Nowadays, Wireless Sensor Networks (WSNs) [1] have gained an increasing attention thanks to the advances in wireless communications and sensor design, which have permitted to reduce the cost and size of sensor devices. These sensor networks are composed of autonomous wireless sensing devices that incorporate sensing, processing, storing, and communication capabilities. In order to classify them, there are diverse criteria in the literature, such as considering only the communication protocols [2], the nature of the specific application [3], and the wireless device functionalities [4]. They have been successfully applied in a wide spectrum of applications, such as search and rescue [5], disaster relief [6], target tracking [7], and smart environments [8], to name but a few.

The low cost of these devices makes them especially suitable for large Intelligent Spaces [9], where the nodes are spatially distributed in order to cooperatively processing and communicating sensed information. The positioning of mobile nodes along an Intelligent Space has special interest for location-dependent applications, such as robot navigation [10,11], geometric-dependent routing [12], location-dependent sensing, and Location-Based Services (LBS) [13].

The WSN localization problem consists of estimating the location or spatial coordinates of some or all the sensor network nodes of the WSN. In order to do so, the different localization approaches make assumptions about their network and device capabilities, including hardware incorporated in devices, signal propagation models, computational and energy requirements, nature of environment (indoor vs. outdoor), communication cost, accuracy requirements, and node mobility. Considering all these constraints, each sensor node makes use of available information, such as position measurements and location of neighbor nodes, to estimate its pose.

The localization problem is much more complex in indoors because Global Positioning System (GPS) coverage is limited and inter-node position measurements are usually unreliable in low-cost sensor devices. For these reasons, indoor WSN localization problem is usually simplified by differentiating between unknown and known sensor nodes. The former nodes make use of known location of latter ones, the so-called beacons or anchor nodes, and position measurements to estimate their location. The position measurements include both information about the sensor node position relative to the WSN, e.g., distance [14] or bearing [15] to beacons, and information on the sensor node motion, such as movement estimation obtained from accelerometers in sensor nodes [16] and from odometers in mobile robots [17].

What really makes indoor WSN localization difficult is the presence of uncertainty in position measurements and the reduced level of accuracy of beacon positioning. The sensor nodes make use of some signal propagation model, which should be calibrated for each specific environment, and hence, it is strongly affected by slight environmental modifications. Besides, the location of beacons is usually configured by hand in indoor applications, which gives rise to a reduced level of accuracy of beacon positioning. All these factors induce different types of uncertainty in position measurements, including vagueness, imprecision, unreliability, and random noise. Measurements may also be affected by several simultaneous factors, which are not necessarily independent.

For all these reasons it is important that the formalism used to address the indoor WSN localization problem is able to represent the different types of uncertainty and account for the differences between them. Fuzzy logic provides powerful tools to represent and handle the different facets of uncertainty in measurements [18], to address matching problems based on similarity interpretation of fuzzy logic [19], and to use approximate models based on experience. These arguments have induced us to make use of fuzzy sets as uncertainty representation of locations in the indoor WSN localization problem.

In this paper, we address the problem of positioning a mobile robot in an Intelligent Space [20–22] using a low-cost and low-density WSN composed of TMote Sky devices, which are equipped with ZigBee (IEEE 802.15.4) communications. The inter-node measurements are estimated using the Received Signal Strength (RSS) of Radio-Frequency (RF) communications. These measurements are really unreliable due to RF signal propagation effects, such as reflections, diffraction, and scattering, which make difficult the signal strength calibration. The robot makes use of a vague description of the environment and position measurements to estimate its pose. Thus, the restrictions of the problem are as follows: the knowledge of the environment is approximate, the density of the WSN is unknown, and the on-site startup cannot be complex or time consuming. We have adopted a fuzzy robot localization framework [23], based on early ideas for representing location uncertainty [24] and ambiguity [25] in position measurements, which combines the typical schema of fuzzy systems with the typical schema of recursive position estimation methods. The advantages of this approach are obvious when high uncertainty and sensor model ignorance, which are the typical conditions of indoor WSN applications using RSS for inter-node distance estimation.

The paper is structured as follows. Section 2 presents a review of relevant related works. Section 3 is devoted to analyze the sensor model used for estimating the distances between the sensor node installed on the robot platform and the beacons distributed along the Intelligent Space. Section 4 describes the theoretical bases of the proposed approach and a reference method used to evaluate the proposed one. The experimental setup, the experimental validation of the proposed method in different situations, and a comparison between the proposed approach and one of most popular localization methods is presented in Section 5. Finally, conclusions are presented in Section 6.

Currently, there is a consensus on classification of WSN localization techniques into range-free (or coarse-grained) and range-based (or fine-grained) schemes [26–28]. Range-free approaches infer the constraints on the proximity to beacon nodes without making use of inter-node measurements, and thus sensing devices do not require special and expensive hardware. Normally, these localization methods use quite simple operations to save computational and energy consumption. They are used when the cost and limitation of hardware on sensing nodes prevent the use of range-based techniques, being a cost-effective alternative, at the cost of accuracy, in some applications [29]. On the other hand, range-based approaches rely on position measurements to estimate the location of unknown nodes. The sensor nodes should be equipped with special hardware to determine the position measurements, distance or bearing, from unknown nodes to beacons. Range-based approaches are the most suitable option when the indoor WSN application requires as accurate as possible position estimation, which is the case of most robotics applications.

The position measurements in range-based approaches rely on hardware incorporated by sensor nodes, such as directional or omnidirectional antennas, RF-communications, and acoustic or optical sensors. The inter-node distance is usually estimated using the propagation time of signals, e.g., the Time of Arrival (TOA) [14] between transmitter and receiver or the Time Difference of Arrival (TDOA) [30], which is based on the correlation of two or more signals with different propagation time in order to obtain accurate distance estimations. The relative angle between sensor nodes, Angle of Arrival (AOA), can be estimated using an antenna array [15] or calculating the TOA difference of two transmitters/receivers separated by a fixed distance [31]. Nevertheless, the most popular inter-node measurement is the distance estimation based on RSS because most of sensor network devices are equipped with RF-based communications, and thus extra hardware is not needed. Moreover, the RSS of RF signals can be measured during communications without needing additional bandwidth or energy requirements [32]. Furthermore, RF-based position measurements permit estimating inter-node ranges through obstacles, which allows reducing the density of WSNs and avoids typical network coverage area problems of sensor networks composed of optics and acoustic devices. The problem is that RF signal strength is very unreliable because it is affected by several signal propagation effects. Range-based approaches deal with uncertainty of position measurements to provide a location estimation of unknown sensor nodes.

The most popular range-based localization approaches are probabilistic methods, which formulate localization as a Bayesian estimation problem where both sensor node state (location) and sensor measurements are modeled using probability distributions. By using this representation, sensor node can believe to be at a certain location with a certain degree. The probabilistic localization problem consists of estimating the probability density over the space of all locations. Markov Localization framework estimates this probability density [33], which captures the probabilistic foundations of many stochastic localization methods currently used. These methods have been broadly used in indoor WSNs, e.g., grid-based methods [34], some variants of particle filters [28], and probabilistic methods for cooperative localization [32]. In the robotics context, different works have used some implementation of the Bayesian Localization Framework [33] in order to estimate the robot location using both Wireless Local Area Network (WLAN) signal strength [35–37] and range readings from radio tags [38] as sensing.

The main problem of range-based approaches is that they are strongly dependent of sensor models. For that reason the procedure for obtaining such sensor models results of paramount importance. Some techniques [39] aim to learn accurate signal strength sensor models in order to make use of available indoor infrastructure, including signals detected from WLAN and RFID beacons. In the case of probabilistic methods, sensor models usually consist of normal distributions, which are determined using the central limit theorem, i.e., by repeating the measurement a sufficiently large number of times under similar conditions to determine the mean and variance of a Gaussian distribution. However, practical experience suggests that these assumptions are often violated in reality, especially when we cannot reproduce the conditions of measurements or they are unknown. In the case of fuzzy approaches, sensor models consist of fuzzy sets that represent the different facets of uncertainty affecting the measurements. These fuzzy sets are adjusted approximately, normally by human-experts that would base on their experience or an expert system, depending on the vagueness, imprecision, and unreliability of position measurements. For that reason fuzzy techniques are applicable in domains where assumptions of other methods are not satisfied, e.g., when sensor model cannot be easily elicited [40]. Some examples of fuzzy logic in localization approaches are tracking in wireless networks [41], multisensor fusion of uncertain information [42,43], location information fusion in multirobot systems [44], dynamic localization using fuzzy matching patterns techniques [45], and fuzzy inference to deal with imprecision [46] or adapt some parameters [47] of other localization methods.

In this work, we propose a range-based indoor WSN localization method that aims to avoid the typical drawbacks of methods strongly dependent on signal strength calibration. In particular, the proposed method is focused on simple on-site startup and robustness.

We use a propagation model of the RF signal strength attenuation (RSS) in order to fit the sensor model used for estimating the inter-node distances. Such a model depends on several factors, such as kind of terrain, obstructions in the wave path, atmospheric conditions, and other phenomena. These factors induce the three phenomenon that cause radio signal distortions and give rise to signal fades, as well as additional signal propagation losses [48]; reflection, diffraction, and scattering. Indoor is probably the worse situation because there are multipath reflections, diffraction around sharp corners or scattering from wall, ceiling, or floor surfaces. The different models depend on environmental conditions, which usually rely on computing the median path loss for a link under a certain probability that the considered conditions will occur.

In our case, we have adopted the shadowing propagation model [48], which consists of two parts: path loss and variation of received power. Path loss predicts the received power mean at the distance d, denoted by P_L(d), that it is calculated relative to a reference distance d₀ as follows, (1) P L ( d 0 ) P L ( d ) = ( d d 0 ) βwhere β is the path loss exponent, which is empirically determined. When path loss is measured in dB it can be expressed as follows, (2) [ P L ( d ) P L ( d 0 ) ] dB = − 10 ⋅ β ⋅ log ( d d 0 )

The variation of received power is represented as a log-normal random variable, i.e., a Gaussian distribution denoted by Ψ_dB when it is measured in dB. Thus, the propagation model is represented as follows, (3) [ P L ( d ) ] dB = [ P L ( d 0 ) ] dB − 10 ⋅ β ⋅ log ( d d 0 ) + Ψ dB

Finally, the received power is the difference between transmitted and attenuated power, (4) [ P r ( d ) ] dBm = [ P t ( d ) ] dBm − [ P L ( d ) ] dBwhere P_r(d), P_t(d), and P_L(d) are received, transmitted, and attenuated power respectively, d and d₀ are the distance and the reference distance respectively, β is the path loss exponent, and Ψ_dB is a standard normal Gaussian distribution N(0, σ).

The propagation model is customized for RF communications of the Tmote Sky commercial device. This device provides two indicators that can be used for elucidating the sensor model: Received Signal Strength Indication (RSSI) and Link Quality Indication (LQI). The latter is the quality parameter, or error rate, of packet reception. The inter-node distance can be estimated by RSS because all anchor nodes are configured for emitting at maximum RF power, and hence, the distance is estimated as the attenuation of signal strength relative to such a reference value.

Thousands of measurements are taken from different locations of an office-like indoor environment in order to fit the propagation model. By knowing the ground truth of the sensor node to estimate and the position of the beacons emitting at maximum power, the Tmote indicators can be correlated for estimating the inter-node distances. Figure 1(a) shows the Tmote indicator values, path loss (dBm) and LQI (dimensionless), at different transmitter-receiver distances in an office-like environment, including measurements through obstacles, such as walls and office furniture. We can observe that Tmote indicators are very unreliable at all distances because the uncertainty of measurements depends on several factors, such as propagation effects and environment layout.

The sensor model is obtained by fitting the RSSI values using a least squares fitting method. The fitting values are [P_L(d₀)]_dB = 59.95, β = 3.72 and d₀ = 1. Figure 1(b) shows the gap of the Tmote indicators received at different distances and the fitted sensor model based on RSSI. We have noticed that LQI indicator cannot be used for estimating distances because these values are so similar along the inter-node range. However, they can be used for filtering out measurements that do not correspond to distance estimations using RSS, e.g., distance estimations shorter than five meters that are not contained in the interval [103,110] of LQI values are rejected. We have to remark that this sensor model is approximate for a certain indoor environment, but it will be used for any office-like environment.

The statistical model permits estimating inter-node distances given the RSSI indicator of Tmote devices, but we can observe that these estimations are highly unreliable. For example, Figure 1(b) shows that a RSSI value of 43 corresponds to a distance of three meters according to the fitted statistical model, however, this value can correspond to any distance within the interval [1, 9] meters according to the scattering of measurements. For that reason we should include uncertainty in the sensor model in order to deal with it. How to represent and handle uncertainty of position measurements is a key point in indoor WSN localization problem. Next section presents the formalism adopted to represent and deal with uncertainty of position measurements obtained both from range estimations and from odometry.

This section presents the experimental validation of the proposed approach using real data. This is a key point because one of most important reasons of failure in localization methods is the unknowledge about sources of noise, which is usually left out when localization approaches are evaluated using simulations. Besides, an experimental comparison with one of most popular stochastic localization methods is performed in order to evaluate the differences between them.

The battery of tests consists of kidnapping and tracking experiments using both the proposed approach and a stochastic reference method. In the robotics context, the kidnapping problem consists of positioning the robot at a location, and all of a sudden it is transferred or “kidnapped” to other location without the robot being aware of this. The kidnapping experiment is useful in order to evaluate the robustness of localization methods in different situations, such as false positive observations and recovery from failures. The tracking experiment consists of estimating the robot’s location when it is in motion. We have to remark that motion is an important source of uncertainty when the robot navigates because RSS is affected by bearing modifications of antenna. Thus, the experiments evaluate usual situations (like tracking) and unusual situations (like kidnapping or recovering from failure).

All the experiments are performed using both the proposed approach and the reference method in order to make the comparison between them. In order to make this comparison as fair as possible, we have used similar sensor and action models. How to do this, however, is not obvious since fuzzy and probabilistic techniques are semantically different: we interpret fuzzy sets to represent degrees of possibilities, while probabilities are more naturally interpreted in terms of stochastic events [23]. Moreover, stochastic methods need sensor models based on frequencies, and hence, the probability function that models the sensor should be experimentally obtained, whereas methods based on fuzzy logic make use of qualitative sensor models. We have ignored these semantic differences, and we have used probabilistic sensor models that directly reflect the fuzzy ones. Thus, the stochastic sensor model is represented by a two-dimensional Gaussian function, whose parameters are chosen so that the core and the support of the fuzzy model correspond to two and four standard deviations of the stochastic Gaussian function, respectively. Figure 5 shows the correspondence between the proposed method and the reference one.

We have presented the development and experimental evaluation of a fuzzy localization framework for addressing the indoor WSN localization problem in general, and the indoor WSN localization of a mobile robot using uncertain inter-node range measurements in particular. The proposed approach is focused on simple setting and robustness; simple setting is achieved by adjusting the fuzzy sets that represent location uncertainty in position measurements, while uncertainty management permits estimating a consensus between the different sources of information, instead of classical weighted average fusion, which improves the robustness of the position estimation. The on-site startup by simply tuning the approximate sensor models supposes an important advantage with respect to popular WSN localization approaches based on signal strength calibration because the setting of these systems is complex and time consuming. The experimental evaluation of the proposed method confirms that the fuzzy localization approach is able to solve the typical local (tracking) and global (recovery from failure and ignorance of initial location) localization problems in robotics. Finally, we have demonstrated that the proposed approach results in feasible and robust low-density WSNs. For all these reasons, we can state that the proposed approach can be simple and quickly configured in indoors providing accurate position estimations, even when high uncertainty in the position measurements.