Adaptive Location Tracking by Kalman Filter in Wireless Sensor Networks

Mauricio A. Caceres∗ †, Francesco Sottile† and Maurizio A. Spirito†∗Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy.†Istituto Superiore Mario Boella, Via P. C. Boggio 61, 10138 Turin, Italy.Email: mauricio.caceresduran@polito.it, sottile@ismb.it, spirito@ismb.it

Abstract—The increasing availability of ubiquitous, small, low-cost devices using wireless communications to build wirelesssensor networks calls for autonomous solutions and algorithmscapable of calculating the location where the information isgathered, processed, used. The requirements are particularlystrict when sensor nodes are mobile; in fact, mobile applicationsdemand more accurate locating and real time tracking, with lim-ited impact on hardware complexity, network load and latency.Despite of remarkable research efforts put into this field by thescientific community, a common unique solution has not beenadopted yet, due to the great variety of scenarios and applicationrequirements. This paper focuses on the design and performanceevaluation of Kalman filters for tracking a mobile target movingat low dynamics and for smoothing range estimations from noisymeasurements. Some adaptive techniques to self-tune the filterand estimate the propagation model parameters are presented.One among the most promising adaptive algorithm presentedis implemented in a real-life wireless sensor network test-bedincluding a mobile node. The resulting experimental resultsillustrate the benefits of this approach with respect to traditionalmultilateration based on least mean squares estimators.

Keywords-Adaptive Kalman filtering; nonlinear estimation;location sensing; radio tracking; wireless sensor networks ∗

I. INTRODUCTION

A Wireless Sensor Network (WSN) is a set of tiny andlow-cost devices equipped with different kind of sensors, asmall microcontroller and a radio transceiver, typically pow-ered by batteries [1]. The applications of this technology arenumerous and still expanding from environment monitoring,home automation, health care, industrial process monitoring,traffic control and several military applications. Irrespectiveof the scenario the information collected within a WSN hasa significant added value when accurate timing and locationdata is included, and for some of these applications, thisinformation is crucial. Due to the limited cost and complexityof off-the-shelf commercial WSN platforms, in most of thecases only the highly noisy Received Signal Strength (RSS)measurements between pairs of nodes are available to solvethe WSN node localization problem.

Several approaches to WSN localization in static conditionsexist. Most of them are surveyed in [2] while a deep analysisof the localization algorithms theoretical accuracies can befound in [3]. Recently, the mobility has been addressed withseveral tracking systems, surveyed in [4], and typically basedon prediction-correction algorithms like Kalman filters (KF)[5]. While these works consider the problem of mobility, RSS-based WSN node tracking has not been addressed, which

∗M. A. Caceres worked as a Jr. Researcher at ISMB. Since January 2008he is enrolled as a PhD. student at Politecnico di Torino.

makes the localization more challenging, especially with asyn-chronous RSS measurements.

The main scope of the research presented in this paper is todesign and evaluate the accuracy of fast-deployable and robustalgorithms based on the Kalman filter principle suitable fortracking mobile nodes within the context of applications whereonly RSS measurements are available. A novel observationmodel based on RSS is presented and the online estimation ofthe propagation model parameters is discussed. Also, someadaptive Kalman filtering approaches are studied and theirperformance evaluated in a real life experimental test bed.

The remainder of the paper is organized as follows. SectionII introduces the extended Kalman filter algorithm basics.Section III presents the typical state models used in trackingapplications with Kalman filters. Section IV describes themeasurement models suitable for WSN node tracking throughRSS measurements. Section V presents some iterative adaptivetechniques with low memory and computational requirements.Finally, section VI reports performance of the algorithmsproposed within a real life experimental test bed.

II. OVERVIEW OF THE KALMAN FILTER ALGORITHM

The KF algorithm, first introduced in its discrete-timeversion by Rudolph Emil Kalman in [6] and followed byits continuous-time version (Kalman-Bucy Filter), offers anelegant, efficient and optimal solution to localization problemswhen the system at hands is linear and random measurementserrors follow a Gaussian distribution. Since these conditionsare not always met, some linearizations and approximationsare needed to transform the KF into the Extended KalmanFilter (EKF), suitable for non-linear systems [7].

The discrete EKF estimates recursively the state of a dy-namic system modeled by discrete-time state equation:

xk = f (xk−1) + wk, (1)

wk ∼ N (0,Qk) ,

where xk is the state vector at time k, f is the state transitionfunction which evolves the state in time given the previousstate xk−1. The process noise vector wk takes into account thenon-linearities and perturbations on the system, modeled by avector of random noise (not necessarily stationary) normallydistributed with zero mean and covariance matrix Qk .

This system is observed through the measurement equation:

zk = h (xk) + vk, (2)

vk ∼ N (0,Rk) ,

2009 IEEE International Conference on Wireless and Mobile Computing, Networking and Communications

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DOI 10.1109/WiMob.2009.30

123

where zk is the measurement vector at time k, h is the obser-vation function which estimates the expected measurementsat the true state xk, and vk is the observation noise vectorassumed as a vector of random variables normally distributedwith zero mean and covariance matrix Rk. Given both models,the EKF algorithm iteratively tracks the state evolution in twophases of the filter: predict and update.

A. Predict phase

During this phase the EKF computes the a priori state vectorestimation (i.e., prediction) xk|k−1 at time k on the basis ofthe previous a posteriori state estimate xk−1|k−1:

xk|k−1 = f(xk−1|k−1

). (3)

Also the covariance matrix Pk|k−1 associated to the pre-dicted state vector xk|k−1 is evaluated from the previousestimate Pk−1|k−1 and process noise covariance matrix Qk:

Pk|k−1 = FkPk−1|k−1FTk + Qk, (4)

where Fk = ∂f∂x

∣∣∣xk−1|k−1

is the Jacobian matrix of the state

transition function f computed around the previous estimates.

B. Update phase

This phase occurs at time k, when an observation zk

becomes available. During this phase, the innovation vectoryk is calculated as residual between the observed measurementzk and the expected measurement h

(xk|k−1

):

yk = zk − h(xk|k−1

). (5)

Along with the innovation vector, its covariance matrix Sk iscomputed as the expected measurement estimation error dueto the a priori state error covariance plus the measurementcovariance matrix Rk:

Sk = HkPk|k−1HTk + Rk, (6)

where Hk = ∂h∂x

∣∣xk|k−1

is the Jacobian matrix of the obser-vation function evaluated around the a priori state estimate.

Finally, the algorithm computes the a posteriori state es-timate xk|k and corresponding covariance matrix Pk|k bycorrecting the a priori state estimate xk|k−1 and Pk|k−1:

xk|k = xk|k−1 + Kkyk, (7)

Pk|k = (In − KkHk)Pk|k−1, (8)

where Kk is the optimal Kalman gain:Kk = Pk|k−1H

Tk S−1

k . (9)

III. STATE MODELS FOR LOW DYNAMICS SCENARIOS

The EKF performance depends heavily on how well thesystem dynamics and measurements (including their statisti-cal characterization) are modeled; hence, the definition of astate model that properly describes the system dynamics isparticularly relevant.

This work focuses on the design of a fast-deployablelow-complexity location tracking system in a low dynamicsscenario (pedestrian speeds). In the following, a n-dimensional(n = 1, 2, 3) system dynamics model suitable for this scenario

is derived, namely the Position-Velocity (PV) [5]. Additionalmodels that are not considered hereafter because suitable fortracking agile targets (e.g. PVA), hence not interesting for thescenario considered in this work, can be found in the surveyby Li and Jilkov (see [8] and references therein).

The following definitions hold: x = [x1, . . . , xn]T repre-sents the vector of n position coordinates, v = [v1, . . . , vn]

T

the n velocity components, and a = [a1, . . . , an]T the n

acceleration components. Δtk = tk − tk−1 is the time elapsedbetween the previous estimation time tk−1 and the currentestimation time tk, In is the n × n identity matrix, and0n is the n × n matrix with all 0 entries. Position, velocityand acceleration components are represented in a Cartesiancoordinate reference system.

A. Position-Velocity (PV) model

This dynamic model is valid under the assumption of targetmoving at near constant velocity between two adjacent inter-vals Δtk apart from each other. Its state vector is composedby the position coordinates and the velocity components:

x =[

x v]T

, (10)

the transition function models a constant speed linear motion:

f (xk−1) = Fkxk−1 =

[In �tkIn

0n In

]xk−1. (11)

The process noise is modeled as independent random accel-erations a normally distributed with zero mean and covariancematrix Qa,k that allow tracking of different forces that couldtemporally affect target’s dynamics (e.g., friction):

Qa,k =

[�t2k

2In

�tkIn

] ⎡⎢⎣

σ2a1

0. . .

0 σ2an

⎤⎥⎦ [

�t2k2

In

�tkIn

]T

. (12)

A correct dimensioning of the process noise covariancematrix is a key factor in the EKF design: zero or small variancerandom accelerations generally lead, on one hand, to a smoothtracking; on the other hand, they lead to slow filter response oreven divergence in case of target maneuvers (i.e., when speedis no longer constant within the interval Δtk).

IV. OBSERVATION MODELS FOR WSN

This section presents the classical position and distanceobservation models along with a new measurement modeldeveloped to design a filter that processes directly raw RSSmeasurements. The possibility of processing at each EKF iter-ation one single measurement is discussed and compared withthe situation where multiple measurements are processed at thesame time. As in section III n represents the dimensional spacewhile m indicates the number of elements in the state vector,which varies according to n and to the state model chosen.For sake of simplicity the observation models presented in thefollowing (in particular, the expression of the Jacobian matrixH) are defined according to the P model (the derivation of H

for the PV model is straightforward since the partial derivativescorresponding to velocities are set to zero).

124

A. RSS-Based Distance Observations

In its typical tracking applications the EKF estimates thetarget node position (and eventually its velocity and accel-eration) by processing distance observations between targetnode and a set of L reference nodes [8], [9] (correspondingto the anchor nodes in WSN applications) located at knowncoordinates xrefl = [x1,refl , . . . , xn,refl ]

T for l = 1, . . . , L. TheEKF observation vector is then defined as

z =[

dref1 · · · drefL

]T, (13)

where drefl = dist (x, xrefl) =

√√√√ n∑i=1

(xi − xi,refl)2.(14)

Consequently, the observation function is defined as thedistances between the position component of the state vectorand the anchors:

h (xk) =

⎡⎢⎣

dist (xk, xref1)...

dist (xk, xrefL)

⎤⎥⎦ , (15)

and, since h (xk) is non-linear, the Jacobian matrix H needsto be computed around the a priori state xk|k−1:

Hk =

⎡⎢⎢⎢⎣

x1,k|k−1−x1,ref1

dist(xk|k−1,xref1)· · ·

xn,k|k−1−xn,ref1

dist(xk|k−1,xref1)...

. . ....

x1,k|k−1−x1,refL

dist(xk|k−1,xrefL)· · ·

xn,k|k−1−xn,refL

dist(xk|k−1,xrefL)

⎤⎥⎥⎥⎦ . (16)

Typically the observation errors are modeled as uncorrelatedwhite Gaussian noises:

Rd,k = diag(

σ2dref1,k

· · · σ2drefL,k

). (17)

In practical WSN implementations, accurate distance ob-servations can be obtained by exchanging e.g. ultrasoundor ultra wide band signals between target node and anchornodes. A cheaper though less accurate alternative, consideredin this work, is to estimate the distance between nodes fromRSS measurements. A number of models express the signalattenuation experienced by radio signals propagating througha wireless channel as a function of the distance [10]; however,the most suitable for the operating frequencies of nowadaysWSN platforms is the widely adopted log-normal shadowingpath loss model [11]. It expresses the power in decibels Preceived at distance d from the transmitter (i.e., RSS value) as

P (d) = P0 − 10α log10 (d/d0) + XσdB , (18)

where P0 is the mean power received at the close-in distanced0 (typically 1 m for frequencies between 1−3 GHz), α is thepath loss exponent (2 for free space) and XσdB ∼ N (0, σdB)is an additive Gaussian random variable modeling multipathand shadowing effects. It can be proved [12] that an unbiasedestimate of the distance d derived from P is

d = K · d010P0−P

10α , (19)

where K = exp

(−

1

2

(ln (10)σdB

10α

)2)

. (20)

B. Received Signal Strength Observations

Since the KF optimality condition of Gaussian measurementerrors does not hold for RSS-based distance measurements[12], a novel approach where the EKF processes directly theRSS measurements is introduced. The observation is thus avector including target-anchor RSS measurements:

z =[

Pref1 · · · PrefL

]T. (21)

The observation function h(xk) and corresponding JacobianHk are derived from the log-normal model (18) using theEuclidean distance function (14):

h(xk) =

⎡⎢⎣

P0 − 10α log10 (dist (xk, xref1) /d0)...

P0 − 10α log10 (dist (xk, xrefL) /d0)

⎤⎥⎦ , (22)

Hk = −10α

ln(10)

⎡⎢⎢⎢⎣

x1,k|k−1−x1,ref1

dist2(xk|k−1,xref1)· · ·

xn,k|k−1−xn,ref1

dist2(xk|k−1,xref1)...

. . ....

x1,k|k−1−x1,refL

dist2(xk|k−1,xrefL)· · ·

xn,k|k−1−xn,refL

dist2(xk|k−1,xrefL)

⎤⎥⎥⎥⎦ .

The measurement noise is Gaussian and assumed white:

RdB,k = diag(

σ2dBref1,k

· · · σ2dBrefL,k

). (23)

V. ADAPTIVE EKF TECHNIQUES

Tracking performance of an EKF depend on how wellstate and observation models fit the system under observation.A good fit includes not only the mathematical expressionsdescribing the model but also the values associated to initialconditions and covariance matrices. When a KF is used offline, usually a sensitivity analysis is performed in order tofind the numerical parameters that best fit the model to theactual target trajectories. When on line such analysis cannotbe easily replicated since these parameters depend on factorsthat change on different scenarios such as target dynamics,sampling frequency and noise variance. Adaptive ExtendedKalman Filters (AEKFs) attempt to automatically changerelevant models parameters according to the conditions wherethe system is implemented and readapt them if the environmentchanges. Several adaptation approaches have been proposedsince the invention of the KF algorithm [13]. Most of themare based on some statistical analysis of the previous epochs,hence increasing both system storage and processing require-ments. This section reviews some recursive adaptive Kalmanfiltering techniques which can be adopted on a tracking systemwithout high computational and storage requirements.

A. Propagation model parameters estimation

The novel idea behind this adaptive approach is to usethe EKF to estimate some of the propagation model pa-rameters. Typically such parameters are found after a sceneanalysis campaign and a posterior linear regression on a semi-logarithmic scale, where P0 is the intercept at the close indistance d0, while the path loss exponent α is the slope.Shadowing variance XσdB is extracted as the variance of thedifference between actual measurements and the model.

125

(a) Anchor locations. (b) Picture of testbed area.Figure 1: Experimental configuration.

Such off-line scene analysis can be in principle avoided ifthe propagation model parameters are estimated by the KFitself. We propose to including the path loss exponent α andthe mean received power P0 at a given close-in distance inthe state vector (x can be any state vector defined accordingto e.g. the P, PV or PVA state models):

x� =[

xT α P0

]T. (24)

Since these parameters are rather static, their state transitionis the identity matrix multiplied by the previous state, while theprocess noise covariance matrix allows to track their changes:

f �

(x

�

k−1

)= F

�

k x�

k−1 =

[Fk 0m×2

0 2×m I2

]x

�

k−1, (25)

Q�

k =

[Qk 0m×2

0 2×m diag(σ2P0

, σ2α)

]. (26)

The observation model is essentially the same presented insection IV-B with the addition of the corresponding partialderivatives ∂h/∂α and ∂h/∂P0 into the Jacobian matrix H:

H�

k =

⎡⎢⎣Hk

−10 log10 (dist (xk, xref1) /d0) 1...

...−10 log10 (dist (xk, xrefL) /d0) 1

⎤⎥⎦ (27)

B. On-line Noise Covariance Estimation

Sage and Husa first presented in 1969 [13] the idea to esti-mate one or both measurement and process noises covariancematrices from the residual innovations. The main advantageof this algorithm is the capability to estimate on line the noisecovariances at each KF iteration, thus avoiding the need toperform statistical analysis on historical data. In the followinga slightly modified Sage-Husa adaptive algorithm that assumesdiagonal covariance matrices (i.e., assuming independent stateand measurement noise vectors components) is proposed.

The measurement noise covariance matrix to be used on thenext iteration Rk+1|k+1 is estimated as a convex combinationof the current estimate Rk|k and the square of the innovationsyk plus the a posteriori state estimation covariance matrix

100

101

−85

−80

−75

−70

−65

−60

−55

−50

−45

−40

(a) Log−Normal Channel Model.Distance [m]

RS

SI [

dBm

]

Measured RSSAdjusted Model

−20 −15 −10 −5 0 5 10 15 200

0.05

0.1

(b) Measurement Error Distribution.Error RSSI [dB]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

0 5 10 150

5

10

15

20

25

(c) RSS−based Distance Estimates.Distance [m]

Est

imat

ed D

ista

nce

[m]

−20 −15 −10 −5 0 5 10 15 200

0.1

0.2

(d) Estimation Error Distribution.Error Distance [m]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

pdfEstimateActual

pdf

Figure 2: Scene Analysis.

Pk|k projected into the measurements. For faster convergencethe learning rate dk is adapted like in an exponential movingaverage truncated to a window size w allowing detection offurther changes in the noise:

Rk+1|k+1 = (1 − dk) Rk|k + dkRk+1|k, (28)

Rk+1|k = diag (yk)2

+ HkPk|kHTk ,

Analogously for the process noise covariance:

Qk+1|k+1 = (1 − dk) Qk|k + dkQk+1|k, (29)

Qk+1|k = diag(xk|k − xk|k−1

)2−

(Pk|k − Pk|k−1 + Qk|k

).

C. Consistency and Maneuver Detection

A filter is consistent if Pk|k and Sk|k are close to the respec-tive state and measurement error covariance matrices. Sincethe exact value of the state is unknown, a consistency test canbe performed only on the measurement innovations, evaluatingthe so called Normalized Innovations Squared (NIS) [14]:

NISk = yTk S−1

k yk. (30)

This value is expected to be χ2 distributed with dim(z)degrees of freedom. If this value falls outside a given confi-dence interval (e.g. at 95%) it is deduced that something iswrong with the model (for instance the target is performing amaneuver) and a different model should be used [8], [15]. Ingeneral, it is easy to detect a maneuver start, but it is difficultto detect when it finishes, reason why the authors propose anincrement on the state estimate covariance matrix, forcing thefilter to weight more the measurement information and lessthe state predictions, when a maneuver is detected.

VI. EXPERIMENTAL RESULTS

To test the performance of the previous developed mod-els, an experimental campaign with dynamic conditions wasperformed. Eighteen wireless sensor nodes (Texas InstrumentsChipcon 2430) were used as reference anchor nodes, placedon an indoor area of 15 m × 7 m (Fig. 1a). SimultaneousRSS measurements were performed each 0.25 s between amobile node and the anchors, forwarded to a gateway (TI

126

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1(a) Radial Error Distribution.

Radial Error [m]

Cum

ulat

ive

Den

sity

Fun

ctio

n (c

df)

0 2 4 6

0

5

10

15

1 2 3

4 5 6

7 8 9

101112

13 14 15

161718

(b) Tracking Performance.

X [m]

Y [m

]

LS distKF LSdistAEKF distAEKF rss

AnchorsExactKF LSdistAEKF distAEKF rss

Figure 3: AEKF observation models comparison.

SmartRF) and stored in a database in order to perform offlineanalysis and compare performance of the different trackingalgorithms proposed. The target node was placed on boarda LEGO Mindstorm NTX robot programmed to follow atconstant speed (0.15 m/s) the stripe depicted in figure 1b.

A. Experimental Measurements Analysis

An analysis of the collected data allows to fully characterizethe radio propagation model. The mean received power atthe close-in distance d0 = 1 m, extrapolated from the mea-surements regression, is P0 = −45.55 dB while the slopeof the adjusted model, α = 2.62, represents the path lossexponent (see figure 2a). Having the model defined, one canappreciate the near-normal distribution of the RSS measure-ments with a standard deviation of σdB = 5.67 dB from figure2b. Typically this model is used to estimate distances fromthe measured RSS values (Fig. 2c), obtaining a distributionwhich is no longer normally distributed (Fig. 2d) and whosevariance increases with the distance. This model holds underthe assumption of equal transmission powers, antenna gainsand radiation/absorption patterns on the radio link between thetarget node and every anchor node. However this assumptionis not always met, so single models for each anchor node couldbe employed, eventually improving overall system accuracy,but certainly making the scene analysis stage or adaptivepropagation model estimation more complex.

B. Observation Models: Processing Distance Estimates de-rived from RSS vs. Processing Raw RSS Measurements

The behavior of the KF is significantly affected by thestatistical distribution of the measurements processed. Sincethe KF is derived assuming a Gaussian distribution for suchmeasurements, when this assumption does not hold the filterbecomes suboptimal. To address this issue, we compared thelocation tracking performance of AEKFs designed upon thePV state model and adopting the adaptive noise covariancematrices estimation approaches. Results are shown in Fig. 3.

A first set of results is obtained by feeding the KF withthe estimates provided by the LS filter that processes RSS-

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1(a) Radial Error Distribution.

Radial Error [m]

Cum

ulat

ive

Den

sity

Fun

ctio

n (c

df)

0 2 4 6

0

2

4

6

8

10

12

14

1 2 3

4 5 6

7 8 9

101112

13 14 15

161718

(b) Tracking Performance.

X [m]

Y [m

]

Adaptive RAdaptive QManeuver DetectionAdaptive R & Q

AnchorsExactAdaptive RAdaptive QManeuver DetectionAdaptive R & Q

Figure 4: EKF adaptive techniques comparison.

based distance estimates (loosely-coupled). It can be observedthe KF hardly follows the true mobile trajectory, with a radialRMS error of 1.39 m; this is because the LS position estimatesare biased and far from being normally distributed.

Feeding the KF directly with the RSS-based distance es-timates (tightly-coupled, Eq. 19) improves the linearizationof the system and therefore its accuracy (RMSE=0.44 m). Asexpected, the use of the RSS measurements also improves ac-curacy and smoothness of the tracking output (RMSE=0.42 m)due to the near Gaussian distribution of such measurements.

C. Performance of Different Adaptive EKF Techniques

Figure 4 presents performance of the adaptive trackingtechniques introduced in section V. The filters are designedwith the PV state model and RSS observation model (Eq. 21).

The baseline for comparison is the non-adaptive EKF (seesection II) with measurement error defined according to thevariance of the measurements from the scene analysis insection VI-A and parameters of process noise set accordingto the variance of the accelerations from a sensitivity analysisof the mobile node trajectory. This filter achieves an RMSEradial accuracy of 0.62 m (plotted in figure 3).

When the R matrix is estimated adaptively as describedin section V-B no significant accuracy improvement can beobserved (the radial RMSE drops to 0.57 m) although theadaptive technique is able to estimate correctly the measure-ment noise variances. Similar behaviour is observed for themaneuver detection approach presented in section V-C, whichalso works based on the innovations.

On the other hand, estimating the Q matrix only degradesthe tracking performance to accuracy worse than the baselinewith a radial RMSE of 1.01 m. These results prove that theintroduction of on line noise covariances estimation techniqueskeeps the tracking capabilities acceptable, avoiding lengthy offline sensitivity analysis needed to correctly tune the filter.

The best performance, with a radial RMSE of 0.42 m,is achieved by a simultaneous adaptive estimation of bothprocess noise and measurement noise covariance matrices.

127

D. Propagation Model Parameters Estimation

The parameters of the log-normal model were estimatedthrough the EKF, as proposed on section V-A. As it can beobserved on figure 5, both the path loss exponent α, and theclose-in received power estimations P0, are quite close to thevalues found on the scene analysis (see section VI-A). Inthe same figure, the standard deviation of the measurementerror (σdB) for anchor number 2 is plotted and comparedagainst the one obtained through the adaptive noise covariancematrices approach, both computed using a sliding window of50 samples. This figure shows how well the measurementnoise standard deviation is estimated, and similar behaviorswere observed for the rest of the anchors.

Computing the measurement covariance matrix offline, weobserved a very low correlation between noises on differentanchors, this observation confirms the choice of diagonalcovariance matrices, at least for RSS measurements.

VII. CONCLUSIONS

The Kalman Filter was shown to be a good strategy for ac-curate node tracking applications on WSN. The computationalrequirements of the EKF are slightly higher than traditionalLS algorithms, but when implemented, it still keeps mini-mum computational and memory costs. On the experimentalresults presented, the KF reported significant improvementson accuracy compared with traditional LS estimators, whilederiving additional information like velocity and a measure ofthe estimate accuracy (through the state covariance matrix).

Thanks to their Normal distribution, RSS measurementswere used directly on the KF observation model, improvingthe accuracy of filters based on distances estimated from apropagation model or positions estimated from a LS filter.Anyway, the high variance of the RSS measurements is stilla discouraging issue for submeter localization and tracking,apart from the promising results presented in this work,a further improvement could be the inclusion of the RSSchange rate on the state equation [16], better filtering of suchmeasurements and predicting temporary lost anchors.

The parameters of the KF can be tuned according to theapplication requirements and characteristics (e.g. beacon time,node physics) and the adaptive techniques exposed can addsome robustness to the system, allowing several deploymentson different scenarios with minimum modifications. In particu-lar, the on line covariance matrices technique adapts the EKFtuning according to the scenario where the tracking systemis deployed; while the estimation of the propagation modelremoves the need of a previous scene analysis, making a fast-deployable tracking solution.

However, the nonlinearity of the EKF does not alwaysguarantee the convergence of the filter, issue that couldbe solved using more advanced algorithms like UnscentedKalman Filter (UKF) [17], Ensemble Kalman Filter (EnKF)[18] or Switching Kalman Filter (SKF) [15] but they are leftfor future work, as well as a distributed implementation [9].

0 20 40 60 80 100 120 140 1601

1.5

2

2.5

3

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Path Loss Exponent

0 20 40 60 80 100 120 140 160−55

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Bm

]

Received Power at d0 = 1 m

0 20 40 60 80 100 120 140 1600

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10

15

Time [s]

σ dB [d

B]

Standard deviation of the shadowing w.r.t. Anchor #2

Estimated with AEKFFitted in Scene Analysis

Estimated with AEKFFitted in Scene Analysis

Estimated with AEKF (50 samples sliding window)Computed Offline (50 samples sliding window)

Figure 5: Propagation model parameters estimation.

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