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This work presents the development and experimental evaluation of a method based on fuzzy logic to locate mobile robots in an Intelligent Space using Wireless Sensor Networks (WSNs). The problem consists of locating a mobile node using only inter-node range measurements, which are estimated by radio frequency signal strength attenuation. The sensor model of these measurements is very noisy and unreliable. The proposed method makes use of fuzzy logic for modeling and dealing with such uncertain information. Besides, the proposed approach is compared with a probabilistic technique showing that the fuzzy approach is able to handle highly uncertain situations that are difficult to manage by well-known localization methods.

Nowadays, Wireless Sensor Networks (WSNs) [

The low cost of these devices makes them especially suitable for large Intelligent Spaces [

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

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

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 [

In this paper, we address the problem of positioning a mobile robot in an Intelligent Space [

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 [

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

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 [

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 [

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 [

In our case, we have adopted the _{L}_{0} as follows,

The variation of received power is represented as a log-normal random variable, _{dB}

Finally, the received power is the difference between transmitted and attenuated power,
_{r}_{t}_{L}_{0} are the distance and the reference distance respectively, _{dB}

The propagation model is customized for RF communications of the

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

The sensor model is obtained by fitting the RSSI values using a least squares fitting method. The fitting values are [_{L}_{0})]_{dB}_{0} = 1.

The statistical model permits estimating inter-node distances given the RSSI indicator of

We define the indoor WSN localization problem as a

The _{t}

The _{t−1} in order to obtain the predicted _{t}. This operation is performed by a fuzzy dilation operator [_{t−1} in all directions in order to represent both the robot’s motion and the uncertainty in the robot’s location. In the case that we know that the sensor node is static, the fuzzy dilation is also applied to guarantee the convergence of the method and to ensure that the recursive estimator is not trapped into a local minimum. Formally, the dilation operation of _{t−1} to _{t}

_{t+2}, shown in _{t}

The update stage consists of intersecting the predicted belief _{t}_{t}_{t}_{t}_{t}_{1}), _{t}_{2}), . . . _{t}_{n}_{1}, _{2},. . ., _{n}

The uncertainty of the observations is represented as different intervals in the inter-node range; the sensor model of each observation is associated with a trapezoidal fuzzy set

The reference method is a variant of Monte Carlo localization approach [_{i} P_{i}_{i}_{i}

As in the case of the proposed localization approach, the Monte Carlo method follows the typical predict-update cycle of recursive state estimators. The prediction stage consists of the simulation of the motion of each sample including random noise in order to improve the convergence.

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 [

The proposed method is evaluated using an indoor WSN composed of several RF beacons,

The sensor node used by the robot is part of the WSN, in particular a commercial

The experiments are performed using a four wheel drive robotic platform,

The experiments consist of driving the robot between known positions, which permits estimating the ground truth and calculates the position error. While the robot navigates between known locations, shown in

The kidnapping experiment consists of positioning a sensor node at whatever initial location estimating its pose using the messages received from beacons, and after some seconds it is transferred to other location without the sensor node being aware of this. This process is repeated several, almost hundred, times. The locations where the sensor node is transferred are known, and the localization techniques are activated when the sensor node is located at a new pose and deactivated when the sensor node is “kidnapped”. The aim of deactivating the localization process, while the sensor node is transferred to a new location, is to simulate an instantaneous transfer which should be interpreted and handled by the localization method, normally as recovery from failure. These experiments permit us to evaluate the convergence and robustness of the localization methods, and the quality of the position estimation. Note that environment information is obviated in these experiments.

The tracking experiments consist of estimating the location of a sensor node installed on the robot platform while it navigates through a route defined by known way-points. When the mobile robot reaches these way-points, an operator notifies it by sending a packet to the robot in order to indicate the ground truth and to calculate the position error. The experiments evaluate two unfavorable situations when there are long corridors in indoor environments: crossing an intersection with a long corridor and navigating through a long corridor. The multipath reflection effects and the line-of-view between emitter and receiver in long corridors induce very noisy RSS measurements with respect to the sensor model elicited above. This is because of such a sensor model considers average signal attenuation, which includes walls and other obstacles; in particular, multipath reflections induce further distance estimation due to higher RSS attenuation, while free line-of-view between emitter and receiver induces closer distance estimation due to lower RSS attenuation.

The reasons for providing the proposed method better position estimations in highly uncertain situations are: the representation of approximate location information and specially the ability of fuzzy logic for addressing the fusion information problem. The reference method makes use of a classical weighted average fusion of the different sources of location information, whereas the proposed method permits maintaining the information making a decision about the sources being combined, and typically obtaining a consensus between the different sources of location information.

Some probabilistic localization methods perform different tests in order to check if the measurement is an outlier given the probabilistic distribution of the robot’s belief, and then avoiding the problem presented in the numerical example. For example, the Extended Kalman Filter (EKF) makes use of the distance of Mahalanobis in order to compare the innovation of the state to estimate and the covariance associated to such an innovation considering the measurement. This comparison is used to filter out outliers,

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.

This work has been supported by Spanish Ministry of Science and Innovation under DPI-2007-66556-C03-02 CICYT project. Special thanks to Alessandro Saffiotti for his invaluable help and comments. We are indebted to Pedro M. Ruiz and Rafael Marín for their help with laboratory equipment and experiments.

Example of

Fuzzy set representation of a position measurement observed at the distance

Example of

Sensor models used to perform the comparison experiments; correspondence between (upper) fuzzy set and (lower) stochastic Gaussian distribution.

The environment and the deployment of the beacons.

Experimental setup:

Position error in kidnapping experiment:

Position error in tracking experiment:

Example of location information fusion using the proposed and the reference localization methods.