFX400
`daughter boards, where both are configured as receivers. In
`order to estimate phase difference, the two receivers must
`be driven with the same sampling clock; otherwise, even a
`tiny mismatch between the clock will result in a huge phase
`difference. The USRP guarantees that the two channels are
`driven by the same sampling clock. In our system, the daughter
`boards are tuned to 433.92 MHz.
`
`A. Communication Model
`The wireless communication between the tags and the
`USRP unit is a typical wireless communication system and
`
`5Specifications available from http://www.rfcode.com.
`6The intervals are randomly perturbed for collision avoidance.
`7Note the algorithms presented can be implemented in hardware efficiently
`if a hardware implementation is desired.
`8http://www.ettus.com/.
`9Available http://gnuradio.org.
`
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`
`(a)
`
`(b)
`
`Fig. 2. Waveforms received at antennas during a transmission of a burst.
`(a) Estimated magnitudes of the signals received at two antennas (top and
`bottom); (b) Each panel shows the received signals at an antenna, here the
`blue plot shows I(t), and the red one shows Q(t), and the black dashed one
`
`shows the magnitudepI(t)2 + Q(t)2.
`
`(a)
`
`(b)
`
`Fig. 3. Phase difference estimation example for one pulse. (a) The signals at
`two antennas, showing clearly the constant phase shift; (b) The estimated
`probability distribution of the estimated phase differences during a burst;
`here it is estimated using a Parzen window and the standard deviation of
`the distribution is 0.954◦.
`of the phase differences is 0.954◦. For the waveforms at
`433.92 MHz, this corresponds to a localization accuracy of 1.8
`millimeters.10 While the estimated accuracy is under an ideal
`situation, it shows clearly the feasibility of phase difference
`estimation for accurate localization.
`
`IV. MAXIMUM LIKELIHOOD ESTIMATION OF THE PHASE
`DIFFERENCE
`While the straightforward estimation the phase difference is
`often sufficient, for more reliable and accurate estimation in
`360 × 299792458433920000 meter = 0.0018 meter, where 299792458
`
`10Given by 0.954
`is the speed of light (meters/second).
`
`here we follow the model in [19]. Based on our observation,
`the wireless signal from an RFID tag in one pulse can be
`described as A cos(2πfct), where A is the constant magnitude
`and fc is the carrier frequency. At each daughter board,
`the received signal at
`its antenna is amplified and down-
`converted to the baseband. A baseband signal is represented
`by the inphase and quadrature components, denoted as I(t)
`and Q(t), respectively. If the carrier of the tag and the USRP
`are on exactly the same frequency, both I(t) and Q(t) should
`be a constant, depending only on the phase of the carriers.
`However, there will always be a frequency difference between
`the carrier of the tag and the carrier of the USRP due to
`the manufacturing process of the oscillator. Let fr denote the
`frequency tuned to at the receivers. The waveforms at receiver
`1 can be represented as
`I1(t) = A1 cos(2π(fr − fc)t + φ1) + σ1n11,
`Q1(t) = A1 sin(2π(fr − fc)t + φ1) + σ1n12,
`where A1 is the received signal magnitude, φ1 is the initial
`phase difference between the carrier at the tag and the carrier
`at the receiver, the initial carrier phase at the receiver, n11 and
`n12 are Gaussian noise terms of unit variance, and σ1 is the
`noise level. Using similar notations, the waveforms at receiver
`2 can be represented as
`I2(t) = A2 cos(2π(fr − fc)t + φ2) + σ2n21,
`Q2(t) = A2 sin(2π(fr − fc)t + φ2) + σ2n22.
`Wireless signals travel at the speed of light, such that φ1
`and φ2 depend on the lengths of the paths from the tag to the
`receivers. However, the exact values of φ1 and φ2 also depend
`on the initialization process of the hardware, such that they
`cannot be used directly for distance and location estimation.
`Fortunately, the phase difference, i.e., φ1 − φ2, captures the
`difference of the distances of the paths, which can be used for
`location estimation.
`
`(2)
`
`(1)
`
`B. Measured Waveforms and Phase Difference
`To demonstrate that the wireless signals are reliable for
`phase difference estimation, Fig. 2 shows one burst received
`at the two antennas along with a zoomed version showing the
`signals during one pulse. These plots show clearly that the
`signals are robust and allow for reliable phase estimation and
`thus the phase difference estimation.
`The waveforms received at the antennas as given in Eqs.
`(1) and (2) allow a straightforward estimation the phase
`difference. That is, at time t, the phase difference should be
`tan−1(Q1(t)/I1(t)) − tan−1(Q2(t)/I2(t)). Figure 3 shows
`one example of estimated phases during a pulse and a typical
`distribution of estimated phase difference during a burst.
`Figure 3(a) plots I1(t) v.s. Q1(t) (green ’+’) and I2(t) v.s.
`Q2(t) (red ’+’); where the time is encoded by the intensity
`of the colors; it shows clearly the constant phase difference.
`Figure 3(b) shows the probability distribution of the phase
`differences of a stationary tag during one burst; here the
`probability distribution is estimated using the Parzen window
`method [10]. In this typical example, the standard deviation
`
`

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`93
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`(a)
`
`(b)
`
`Phase differences on a surface patch. (a) Top-down view; (b) side
`Fig. 4.
`view to show the distribution in the three dimensional space.
`
`we vary both the pan and tilt of the pan-tilt unit to cover a
`portion in the three dimensional space, which is similar to
`a portion of a sphere. For accurate measurements of phase
`difference, we systematically move the tag; at each location
`when the tag stops moving, we wait until we capture an
`active burst of pulses and then we move the tag to the next
`location. Figure 4 shows the phase difference on the surface;
`Fig. 4(a) gives a two-dimensional view of the surface to show
`the detailed variations and Fig. 4(b) shows a three-dimensional
`view. It is clear that the phase difference varies smoothly,
`depending on the three dimensional location of the tag. In
`other words, the phase difference provides information of the
`tag position in the three dimensional space.
`Figure 5 shows a one-dimensional localization experiment.
`Due to an equipment constraint (as we have only one USRP
`unit with complete configurations), the localization is one
`dimensional. In these particular experiments, we demonstrate
`the localization accuracy based on profiling. Here we fix the
`tilt angle and change the pan from -130◦ to 70◦ with a 25◦ step
`size. For each run, we generate a profile as in [13], i.e., the
`phase differences along the path, and use the phase differences
`
`cases such as phase difference tracking for moving RFID tags,
`one can use the maximum likelihood estimation. One option
`is to estimate the phase for each antenna separately and then
`compute the phase difference. The other option is to directly
`estimate the phase difference. In the first case, suppose we
`have n samples from the first antenna, I1(t1), . . . , I1(tn), and
`Q1(t1), . . . , Q1(tn). As the sampling rate of the channels is
`constant and known, we have ti = i × ∆t, where ∆t is given
`by the sampling rate.
`Under the common assumption that the noise terms are
`statistically independent and follow the Gaussian distribution,
`
`we havecφ1 = arg maxφ1
`
`Qi=n
`Pi=n
`i=1 (P (I1(ti)|φ1) × P (Q1(ti)|φ1)
`i=1 (I1(ti) − A1 cos(∆ω × i + φ1))2
`= arg minφ1
`+(Q1(ti) − A1 sin(∆ω × i + φ1))2,
`(3)
`where ∆ω = 2π(fr−fc)∆t. Here we assume that the original
`waveform is a pulse with a constant amplitude and therefore
`A1 does not depend on i; we utilize the assumption that the
`I1(ti) − A1 cos(∆ω × i + φ1) and Q1(ti) − A1 sin(∆ω ×
`i + φ1) are Gaussian distributed. This leads to a nonlinear
`optimization problem and it can be solved through a gradient
`method by initializing the variables with the mean estimation
`of the variables. For example, A1 can be initialized with the
`average amplitude during the active pulse transmission.
`Note that the joint optimization of φ1 and φ2 can be done by
`
`
`weighting the criterion used in Eq. (3) by σ21 and σ22, which
`can be estimated using the channel signals when no pulses
`are being transmitted. We have implemented the maximum
`likelihood using a nonlinear optimization function in Matlab11.
`In typical waveforms, maximum likelihood estimation gives
`an improved phase difference estimation, even though the
`improvement is not always significant.
`
`V. EXPERIMENTAL RESULTS
`In this section we show the experimental results using the
`system setup outlined in Section II. In these experiments, we
`mount an RFID tag on the pan-tilt unit and set up the USRP
`unit with two receiving antennas tuned to 433.92 MHz; all the
`experiments were carried out in a room (roughly of 3.0m ×
`6.0m × 3.5m) with all the fixtures (desks, chairs, and books
`so on) in the room. While the set up we have may not be
`as realistic as in situations required by some applications, all
`the effects including multiple path, noise, and environment
`factors are intrinsically part of the measurements. Compared to
`simulation only studies (e.g. [20], [25]), our results are directly
`relevant and applicable to localization applications.
`A critical test is whether the phase difference can be esti-
`mated reliably and whether the phase difference is discriminat-
`ing, i.e., whether it changes smoothly when the tag is moved.
`Figure 4 shows one of the experiments that demonstrates these
`important features of the phase difference. In this experiment,
`
`11We
`fminsearch
`used
`http://www.mathworks.com.
`
`function;
`
`the Matlab
`
`is
`
`available
`
`from
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`94
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`distance, they can be used to estimate motion and can then
`be used in human activity recognition. In these experiments,
`we move the mounted tag with a constant pan motion while
`we capture the wireless signals; the moving speed is roughly
`1.3 meters per second, corresponding to a typical human
`walking speed. Note that we do not stop the tag to acquire
`data as in the previous experiments. Here we estimate the
`phase difference using the samples within each pulse; the
`pulses are detected based on a threshold of the magnitude
`above a constant factor of the noise level, that is estimated
`automatically. The plots in Fig. 6(a)-(c) shows the estimated
`phase difference during a burst while the tag is in motion;
`Fig. 6(d) shows the phase difference when the tag is static for
`comparison. These plots show interesting patterns and may
`lead to new and efficient ways of modeling activities. In the
`three examples when the tag is moving, the phase difference
`changes smoothly in all the three cases, but with different
`changing patterns. Additionally, these plots show the phase
`difference can be estimated accurately and reliably even when
`the tags are moving. The results show again the accuracy of
`estimated phase difference and the sensitivity of the phase
`difference relative to the motion.
`For comparison, Fig. 7 shows the received signal strength
`corresponding to the two cases in Fig. 6(a) and (b). While
`received signal strength does also change, it does not show
`as large changes as the phase difference. Additionally, the
`patterns of changes are much similar, compared to the phase
`difference ones. These experiments suggest that phase differ-
`ence would be more effective for activity characterization and
`recognition.
`
`VI. CONCLUSION
`In this paper we exploit the phase difference between two
`receiving antennas for localization. Using a software defined
`radio implementation, we demonstrate that phase difference
`can be estimated reliably for commercially available RFID
`tags and they can be used for localization in three dimensional
`and for motion estimation and tracking. The experiments
`demonstrate clearly the advantages of phase difference for
`accurate localization. The experiments show millimeter accu-
`racy localization is achievable under ideal situations. While
`in more realistic settings, the performance may degrade and
`but we expect the results should be robust. While further
`experiments are needed for complete evaluation, the results
`show clearly the potential usefulness of phase difference. For
`motion estimation and recognition, the phase difference may
`provide a unique method to achieve energy efficient motion
`estimation. Additionally, the phase difference estimation can
`be directly integrated with RSS based methods to improve the
`local estimation or to reduce the number of reference tags
`required. Given all the experiments reported, the next logical
`step is to implement a full localization system using several
`USRP units for three dimensional localization and evaluate the
`accuracy of the approach.
`As the system we have consists of a software-defined radio
`component for its flexibility to set up and test various algo-
`
`(a)
`
`(b)
`
`Fig. 5. One dimensional localization experiments along an arc. Here two
`experiments are shown. (a) Prediction for phase difference; note that the
`absolute value of the phase difference is not essential as each USRP run
`gives a different systematic bias to the phases at the receivers; (b) Prediction
`for average signal strength at the two channels.
`
`as training data. Then we collect test samples by starting from
`-117.5◦ with the same step size. We use the training profile to
`predict the values along the path by fitting the training samples
`to a spline and use the trained spline to predict the values at
`the test samples. To quantify the error between the prediction
`Pn
`and the actual measurements, we define
`i=1(p(i) − a(i))2
`var(a)
`
`,
`
`(4)
`
`1 n
`
`s
`
`e =
`
`where p(i) and a(i) are the predicted and actual values at
`location i, n is the total number of test locations, and var(a)
`is the variance of the actual measurements. It is clear that the
`error given by Eq. (4) is unitless, and scale and translation
`invariant. Figure 5(a) shows two different experiments and
`standard deviation between the predicted and actual phase
`difference values is 0.34◦ and 2.3◦ respectively; the error
`according to Eq. (4) is 0.02 and 0.12 for the top and the bottom
`experiment respectively. These examples show clearly that
`phase difference is a reliable measurement of the difference in
`distances from the antennas to the tag, allowing for millimeter
`accuracy prediction. To compare with received signal strength
`estimation, Fig. 5(b) shows the corresponding plots for the
`average RSS from the antennas. Here the error according
`to Eq. (4) is 0.02 and 0.28 respectively. While both phase
`difference and RSS are reliable with small error, this result
`show that when the signal to noise ratio is lower, the error for
`RSS tends to be larger.
`Figure 6 demonstrates a unique advantage of phase dif-
`ference. As phase differences change with small changes in
`
`

`
`95
`
`(a)
`
`(c)
`
`(b)
`
`(d)
`
`Fig. 6. Three examples ((a)-(c)) of phase differences estimated during pulses within a burst when the tag is moving; for comparison, (d) shows the phase
`difference when the same tag is static.
`
`rithms, one potential issue is the complexity of the algorithms
`when a hardware system needs to be realized. The phase
`difference algorithm can clearly be streamlined and so its
`implementation should not require special parts beyond typical
`digital signal processing components.
`Based on the experimental results, estimated phase differ-
`ences can be used in a number of applications to improve
`the localization accuracy. For example, for searching book
`in library, high localization accuracy is needed to make the
`RFID techniques effective [9]. Combined with other coarser
`level localization, phase difference may provide the millimeter
`localization accuracy when books to be interested are known
`to be an area; this is being investigated further. For robot
`navigation, robots need to sense their environment and require
`accurate localization of obstacles and other objects and esti-
`mated phase difference may achieve the required accuracy that
`is otherwise