Enhanced Inertial-Aided Indoor Tracking System for Wireless Sensor Networks: A Review

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/JSEN.2014.2325775, IEEE Sensors Journal

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Enhanced Inertial-aided Indoor Tracking System forWireless Sensor Networks

Alejandro Correa, Marc Barcelo, Antoni Morell, Jose Lopez VicarioUniversitat Autonoma de Barcelona

Telecommunications and Systems Engineering DepartmentAlejandro.Correa, Marc.Barcelo, Antoni.Morell, [email protected]

Abstract—In recent years, there has been a growing interestin localization algorithms for indoor environments. In this work,we have developed an enhanced filtering method for indoorpositioning and tracking applications using a Wireless SensorNetwork (WSN). The method combines position, speed andheading measurements with the aim of achieving more accurateposition estimates both in the short and the long term. Using asa base the well-known Extended Kalman Filter (EKF), we haveincorporated two novel measurement covariance matrix tuningmethods. The Power Threshold Covariance Matrix Tuning (PT-CMT) method and the Distance Statistics Covariance MatrixTuning (DS-CMT) method, both based on the statistical char-acteristics of the distance estimations. In addition, we take intoaccount the inertial measurements obtained from a 9-Degrees ofFreedom (DoF) Inertial Measurement Unit (IMU). The systemhas been validated in real scenarios and results show that itprovides long-term accuracy, that is, the accuracy remains below1 meter during a 20 minutes test. In summary, our methodsbenefit from the reduced observation error of the inertial sensorsin the short term and extend it over a long period of time.

Index Terms—RSSI, Inertial, Kalman filters

I. INTRODUCTION

IT is widely accepted that GPS has become the de factostandard for outdoor positioning and tracking applications.

However, there is no equivalent system for indoor scenarios.Therefore, considerable research effort has been focused onthis topic recently. This work presents an indoor trackingsystem based on the Received Signal Strength Indicator (RSSI)measurements of a Wireless Sensor Network (WSN)[1], [2].Note that RSSI-based techniques do not require additionalhardware to be implemented. Furthermore, the RSSI valuecan be read without being part of the network, that is, justlistening to the network packets. In this paper we focus ourattention on the localization of a mobile node in an indoorenvironment. The main application is the guidance of peopleinside buildings.

A. Related Work

The main problem when dealing with applications usingpure RSSI-based localization methods is that, we experi-ence an accuracy limitation. The reason is that the RSSI

This work was supported by the Spanish Research and Development underProject TEC2011-28219.

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

observations are error-prone mainly due to the well-knownwireless channel variability. This fact impinges directly on theperformance of most of the RSSI-based localization methodsproposed in the literature [1].

Alternately, there is a large number of studies describingtracking systems based on inertial measurements [3]. Typi-cally, there are two different kinds of inertial solutions: i) thepedestrian dead-reckoning solutions, which detect the numberof steps and the heading of the user [4] and ii) the strapdownnavigation systems, which integrate the accelerometer andgyroscope readings to compute the position and attitude ofthe person [5]. However, a major problem with this kindof solutions is that the estimation error growths with timedue to the typical drift of the inertial measurements [6].In practice, the positioning error deviates over the meter inseconds. Recent developments in this field have achieved areduction in the error growth using the Zero-Velocity-Updatestrategy (ZUPT) and placing the IMU on the foot of the user[3], [7], [8]. In this case, the positioning error is below 5% ofthe total travelled distance [4].

One possible amendment recently proposed is the use ofhybrid systems based on both RSSI and inertial measurements.As far as inertial solutions are affected by the placementof the IMU on the body, it is then meaningful to classifythe hybrid positioning systems considering the position ofthe IMU on the body. On one hand, there are foot-mountedhybrid systems which obtain high accurate estimations dueto the ZUPT strategy. Some examples can be found in [5],[9], [10]. These systems usually achieve an accuracy below1 meter [3]. On the other hand, there are authors that placethe IMU on other parts of the body looking for the usercomfortability. These methods usually obtain lower accuracythan the foot-mounted hybrid systems because they cannotapply the ZUPT strategy. In this work we consider that theuser comfortability is mandatory even at the expenses of aloss in accuracy. Consequently this work follows this secondmethodology. Some examples can be found in [11], [12] wherethe authors propose a Kalman Filter (KF) that combines RSSImeasurements from a WSN with inertial measurements froma hip-mounted IMU. Similarly, in [13] the authors use achest-mounted IMU and an Extended Kalman Filter (EKF).Moreover, in [14] a KF is used for combining inertial andRSSI measurements from a Wi-Fi network. Other authors useParticle Filters (PF) such as in [9], [15] or in [16] where mapinformation is also taken into account. Typically the accuracy



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of this systems is below 2 meters.

B. Contribution

Typically, hybrid positioning systems described in the liter-ature present one of these two drawbacks: low accuracy in thelong term or high accuracy only in the short term. The aim ofthis work is the design of a system that solves these drawbacks,that is, a system with high accuracy also in the long term. Thisis achieved with the appropriate tuning of the measurementnoise covariance matrix of the EKF, which is based on thestatistical characteristics of the measurements. Indeed, far toolittle attention has been paid to the tuning of the measurementnoise covariance matrix of the EKF in hybrid positioningsystems and typically this matrix is ad-hoc adjusted withoutconsidering the statistics of the measurements. In our work,we present two different covariance matrix tuning methodsthat take into account those statistics.

First of all we analyse the statistical characteristics of theRSSI-based position measurements. Following this analysis,two automatic methods for the tuning of the measurementnoise covariance matrix of the EKF are designed: i) the PowerThreshold Covariance Matrix Tuning (PT-CMT) method andii) the Distance Statistics Covariance Matrix Tuning (DS-CMT) method. These methods allow the EKF to benefit fromthe goodness of the inertial sensors in the short term and,assisted by the RSSI measurements, extend their accuracy alsoin the long term. As a consequence, the presented system isable to be as accurate as, for example, the foot-mounted hybridsystems. Finally, both methods have been tested experimen-tally. To the best of the author’s knowledge, there are no otherworks considering the covariance matrix tuning of the EKF inthe context of indoor hybrid positioning solutions for WSNsbased on inertial and RSSI measurements.

The rest of the paper is organized as follows: Section IIintroduces the problem of indoor pedestrian tracking. SectionsIII, IV and V detail the proposed system whereas Section VIpresents the experimental validation. Finally, the conclusionsof our work are presented in Section VII.

II. PROBLEM STATEMENT

Let us consider an arbitrary indoor area with N anchornodes with known positions si =

[xi, yi

]Tfor i = 1, 2, ..., N

defining a set S = s1, s2, ..., sN, and a mobile node withunknown position mk =

[xkm, y

km

]T, where k stands for the

time index with corresponding sampling period T . The mobilenode listens to the network packets in order to get the RSSIvalues RSSIksi→mk of each radio link between si and mk. Letrk denote the vector of RSSI measurements,

rk =[RSSIks1→mk , RSSI

ks2→mk , ..., RSSI

ksN→mk

]T(1)

Note that at a certain time instant k, the mobile node may ormay not receive a packet from every anchor node. Similarly,the inertial sensors attached to the mobile node providethree matrices with inertial measurements, Φk the accelerationobservation matrix (LΦ×3), Ψk the magnetic field observationmatrix (LΨ×3), and Ωk the angular speed observation matrix(LΩ × 3).

Positioning Processing

Extended Kalman Filter

Pre-Processing Block

rk

Φk [xk yk V k θk

]

[xk− yk−

]

V k−

Inertial ProcessingΨk

Ωk

θk−

Covariance Matrix Tuning

Fig. 1. Navigation system architecture.

Additionally, let us consider the following state space rep-resentation of the mobile node. First, the state variables are,

xk =[xk yk V k θk

]T(2)

where xk, yk represent the position of the mobile node at thek-th time instant in Cartesian coordinates, V k is its speedmodulus and θk its heading. Taking into account that thepedestrian motion fits well to a constant velocity model, wework with the following state-space model,

xk = F(θk−1

)xk−1 + vk (3)

where vk is a zero mean Gaussian noise with covariance matrixQ and F

(θk−1

)is the model transition matrix that describes

the constant velocity movement with the velocity representedin polar coordinates. Namely,

F(θk)

=

1 0 T cos θk 00 1 T sin θk 00 0 1 00 0 0 1

(4)

Note that the polar representation of the velocity matches theavailable measurements (see Section III) and that the modelbecomes non-linear then.

III. SYSTEM ARCHITECTURE

This work presents a tracking system based on an EKF,which combines RSSI-based position and inertial measure-ments using the architecture depicted in Fig. 1. The systemarchitecture is divided into three blocks, i) a pre-processingblock that transforms the available set of measurements intoestimated observations of the state variables, ii) a covariancematrix tuning block that tunes the measurement noise covari-ance matrix of the EKF based on the analysis of the RSSI-distance (measurement) statistics and iii) an EKF block thatminimizes the positioning error thanks to the kinematic modeland the information given by the previous blocks.

The pre-processing block is divided into two sub-blocks:i) the positioning processing sub-block, which transforms theRSSI observations into estimates of the mobile node positionmk =

[xk− yk−

]and ii) the inertial processing sub-block,

which estimates the speed and heading of the mobile nodeV k− ,θk− from the inertial observations.

The EKF block uses the prior estimations of the statevariables, the statistical information about the model and theprevious state estimation xk−1 to compute a refined estimationof the state vector xk. This refined estimation achieves high



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accuracy thanks to the two novel measurement noise covari-ance matrix tuning methods designed in this work (See V-B).

During the design of the positioning system we assume:• The radio propagation follows a log-distance path loss

model.• The position of the anchor nodes is known.• The user walks at approximately constant velocity (un-

known and to be estimated) and with constant step length(known and user-dependant).

• The user manually aligns (with error) the IMU on themiddle of the back during the initialization.

In what follows, we first describe how the set of RSSIvalues and the inertial measurements are pre-processed and,afterwards, we discuss our particular configuration of the EKFto take into account the statistics of the observations.

IV. PRE-PROCESSING BLOCK

This section describes: i) the propagation model (log-distance path loss model) used to obtain distance measure-ments from RSSI readings; ii) how the distance measurementsare then converted to a position estimation by means of theWeighted Least Squares (WLS) algorithm; and iii) the methodsemployed to extract heading and velocity information from theIMU readings. All the techniques and models described in thissection have been chosen according to complexity, versatilityand acceptation criteria, that is, we selected computationallylow-complex (to be implemented in a WSN node) and widely-used solutions in the literature.

A. Positioning Processing Sub-Block

The positioning processing sub-block obtains a positionmeasurement from the received RSSI values. In this work weemploy the Least Squares (LS) approach, which obtains theposition of the mobile node as the position that minimizes thesquared error of the measured distances [17]. Notwithstanding,the ideas developed in this article can be easily extrapolatedto other RSSI-based location methods [18].

Using the LS method, the first step is to estimate thedistance between the mobile node and the anchor nodes. Thisis done using the log-distance path-loss model [19], typically,

RSSIksi→mk = P1m − 10α log10 dsi→mk − γ (5)

where dsi→mk is the distance to the i-th node, RSSIksi→mk isthe received power from node i, P1m is the received powerat 1 meter from the transmitter, α is the path-loss exponentand γ ∼ N

(0, σ2

γ

)is a zero mean Gaussian noise that models

the shadowing effects. Note that the parameters of the model,i.e. P1m and α , have to be experimentally determined foreach scenario, which requires a small measurement campaignto adjust the model to the scenario.

The maximum likelihood estimator of the distance betweenan anchor node and the mobile node is [20]:

dsi→mk = 10RSSIk

si→mk−P1m

10α (6)

where dsi→mk is the estimated distance to the i-th node.Note that the distance estimation does not follow a Gaussian

X

Y

Z

X

Y

Z

MoteIMU

Fig. 2. System axes.

distribution due to the exponential relationship between thedistance and the RSSI value. In fact, the distance estimationfollows a log-normal distribution [20], that is

ln dsi→mk ∼ N(ln dsi→mk , σ

2d

), (7)

where σd = (σγ ln 10) / (10α) is the standard deviation [20].Moreover, the mean and variance of the distance estimationare,

E[dsi→mk

]= dsi→mke

σ2d/2 (8)

Var[dsi→mk

]= d2

si→mkeσ2d

(eσ

2d − 1

)(9)

Therefore the estimator is biased with a bias directly pro-portional to the distance value. Note also that the varianceexhibits a quadratic growth with the distance value. Suchstatistical characteristic of dsi→mk makes the estimation ofsmall distances more reliable than the estimation of large ones,thus having an impact on the optimal design of localizationalgorithms.

The LS approach estimates the mobile node position inorder to minimize the overall squared error of the distancesestimated. Note that for a given realization of the LS approach,the distances estimated from different nodes have differentaccuracies. In order to take this into account, we use the well-known weighted LS (WLS) alternative [21], [22]. It computesthe current position of the mobile node as the solution of thefollowing minimization problem,

minmk

J =∑

i∈Rωi

(dsi→mk − ‖si − mk‖

)2

(10)

where R is the set of RSSI values available at the k-th timeinstant and ωi = 1/Var

[dsi→mk

]are the weights [22]. The

problem in (10) can be solved in an iterative way [21].

B. Inertial Processing Sub-Block

The inertial processing sub-block processes the inertialobservations into estimations of the speed and heading of themobile node. In this work we place the IMU sensor on themiddle of the back at the waist level (see Fig. 2) for the usercomfortability and versatility (it is much easier to fix a smalldevice in a belt than in a shoe). However this placement hastwo main disadvantages: i) the ZUPT strategy cannot be usedfor correcting the inertial drift [4], and ii) the sensor axishave to be perfectly aligned with the system axis in order



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to avoid misalignment errors. As stated in Section III, thiswork does not consider perfect alignment and copes with smallalignment errors (due to the user manual adjustment) instead.Nevertheless, these disadvantages are circumvented thanks tothe use of the designed measurement noise covariance matrixtuning methods (see Section V), which allow us to achieveaccuracies similar to the ones obtained with the foot-mountedhybrid systems.

Let us first focus on the speed computation block, where V k−is estimated as the product of the number of steps per secondtimes the length of each step since we assume a constant steplength per user lstep. In order to compute the number of stepsper second, we work with the modulus of the accelerationas far as it is not affected by the particular alignment of thesensor. The corresponding discrete signal is first filtered usinga low pass linear-phase Finite Impulse Response (FIR) filter(order 20 and 3 Hz cut-off frequency) in order to mitigatethe higher frequency accelerations due for example to sensorvibrations and that are not of interest [6]. Finally the numberof local maximums in the sequence that are above a predefinedthreshold (Nmax) is computed and we obtain V k− as,

V k− =NmaxT

lstep (11)

Second, the heading or speed direction of the mobile nodeis computed using a combination of the magnetometer andthe gyroscope measurements. The magnetometer gives vectorinformation of the main magnetic field, which is usually theearth magnetic field. Therefore, it is possible to obtain theangle between the magnetic field and the mobile node [23].Hence, using the initial angle measurement as a reference, theheading of the sensor at each moment is obtained as,

θkmag = tan−1Ψky

Ψkx

− θ0mag (12)

where θkmag is the heading estimation from the magnetometerat time-instant k and Ψk

x, Ψky are the mean of the magnetic field

readings at the k-th period in the x and y axis, respectively.Note that the magnetometer provides long term stability butsuffers from local alterations on the magnetic field produced,for example, by home appliances, which introduce some errorin the measurement. Alternatively, the change of heading ofthe mobile node during an specific interval can be obtained bymeans of integrating the gyroscope signal, since it providesinformation about the angular speed. In this case, externalsources of interference are not considered but the drift of thesensors plays an important role. As shown in [16], the combi-nation of both measurements provides an accurate estimate ofthe heading and mitigates the particular drawbacks associatedto each type of sensors. Mathematically, the combination isexpressed as,

θk− = (1−W )(θk−1 + ωkT

)+Wθkmag (13)

where θk− is the heading estimation at time instant k, W theweighting factor and ωk the integration of the gyroscope signalat the k-th period [15].

In what follows, we describe how the EKF is configuredto take advantage of the statistical information of the RSSI

measurements in order to benefit from the goodness of theinertial measurements also in the long term. Obviously, moresophisticated positioning and inertial pre-processing blockswill lead to better system performance, but important is thatthe ideas developed next can be easily extrapolated to possiblemodifications in the pre-processing block.

V. NOVEL DISTANCE-STATISTICS-BASED ADAPTIVEEXTENDED KALMAN FILTER (DSB-EKF)

In this section, two novel configuration methods of the EKFare presented. These new methods are based on the statisticalcharacteristics of the distance estimations that are obtainedfrom the positioning method included in the pre-processingblock (a WLS approach in our work). In this way the EKFtakes into account the different degrees of reliability in thepositioning data and the overall accuracy of the system isincreased as a result. The rest of the section is organizedas follows: first the EKF is briefly introduced and then theproposed methods are detailed.

A. Basics of the EKF

The EKF is an extension of the KF designed to cope withnon linear models [24]. The EKF algorithm is divided in twosteps: i) the prediction step and ii) the correction step. In theprediction step, the a priori estimations of the state vector xk+1

−and the state covariance Pk+1

− are updated using the kinematicmodel [25], that is

xk+1− = F

(θk)

xk (14)

Pk+1− = MkPk

(Mk)T

+ Q (15)

where Mk is the Jacobian matrix of the partial derivatives ofthe model function F

(θk)

xk with respect to xk, that is,

Mk =

1 0 T cos(θk) −T sin(θk)V k

0 1 T sin(θk) T cos(θk)V k

0 0 1 00 0 0 1

(16)

In the second step of the method, i.e. the correction step, theprevious predictions are updated thanks to the measurementsand the so-called Kalman gain Kk [26], that is,

Kk+1 = Pk+1− HT (HPk+1

− HT + Rk+1)−1 (17)

where R is the measurement noise covariance matrix and His the measurement matrix, the identity in our case, that is,H = I4×4. In particular, the Kalman gain in (17) has beenderived in order to minimize the a posteriori covariance of thestate estimation [24]. The next step is to compute the errorcommitted in the estimation of the measurements,

ek+1 = zk+1 − h(

xk+1−)

(18)

where h(xk+1− ) is the measurement function that is linear in

our case, i.e. h(xk+1− ) = Hxk+1

− . Finally, the error in (18)



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updates both the state vector and state covariance matrix asfollows,

xk+1 = xk+1− + Kk+1ek+1 (19)

Pk+1 = (I−Kk+1H)Pk+1−

According to (19) and (17), it is obvious that the per-formance of the filter depends on the existing measurementnoise as expected. However, an accurate adjustment of themeasurement noise covariance matrix is not straightforwardin practice [9], [11], [12] and most works adopt an ad-hoc solution. This ad-hoc adjustment is not efficient due tothe variations of the statistics of the distance measurements(see Section IV-A). In Section V-B we propose two differentmethods to tune the measurement noise covariance matrixbased on those statistics.

B. Covariance Matrix Tuning

This section presents two automatic methods that exploit thedifferent degrees of reliability in the measurements to adjustthe corresponding covariance matrix. They are based on thestatistical characteristics of the distance estimations in indoorenvironments and allow us to design a system with simpleinertial algorithms that performs similar to other more complexstrategies (e.g. foot-mounted hybrid systems).

The proposed methods are: the Power Threshold CovarianceMatrix Tuning method (PT-CMT) and the Distance StatisticsCovariance Matrix Tuning method (DS-CMT). On one hand,the PT-CMT method is a simple solution that considers twodegrees of reliability in the measurements. It is designed forindoor areas with many small rooms (e.g. houses or offices).On the other hand, the DS-CMT takes into account thewhole range of reliabilities. This method is specially designedfor indoor open areas (e.g. large halls, museums, universityclassrooms).

Before introducing the methods, let us define the measure-ment noise covariance matrix as,

R =

C 0

0[σ2V 00 σ2

θ

] (20)

where C is the noise covariance matrix of the position mea-surements, σ2

V is the variance of the speed modulus measure-ment and σ2

θ is the variance of the heading measurement. Bothσ2V and σ2

θ are considered time-invariant in our work whereasthe distance statistics modify C.

Fig. 3 shows the bias and the variance of the distanceestimation as a function of the distance itself according to(8)-(9). Note the exponential growth of the variance and alsothe linear increase in the bias. Consequently, the closer themobile node is to an anchor node, the higher the reliability ofthe estimated distance.

1) Power Threshold Covariance Matrix Tuning (PT-CMT):The PT-CMT method considers two types of position mea-surements: i) highly reliable measurements when the node isclose to an anchor node and ii) low reliable measurementsin the other cases. According to Fig. 3, this distinction ismade in terms of power by comparing the received power

0 1 2 3 4 5 6 7 8 9 10−80

−60

−40

−20

0

Log−distance Path loss model

Distance (m)

Re

ce

ive

d P

ow

er

(dB

W)

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

Bias and Variance of distance estimation

Distance (m)

Bia

s (

m)

0 1 2 3 4 5 6 7 8 9 100

10

20

Va

ria

nce

(m

2)

Fig. 3. Log-distance path loss model and Variance of the distance estimation.

to a given threshold Pth. When the highest RSSI (the positioncomputation involves several RSSI values from several anchornodes) or Pmax is higher than Pth, then the position estimationof the mobile node is directly the location of the anchor nodethat gives the highest RSSI. Note that in that case there is noneed to estimate the position using the WLS approach, thussaving energy. Note also that in order to minimize the errorsin the distinction of the measurements reliability, an adequatevalue of Pth is necessary. In particular the power threshold hasto be greater than the value of the received power at 1 meterto the transmitter fixed on the log distance path-loss model.Finally, the tuning of the covariance matrix is defined as:

C =

εI if Pmax ≥ Pthσ2pI if Pmax < Pth

(21)

where ε 1 and σ2p is a standard value of the variance defined

by the user.The PT-CMT method is designed to be applied in indoor

areas with small rooms and narrow corridors, as for examplein houses or offices. In this scenarios an adequate placement ofthe anchor nodes will produce highly reliable measurementsfrequently. For example, consider a node placed below theframe of a door or in a corridor.

2) Distance Statistics Covariance Matrix Tuning (DS-CMT): In open indoor areas such as large halls or museumsthe previous hypothesis is no longer valid, that is, the trajectoryof the mobile node is not necessarily close to any anchor nodeat any point. Therefore, the PT-CMT method is not adequate.In the DS-CMT method each position has a different degreeof reliability that depends on the individual distances to theanchor nodes. In the following, we describe how the degreeof reliability is computed and how the covariance matrix ofthe EKF is adjusted afterwards.

First of all, the probability density function (pdf) of thedistance estimation from the anchor’s position si to the mobilenode position mk is defined as [27],

f (x) =

1√2πσdx

exp

(ln x−ln dsi→mk

)2

−2σ2d

if x > 0

0 if x ≤ 0(22)

where x = dsi→mk . From the pdf of the distance estimation



6

Anchor Node

Mobile Node

d

ri

Fig. 4. Basics of the DS-CMT method.

it is possible to define a confidence region (see Fig. 4) wherethe mobile node will be with a given probability definedby the user p. This confidence region is a circle centeredon the anchor’s node location and with radius ri fulfillingPrdsi→mk ≤ ri = p. Notwithstanding, the mean andvariance of the distance are unknown and therefore we usethe estimated values, that is,

∫ ri

0+

1√2πσdx

exp

(lnx− ln dsi→mk

)2

−2σ2d

dx ' p (23)

where σd = (σγ ln 10) / (10α) and σγ ,α are parametersof the log-distance path loss model obtained in the systemcalibration. Afterwards and since the mobile node is simulta-neously inside all the confidence regions with high probability(p=0.95 in our case), it is then meaningful to select the regionwith smaller area. Note that this region corresponds to theclosest anchor node. Finally the measurement noise covariancematrix of the EKF is adjusted using the radius of the smallerconfidence region rimin , that is,

C = r2iminI (24)

Next section evaluates the performance enhancementsachieved thanks to the proposed DSB-EKF.

VI. EXPERIMENTAL VALIDATION

In the experimental validation, we test the performance ofthe system using the Iris motes from Crossbow, equipped withthe ATmega 1281 microcontroller and the rf230 radio chip.The IMU used is the 9DOF Sensor Stick from Sparkfun,which includes a 3 axis accelerometer (ADXL345), a 3 axismagnetometer (HMC5883L) and a 3 axis gyroscope (ITG-3200).

The anchor nodes are configured to broadcast a packet everysecond with an output power of 0 dBm. The mobile node (anode connected to the IMU stick) is attached to the personwith the help of a belt. The accelerometer is sampled at 50Hz and the magnetometer and gyroscope at 15 Hz. Finally,there is one more mote connected to a computer that acts as agateway. This mote receives a message from the mobile nodeevery second and stores the data on the computer.

In order to evaluate the performance of the proposedtechnique, the system is tested in two different scenarios.The Scenario 1 is a big classroom of 154.95 m2 that isrepresentative of a large indoor area. Covered with 8 anchor

Fig. 5. Scenario 1 (size 8.6m x 18m).

motes as shown in Fig. 5, there is one node every 19.3 m2.The true path is a square trajectory of 46.4 m length.

Scenario 2 is a house with an area of 76.16 m (5.6 m x13.6 m) covered with 8 motes (See Fig. 6), that is, one nodefor every 9.52 m2. Therefore, this scenario is representative ofan indoor area with small rooms and corridors. The definedpath starts at point A, goes to point B and returns to point Aas depicted in Fig. 6. There are stops programmed at pointsA and B of 15 seconds duration.

Common to both scenarios is the duration of the test, whichis fixed to 20 minutes. Note that this duration is enough toevaluate the long term stability of the algorithms presentedas far as, typically, inertial-based positioning methods deviatein seconds or a few minutes in the best cases. The testsare repeated ten times and averaged afterwards. The powerthreshold of the PT-CMT strategy is set to −61 dBm forScenario 1 and to −63 dBm for Scenario 2.

During the experimental validation we compare the resultsof an EKF configured with the PT-CMT method, an EKFconfigured with the DS-CMT method and a reference casewith an EKF configured in the ad-hoc manner. In the sequel,these systems are referred to as PT-CMT-EKF, DS-CMT-EKFand EKF.

Let us first focus on Scenario 1. Figures 7 and 8include an example of the estimated paths of the PT-CMT-EKF and DS-CMT-EKF systems. The reader can appreciatethe higher accuracy of the DS-CMT-EKF system compared tothe PT-CMT-EKF. In the different tests carried out the RootMean Squared Error (RMSE) achieved is 0.9 m for the DS-CMT-EKF and 1.3 m for the PT-CMT-EKF, which representsan improvement of 30%. This improvement is due to thecharacteristics of the Scenario 1, i.e. an open area where themobile node does not pass near the anchor nodes and thereforethe PT-CMT-EKF is not the best option.

Note that in general the RMSE does not fully representthe real performance of a system. Instead, the Cumulative

Anchor node

A

B

Fig. 6. Scenario 2 (size 5.6m x 13.6m).



7

Fig. 7. PT-CMT in Scenario 1 (size 8.6m x 18m).

Distribution Function (CDF) of the positioning errors providesmore information. This CDF has been calculated for bothmethods and plotted in Fig. 9. We appreciate that the error isbelow 2.65 m in 90% of the occasions for the EKF. This erroris 2.3 m for the PT-CMT-EKF and it is significantly reducedto 1.7 m in the case of the DS-CMT-EKF.

Considering now the Scenario 2, an example of the es-timated paths for both methods is shown in Fig. 10 andFig. 11. In this case the performance of the algorithms followsa different pattern and it is the PT-CMT-EKF who presentsbetter results. The tests carried out show a RMSE of 0.85 mfor the DS-CMT-EKF and 0.64 m for the PT-CMT-EKF, whichrepresents an improvement of 24%. Moreover, Fig. 12 showsthe CDF for Scenario 2. If we analyse again the error in the90% of the cases, we observe that it is situated at 1.8 m forthe EKF. This error is below 1.5 m for the DS-CMT-EKFand 1.3 m for the PT-CMT-EKF. Note that in this case, thetrajectory of the mobile node is often very close to the anchornodes and this explains the superior performance of the PT-CMT-EKF.

Finally, we evaluate the different methods as a function ofthe number of anchor nodes, which strongly influences theperformance of the techniques. The CDFs obtained with theproposed methods for a different number of nodes are shown inFig. 9 and Fig.12. As it is expected the accuracy of the systemis degraded when less anchor nodes are available. Particularlyremarkable is the behaviour of the DS-CMT-EKF, whoseperformance is slightly degraded with the number of nodes.Contrarily, the PT-CMT-EKF is clearly degraded because closeanchor nodes are not present along the trajectory.

Notice that our solutions extend in both scenarios the short-term accuracy of the inertial sensors over time as desired.Note also that the presented CMT methods do not avoid thedrift of the inertial sensors but they are able to bound this

Fig. 8. DS-CMT in Scenario 1 (size 8.6m x 18m).

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RMSE (m)

F(x

)

Cumulative Distribution Function

EKF 8 Nodes

PT−CMT−EKF 8 Nodes

DS−CMT−EKF 8 Nodes

EKF 6 Nodes



Fig. 9. Cumulative Distributed Function of the error in the Scenario 1.

drift by tuning the measurement noise covariance matrix of theEKF taking into account the statistics of the distance readings.That is because the proposed methods are able to convey thelow MSE of the good position measurements to the output ofthe EKF. Furthermore, the presented methods achieve similaraccuracies to other hybrid systems using more complex inertialalgorithms like the ZUPT strategy for the foot-mounted inertialalgorithms [5], [9], [3]. In particular, our proposed systemsachieve accuracies below the meter (i.e. the same as foot-mounted hybrid systems) and this accuracy is maintained overa long period of time, that is, the accuracy remains below 1meter during a 20 minutes test.

VII. CONCLUSIONS

In this paper we present an enhanced inertial-aided indoortracking system for WSNs based on the Extended KalmanFilter. Our system combines distance measurements extractedfrom the RSSI of a set of anchor nodes together with inertialmeasurements obtained from an on-board IMU. It is wellknown that dead reckoning solutions provide good accuraciesin the short term but not in the long term. On the contrary,RSS-based position estimations are not so accurate but stablein time. In this work, we statistically analyse the RSSI-basedposition measurements and design two covariance matrix tun-ing methods that auto-adjust some of the filter parameters, inparticular the coefficients of the measurement noise covariancematrix. The PT-CMT method suits indoor scenarios withmany small rooms and the DS-CMT method is better forindoor open areas. In summary, we show that it is possible

Anchor node

A

B

Fig. 10. PT-CMT in Scenario 2 (size 5.6m x 13.6m).



8

Anchor node

A

B

Fig. 11. DS-CMT in Scenario 2 (size 5.6m x 13.6m).

to design simple EKF-based solutions that efficiently combineobservations with different degrees of reliability.

The system has been experimentally validated in two differ-ent, representative indoor scenarios with different densities ofnodes and the proposed enhancements in the EKF reduce thepositioning RMSE with respect to a regular EKF up to 40% inthe scenarios tested. As a result, the proposed system is keptsimple in terms of computational complexity, the accuracy isbelow the meter in terms of RMSE and also kept in the long-term as it is shown in Section VI during a 20 minutes test.Therefore, our contribution suits applications that require thetracking of objects or people inside buildings.

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0 0.5 1 1.5 2 2.5 30

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RMSE (m)

F(x

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EKF 6 Nodes



Fig. 12. Cumulative Distributed Function of the error in the Scenario 2.

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9

Alejandro Correa received his B.Sc and M.Sc. inElectrical Engineering (with honors) from Univer-sitat Autonoma de Barcelona (UAB), in 2008 and2010, respectively. Since 2011 he is a PhD candidateat the Telecommunications and Systems EngineeringDepartment of UAB, supporting both research andteaching. He has published in 2 international journalsand 5 international conferences. Furthermore, he hasbeen involved in several R&D projects, such as AT-LANTIDA and 3SENS. His main research interestsinclude pedestrian indoor positioning systems and

wireless sensor networks.

Marc Barcelo received his M.Sc. in Electrical En-gineering (with honors) in 2010 from UniversitatAutonoma de Barcelona (UAB). Since 2010 he isa PhD candidate at the same university, supportingboth research and teaching at the Telecommunica-tions and Systems Engineering Department. Duringthis period, he has published in 3 internationaljournals and 9 international conferences. Moreover,he has been involved in several european R&Dprojects, such as ADIBEAM and SINTONIA. Hismain research interests include cooperative com-

munications, digital beamforming and energy efficient routing strategies inWSNs.

Antoni Morell received the M.Sc. degree in elec-trical engineering and the Ph.D. degree from Uni-versitat Politecnica de Catalunya (UPC), Barcelona,in 2002 and 2008, respectively. He was with theSignal Theory and Communications Department,UPC, from 2002 to 2005. He joined UniversitatAutonoma de Barcelona, as a Research and TeachingAssistant in 2005 and an Assistant Professor in 2008,teaching courses on communications, signals, andsystems. He has been involved over 10 researchand development projects, national and international,

being the Principal Investigator in one of them. He has expertise in opti-mization techniques applied to communications, also in the field of wirelesssensor networks. He has published over 30 papers in recognized internationaljournals and conference proceedings and his current research interests includemachine learning, inertial-aided indoor positioning, distributed multiple accessprotocols and routing strategies in WSNs.

Jose Lopez Vicario was born in Blanes, Spain, in1979. He received both the degree in electrical en-gineering and the Ph.D. degree from the UniversitatPolitecnica de Catalunya (UPC), Barcelona, in 2002and 2006, respectively. During 2002, he served asDSP programmer and participated in the Spanishgovernment R&D project TIC99-0849. From Octo-ber 2002 to September 2006, he was a Ph.D. can-didate at UPCs Signal Theory and CommunicationsDepartment and, from January 2003, he pursued histhesis at the Centre Tecnologic de Telecomunica-

cions de Catalunya (CTTC), where he was involved in several EuropeanR&D projects (IST ACE and IST NEWCOM). Since September 2006, heis an Assistant Professor at the Universitat Autonoma de Barcelona (UAB)teaching courses in digital communications, signal processing and informationtheory. His research interests are in the area of cooperative communicationsand positioning for wireless sensor networks. Dr Vicario received the 2005/06best Ph.D. prize in Information Technologies and Communications by theUPC.

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Enhanced Inertial-Aided Indoor Tracking System for Wireless Sensor Networks: A Review

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