Self-Localization in RFID-Tag Information Networks UsingExtended UFIR Filtering

JUAN POMARICO-FRANQUIZ, YURIY S. SHMALIYUniversidad de Guanajuato

Department of Electronics EngineeringPalo Blanco, 36885, Salamanca

MEXICOjuanjose2003@hotmail.com, shmaliy@ugto.mx

SHUNYI ZHAOJiangnan University

Key Lab. Adv. Proc. Contr. for Light IndustryWuxi, JiangsuP. R. CHINA

shunyi@alberta.ca

Abstract: The radio frequency identification (RFID) tags have proved their usefulness for vehicle self-localizationin grid navigation spaces. Each tag can deliver information about the 2D or 3D local surrounding. To use thisinformation, high accuracy in vehicle localization is required. We show that the recently designed extended finiteimpulse response (EFIR) filter meets this need. The EFIR filter produces an unbiased estimate while ignoring thenoise statistics which are often unknown to the engineer. The EFIR filter is tested and a compared to the extendedKalman filter (EKF). Better performance of the EFIR filter is demonstrated.

Key–Words: Extended FIR filter, extended Kalman filter, RFID tag, indoor localization.

1 Introduction

The methods which utilize facilities of the radio fre-quency identification (RFID) tags [1] have gained cur-rency for indoor vehicle (robot) localization in thelast decade. Each tag has its own identification (ID)number corresponding to unique coordinates of loca-tion and may be either active [2] or passive [3, 4].Information describing the surrounding can also beprogrammed in the tag [5] that makes the RFID tag-nested grids highly attractive for industrial and otherneeds. This information, however, may be useful onlyif vehicle localization is provided with high accuracy.The multilateration algorithms based on observationand averaging over some time interval are most widelyused here [6, 7]. Other algorithms [8, 9] can also beemployed, including the directional ones [10, 11] andhybrid structures [1, 9, 12–15].

A common drawback of the multilateration andother “algebraic” algorithms is that noise reductionoften cannot be provided efficiently or otherwise thebias error can be large. The probabilistic particle orMonte Carlo filters were constructed in [16, 17] toshow much better performance. An application ofthe extended Kalman filter (EKF) [18] was shownin [19, 20] and a comparison of the extended, quadra-ture, and particle Kalman filters was recently givenin [21]. A disadvantage of the Kalman filter-based es-timators is that noise is required to be white and itsstatistics and the initial error statistics are known inorder for the EKF to be suboptimal. Otherwise, the

performance of EKF may be poor [22–25].The FIR alternative to the Kalman filter has been

under the development for decades [26–28]. It isknown to be more robust than the Kalman filter underthe unbounded disturbances [29]. It is also lesser sen-sitive to noise and distributions and produces smallerround-off errors owing to averaging. Furthermore,complex optimal FIR (OFIR) structures [26,27] do notdemonstrate essential advantages against simple un-biased FIR (UFIR) ones [30] which ignore the noisestatistics and initial error statistics [23,27]. The differ-ence between the OFIR and UFIR estimates vanishesby large averaging intervals that makes the iterativeUFIR filter [31] highly attractive for applications.

2 RFID Tag-Based Vehicle Localiza-tion

We consider a schematic diagram given in Fig. 1 as-suming that a vehicle travels in direction d and its tra-jectory is controlled by the left and right wheels. Theincremental distances vehicle travels by these wheelsare dL and dR, respectively. The distance between theleft and right wheels is b and the stabilized wheel isnot shown. The vehicle moves in its own planar Carte-sian coordinates (xr, yr) with a center at M(x, y).

It is supposed that the vehicle is equipped witha fiber optic gyroscope (FOG) [32] which providesmeasurements of the pose angle Φ. On a grid RFIDtag-nested floorspace, a vehicle always passes by a

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 286

Figure 1: Two-dimensional schematic geometry of a vehicle travelling between two RFID tags with an angle Φ measuredusing a FOG.

pair of tags A(x1, y1) and B(x2, y2) and the readerinstalled on a vehicle is able to measure the distancesd1 and d2. Because altitudes are generally differentof the points of installation of the reader and tags, theprojections a1 and a2 to the vehicle plane are calcu-lated following Fig. 1b and Fig. 1c, where c1 and c2

are known. From the vehicle odometry, the incremen-tal distance dn and change in heading φn are providedat discrete time index n by

dn =12(dRn + dLn) , (1)

φn = arctandRn − dLn

b∼= 1

b(dRn − dLn) . (2)

The unknown vehicle coordinates xn and yn andheading Φn are obtained by the vehicle kinematicswith equations

f1n = xn = xn−1 + dn cos(

Φn−1 +12φn

),(3)

f2n = yn = yn−1 + dn sin(

Φn−1 +12φn

),(4)

f3n = Φn = Φn−1 + φn , (5)

in which the values xn−1, yn−1, and Φn−1 at timen − 1 are projected to time n by the time-variant in-cremental distances dLn and dRn via (1) and (2).

2.1 Vehicle State-Space Model

We now introduce a state vector xn = [ xn yn Φn ]Tof unknown variables and an input vector un =

[ dLn dRn ]T of incremental distances. The randomcomponents in these values are supposed to be ad-ditive, zero mean, white Gaussian, and uncorrelated.Accordingly, we introduce the state noise vectorwn = [ wxn wyn wΦn ]T and the input noise vectoren = [ eLn eRn ]T . Then equations (3)-(5) suggestthat the vehicle nonlinear state equation is

xn = fn(xn−1,un,wn, en) , (6)

where fn = [ f1n f2n f3n ]T has components given by(3)-(5). The noise sources wn and en are zero mean,E{wn} = 0 and E{en} = 0, have the covariancesQ = E{wnwT

n} and L = E{eneTn} and a property

E{wieTj } = 0 for all i and j.

Following Fig. 1, the measured distances d1n andd2n as well as angle Φn are coupled with unknownstate variables xn, yn, and Φn as

α1n = d1n =√

(y1 − yn)2 + (x1 − xn)2 + c21 ,

(7)

α2n = d2n =√

(y2 − yn)2 + (x2 − xn)2 + c22 ,

(8)α3n = Φn = Φn . (9)

For the observation vector zn =[ z1n z2n z3n ]T , nonlinear function vectorhn(xn) = [α1n α2n α3n ]T , and measurementadditive noise vector vn = [ v1n v2n v3n ], the stateobservation equation can be written as

zn = hn(xn) + vn , (10)

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 287

where noise vn is white Gaussian with zero mean,E{vn} = 0, the covariance R = E{vnvT

n }, and theproperties E{viwT

j } = 0 and E{vieTj } = 0 for all i

and j.

2.2 Expanded State-Space Model

To use EFIR filtering, we expand fn ,fn(xn−1,un,wn, en) as follows:

fn = Fnxn−1 + un + Wnwn + Enen , (11)

where xn = [ xn yn Φn ] is the estimate of xn, un =fn(xn−1,un,0,0)−Fnxn−1 is known and Fn, Wn,and En are Jacobian. Matrix Fn = ∂fn

∂x

∣∣xn−1

can befound to be

Fn =

1 0 −dn sin(Φn−1 + 12φn)

0 1 dn cos(Φn−1 + 12φn)

0 0 1

. (12)

and it is equal to Wn for the model considered. Ma-trix En = ∂fn

∂u

∣∣x−n

can be written as

En =12b

becn + dnesn becn − dnesn

besn − dnecn besn + dnecn

−2 2

, (13)

where ecn = cos(Φ−n + φn

2

)and esn =

sin(Φ−n + φn

2

).

Similarly to (6), hn(xn) can be expanded at n as

hn(xn) = Hnxn + zn , (14)

where zn = hn(x−n )−Hnx−n is known and

Hn =

x−n−x1u1n

y−n−y1

u1n0

x−n−x2u2n

y−n−y2

u2n0

0 0 1

, (15)

where u1n =√

(y1 − y−n )2 + (x1 − x−n )2 + c21 and

u2n =√

(y2 − y−n )2 + (x2 − x−n )2 + c22.

The estimation error is computed as

Pn = E{(xn − xn)(xn − xn)T } . (16)

The extended Kalman filtering (EKF) algorithmdeveloped for this model is listed in Table 1 and EFIRfiltering algorithm is listed in Table 2. The latter re-quires only N and K to start computing and updat-ing iteratively all the matrices via zn and yn [33, 34].Since linear measurement yn is unavailable, we em-ploy the output of the EKF on an interval of first Nopt

points. To run the EKF, we set approximately thenoise covariances and initial errors. To run the EFIRfilter, N = Nopt is found via test measurements as-suming known xn by minimizing (16).

Table 1: Extended Kalman Filtering Algorithm

Input: zn, x0, P0, R, Q, L

1: for n = 1 : M do2: x−n = fn(xn−1,un,0,0)

3: P−n = Fn(Pn−1 + Q)FT

n + EnLETn

4: Kn = P−n HT

n (HnP−n HT

n + Rn)−1

5: xn = x−n + Kn[zn − hn(x−n )]

6: Pn = (I−KnHn)P−n

7: and forOutput: xn

Table 2: Extended UFIR Filtering Algorithm

Input: zn, yn, K, N

1: for n = N − 1 : M do2: m = n−N + 1, s = m + K − 1

3: xs ={

ys , if s < N − 1xs , if s > N − 1

4: Gs = I

5: for l = m + K : n do6: x−l = fl(xl−1,ul,0,0)

7: Gl = [HTl Hl + (FlGl−1FT

l )−1]−1

8: Kl = GlHTl

9: xl = x−l + Kl[zl − hl(x−l )]

10: and for11: xn = xn

12: and forOutput: xn

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 288

3 Mobil robot Localization

In this section, we consider a robot travelling on anindoor grid floorspace. The floorspace is nested withRFID tags which coordinates of locations are saved inrobot memory. Each tag has a circular detection areaswith the detection range r. We suppose that a robothas a reader that is able to measure distances to at leasttwo RFID tags at once. We also assume that the robotis equipped with a FOG to measure the pose angle Φn.The reading region is such that two or more tags areobserved at the same time. An example is a readerwith an elliptical antenna diagram used to detect tagson a floor or ceiling [21].

To test the EFIR and EKF algorithms, all noisesources are supposed to be additive, stationary, zeromean, white Gaussian, and uncorrelated. Accord-ingly, we introduce the estimation error variances σ2

x,σ2

y , and σ2Φ and specify the noise covariance matrix

(7) with the main diagonal diagQ = [ σ2x σ2

y σ2Φ ]

and all other components zeros. For the noise vari-ances σ2

L and σ2R in the input distances dLn and dRn,

we specify (8) with the main diagonal diagL =[ σ2

L σ2R ] and all other components zeros. Finally, for

the measurement noise variances σ2v1, σ2

v2, and σ2v3,

we specify (13) with the main diagonal diagR =[ σ2

v1 σ2v2 σ2

v3 ] and all other components zeros.A robot travels free on a grid floorspace nested

with 35 tags (Fig. 2) without the corrections of itsdeviation from the planned path. In order to learnthe effect of noise upon the estimates, we set realis-tic variances for the noise sources, σL = σR = 1 sm,σv1 = σv2 = 15 sm, and σv3 = 2◦, and require thevariances in the state noise to be σx = σy = 1 sm andσΦ = 0.5◦. To run the EKF, we roughly set the noisecovariances with p 6= 1 as pQ, R/p, and L/p, the ini-tial state with an error of 10%, and allow P0 = 0. Wethen employ the EKF output as linear measurementyn for the EFIR filter at the beginning interval of Npoints.

Employing test reference measurements, we findNopt = 20 by minimizing the MSE (16) by N as

Nopt = arg minN

{trP(N)} . (17)

The robot path was planned to be stepwise asdashed in Fig. 2. In free travelling, noise correctsthe trajectory and we notice that in the ideal case ofp = 1 and exactly known x0 the estimates providedby the EFIR filter and EKF are consistent and fit wellthe actual robot path (not shown).

An analysis of errors sketched in Fig. 3 revealsthe following. Under the ideal conditions of fullyknown model and noise statistics, the EKF slightly

outperforms the EFIR filter. However, it loses an abil-ity of accurate filtering under the more realistic condi-tions implying p 6= 1 and unknown initial state. Fig-ure illustrates this case for p = 5 and error of 10%in the initial state. Table 3 gives average errors com-puted for the EFIR filter with Nopt = 20 and EKF forp set around unity. As can be observed, even relativelysmall errors associated by p = 3 and p = 0.3 make theEKF more noisy. Moreover, the EKF demonstratesdivergence with p < 0.4 that is exhibited in Fig. 4for p = 0.2. Note that divergence can be watched atsome intervals and it may disappear after the tags areswitched out. Namely this effect causes large errors inthe EKF for the coordinate xn with p = 0.3 in Table 3.Overall, the EKF produced unacceptable and rapidlyincreased errors with p > 3 and p < 0.4.

4 Concluding Remarks

One of the powerful tools for industrial and other ap-plications is the recently developed technique calledthe grid RFID tag-nested navigation space. Usinginformation about the surrounding delivered by thetag, a vehicle can fulfil its duties most completely.To reach and use this information efficiently, eachtag must be identified reliably and vehicle localiza-tion provided with high accuracy. We have shownthat recently derived the EFIR filter is more accuratethan the EKF in vehicular localization in RFID tag-nested navigation space under the conditions of notfully known noise covariances and initial state. TheEFIR filter that produces unbiased estimates by itera-tive averaging completely ignores the noise statisticswhich are typically unknown to the engineer. Its al-gorithm has the Kalman form and noise reduction inits output becomes more efficient when N À 1. Al-though higher accuracy and stability of the EFIR fil-ter were demonstrated in a comparison with the EKF,some concern about the environmental effects and realoperation conditions still remains. We work on it nowand plan to report the results un near future.

References:

[1] T. Sanpechuda and L. Kovavisaruch, “A review ofRFID localization: Applications and techniques,” inProc. 5th Int. Conf. Elect. Eng./Electron., Comput.,Telecommun. Inf. Technol., May 2008, pp. 769772.

[2] M. N. Lionel, Y. Liu, Y. C. Lau, and A. P. Patil,“LANDMARC: Indoor location sensing using ac-tive RFID,” Wirel. Netw., vol. 10, pp. 701-710, Nov.2004.

[3] S. Park and S. Hashimoto, “Autonomous MobileRobot Navigation Using Passive RFID in Indoor En-

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 289

Figure 2: EKF and EFIR filtering estimates of robot localization over 5260 points on a grid navigation floorspace nestedwith RFID tags for p = 3, initial state error of 10%, and Nopt = 20. The planned path is dashed and the estimates fit theactual path (not shown).

(a)

2 4

-0.6

-0.4

-0.2

0.2

0.4

0

n × 103

Esti

mati

on

err

or,

m

Coordinate xn EFIR

EKF

1 3

(b)

2 4

-0.6

-0.4

-0.2

0.2

0.4

01

3

Coordinate yn

n × 103

Esti

mati

on

err

or,

m

EKF

EFIR

(c)

2 103

´ 4 103

´

-0.4

-0.2

0.2

0.4

0

n × 103

Heading Fn

Esti

mati

on

err

or,

rad

EKF

EFIR

Figure 3: Typical estimation errors provided by EKF and EFIR filter for the location of a robot travelling free on a gridnavigation floorspace (Fig. 2): (a) coordinate x, (b) coordinate y, and (c) heading angle Φ.

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 290

Table 3: Average Errors (Excluded Nopt = 20 points of Transients) Corresponding to Fig. 2 by EFIR Filter and EKF.

x, sm y, sm Φ, 10−4 radbias σ bias σ bias σ

EFIR -1.470 5.710 -0.465 5.280 -2.166 400.0EKF (p = 3) -5.820 8.520 -5.160 9.960 7.756 493.0EKF (p = 1) -1.440 4.810 -0.477 5.010 4.730 231.0EKF (p = 0.3) 27.48 113.46 -0.281 12.10 6.579 349.0

2 4-2

2

4

6

8

01 3

Coordinate xn

Es

tim

ati

on

err

or,

m

EKF divergenceEFIR divergence

n × 103

Figure 4: Divergence of the EKF with p = 0.2. Divergence in the EFIR/Kalman filter during the first Nopt = 20 points iscaused by the EKF divergence. With n > Nopt, the EFIR filter is stable.

vironment”, IEEE Transactions on Industrial Elec-tronics, vol. 56, pp. 2366–2373 Jul. 2009.

[4] S. S. Saab and Z. S. Nakad, “IEEEA standaloneRFID indoor positioning system using passive tags,”IEEE Trans. on Industr. Electron., vol. 58, May2011.

[5] S. Willis and S. Helal, “RFID information grid forblind navigation and wayfinding,” in Proc. IEEE Int.Symp. on Wearable Computers, 2005, pp. 3437.

[6] A. Smaliagic, and D. Kogan, “Location sensing andprivacy in a context-aware computing environment,”IEEE Wireless Communications, vol. 9, pp. 1017,Oct. 2002.

[7] D.G. Seo and J.M. Lee, “Localization algorithmfor a mobile robot using iGS,” in Proc. 17th WorldCongress The Int. Fed. of Autom. Control, Seoul,Korea, July 6–11, 2008, pp. 742–747.

[8] S. Han, H. Lim, and J. Lee, “An efficient localizationscheme for a differential-driving mobile robot basedon RFID system,” IEEE Trans. Ind. Electron., vol.54, pp. 3362-3369, Dec. 2007.

[9] J. Zhou and J. Shi, “RFID localization algorithmsand applicationsa review,” J. Intell. Manuf., vol. 20,pp. 695-707, Dec. 2009.

[10] Y. Zhang, M. G. Amin, and S. Kaushik, “Localiza-tion and Tracking of Passive RFID Tags Based onDirection Estimation,” Int. Journal of Antennas andPropagation, vol. 2007, art. 17426, pp. 1–9, 2007.

[11] A. Papapostolou and H. Chaouchi, “RFID-assistedindoor localization and the impact of interference on

its performance,” Journal of Network and ComputerApplications, vol. 34, pp. 902913, May 2011.

[12] H. Chae and K. Han, “Combination of RFID andvision for mobile robot localization,” in Proc. IEEEInt. Conf. Intell. Sensors, Sensor Netw. Inf. Process.,2005, pp. 7580.

[13] B.-S. Choi, J.-W. Lee, J.-J. Lee, and K.-T. Park,“A Hierarchical Algorithm for Indoor Mobile RobotLocalization Using RFID Sensor Fusion,” IEEETrans. on Industr. Electron., vol. 58, Jun. 2011.

[14] W. Gueaieb and M. S. Miah, “An intelligent mobilerobot navigation technique using RFID technology,IEEE Trans. Instrum. Meas., vol. 57, pp. 19081917,Sep. 2008.

[15] T. Deyle, H. Nguyen, M. S. Reynolds, and C. C.Kemp, “RFIDguided robots for pervasive automa-tion, Pervasive Comput., vol. 9, pp. 3745, Apr.Jun.2010.

[16] D. Hahnel, W. Burgard, D. Fox, K. Fishkin, andM. Philipose, “Mapping and localization with RFIDtechnology,” in Proc. IEEE Int. Conf on Roboticsand Automation, vol. 1, pp. 1015–1020, 2004.

[17] A. Howard, “Multi-robot simultaneous localizationand mapping using particle filters,” The Int. Journ.of Robotics Research, vol. 25, pp. 1243-1256, Dec.2006.

[18] H. Cox, “On the estimation of state variables and pa-rameters for noisy dynamic systems,” IEEE Trans.Automat.Contr., vol. AC-9, pp. 5–12, Jan. 1964.

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 291

[19] U, Klee, T. Gehrig and J. McDonough, “Kalman fil-ters for time delay of arrival-based source localiza-tion,” EURASIP Journal on Applied Signal Process.,vol. 2006, pp. 1–15, Jan. 2006.

[20] E. DiGiampaolo and F. Martinelli, “A passive UHF-RFID system for the localization of an indoor au-tonomous vehicle,” IEEE Trans. on Industr. Elec-tron., vol. 59, pp, 3961–3970, Oct. 2012.

[21] E. DiGiampaolo and F. Martinelli, “Mobile robot lo-calization using the phase of passive UHF-RFID sig-nals,” IEEE Trans. on Industr. Electron., vol. 61, pp.365–376, Jan. 2014,

[22] B. Gibbs, Advanced Kalman Filtering, Least-Squares and Modeling, New York: Wiley, 2011.

[23] Y. S. Shmaliy, “An iterative Kalman-like algorithmignoring noise and initial conditions,” IEEE Trans.Signal Process., vol. 59, pp. 2465–2473, Jun. 2011.

[24] R. J. Fitzgerald, “Divergence of the Kalman filter,”IEEE Trans. Autom. Control, vol. AC-16, pp. 736–747, Dec. 1971.

[25] F. Daum, “Nonlinear filters: beyond the Kalman fil-ter,” IEEE A&E Syatems Magazine, vol. 20, pp. 57–69, Aug. 2005.

[26] W. H. Kwon and S. Han, Receding Horizon Control:Model Predictive Control for State Models. London:Springer, 2005.

[27] Y. S. Shmaliy, “Linear optimal FIR estimation ofdiscrete time-invariant state-space models,” IEEETrans. Signal Process., vol. 58, pp. 3086–3096, Jun.2010.

[28] A. M. Bruckstein and T. Kailath, “Recursive limitedmemory filtering and scattering theory,” IEEE Trans.Inf. Theory, vol. IT-31, pp. 440–443, May 1985.

[29] A. H. Jazwinski, Stochastic Processes and FilteringTheory, New York: Academic, 1970.

[30] Y. S. Shmaliy, “Unbiased FIR filtering of discretetime polynomial state space models,” IEEE Trans.on Signal Process., vol. 57, pp. 1241–1249, Apr.2009.

[31] Y. S. Shmaliy, “Suboptimal FIR filtering of nonlin-ear models in additive white Gaussian noise,” IEEETrans. Signal Process., vol. 60, pp. 5519–5527, Oct.2012.

[32] K. Komoriya and E. Oyama, “Position estimationof a mobile robot using optical fiber gyroscope,” inProc. IEEE/RSJ/GI Int. Conf. Intell. Robots Syst.,vol. 1, pp. 143-149, 1994.

[33] J. Pomarico-Franquiz, S. H. Khan, and Y. S.Shmaliy, “Combined extended FIR/Kalman filter-ing for indoor robot localization via triangulation”,Measurement, vol. 50, pp. 236–243, Apr. 2014.

[34] J. Pomarico-Franquiz, Y. S. Shmaliy, “Accurate self-localization in RFID tag information grids using FIRfiltering,” IEEE Trans. Industrial Informatics, vol.10, no. 2, pp. 1317–1326, May 2014.

[35] F. Ramirez-Echeverria, A. Sarr, and Y. S. Shmaliy,“Optimal memory for discrete-time FIR filters instate space, IEEE Trans. Signal Process, vol. 62, pp.557–561, Feb. 2014.

Advances in Robotics, Mechatronics and Circuits

ISBN: 978-1-61804-242-2 292