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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/)

In recent years, various received signal strength (RSS)-based localization estimation approaches for wireless sensor networks (WSNs) have been proposed. RSS-based localization is regarded as a low-cost solution for many location-aware applications in WSNs. In previous studies, the radiation patterns of all sensor nodes are assumed to be spherical, which is an oversimplification of the radio propagation model in practical applications. In this study, we present an RSS-based cooperative localization method that estimates unknown coordinates of sensor nodes in a network. Arrangement of two external low-cost omnidirectional dipole antennas is developed by using the distance-power gradient model. A modified robust regression is also proposed to determine the relative azimuth and distance between a sensor node and a fixed reference node. In addition, a cooperative localization scheme that incorporates estimations from multiple fixed reference nodes is presented to improve the accuracy of the localization. The proposed method is tested via computer-based analysis and field test. Experimental results demonstrate that the proposed low-cost method is a useful solution for localizing sensor nodes in unknown or changing environments.

Wireless sensor networks (WSNs) [

There are two easy ways to determine the location of each sensor node. The location information may be obtained while the network was deployed manually. The other approach is to equip each sensor node with a self-positioning device, e.g., a global positioning system (GPS) [

The range-aware approaches measure the distance between two sensor nodes based on physical measurements. Existing localization methods make use of four types of physical measurements: time of arrival (TOA) [

Because of the drawback of range-aware approaches, a number of range-free localization methods have been proposed, such as centroid [

To address these challenges, we propose a localization framework for WSNs without adding expensive hardware (e.g., GPS, time synchronizer, and sensitive timer) to the sensor nodes. The basic principle of the proposed framework is to make use of the phenomenon of radio irregularity in WSNs using rotatable antennas. Rotatable antennas have been widely used in most of the AOA-based localization methods. However, the antennas used in those approaches are directional antennas. This is because directional antennas can concentrate energy on a particular narrow direction with a large gain. Therefore, most of recently proposed AOA-based localization methods were developed using directional antennas. The interference caused by surrounding noises can be reduced, and the localization accuracy was deemed an impracticable approach in the past. In this study, unlike other approaches, the major breakthrough is that we can achieve accurate localization of sensor nodes solely using omnidirectional antenna even if only one reference node exists. Besides, we can be benefit from the advantages of using omnidirectional antennas, e.g., low-cost (simplicity) and easy deployment (efficiency).

In this work, a robust correlation is incorporated in analyzing the relative positions between two sensor nodes using the received signal strength indication (RSSI) pattern. A cooperative localization scheme is also developed to improve the accuracy of the estimation as multiple reference nodes are available. The performance of the proposed framework has been evaluated by computer simulations and real world experiments under various experimental conditions.

The rest of this paper is organized as follows: Section 2 describes the definition of localization problems in WSNs, including network configuration, a pair of customized antenna modules, an azimuth dependent radio power model, and RSSI patterns. Section 3 presents the modified robust correlation to provide a better metric for matching RSSI patterns. Section 4 provides the collaborative localization scheme for precise localization. Experimental results yielded by computer simulation and field test are reported in Section 5. Finally, the discussion and conclusion are given in the last section.

Suppose a WSN is composed of sensor nodes and reference nodes that are deployed in a given sensing field. The objective of this study is to provide accurate location information of the sensor nodes in WSNs. The coordinates of the reference nodes are assumed known

➢ _{1}, _{2}, …, _{num_S}_{1}, _{2}, …, _{num_R}

➢ Sensor nodes

➢ Physical positions of

➢ <_{i}_{j}_{i}_{j}_{i}

➢ Given that a network _{r}_{r}_{s}_{s}

In this study, all nodes

_{c}

Suppose that a sensor node _{s}_{s}_{r}_{r}_{<r, s>} is the measured distance between _{c}

The theoretical basis of RSSI measurements using the antenna configurations shown in _{r}_{s}_{r}_{s}_{r}_{r}_{s}_{s}_{r}_{s}_{r}_{s}_{s}_{<r, s>}, but also by the antenna orientations of

The spatial orientations of the antennas of _{s}

Many media and interfaces can function affect the polarization of the EM wave. According to the _{r}_{r}_{r}_{1} that has the normal vector _{1}. Again, _{r}_{r}_{2} that has the normal vector _{2}. The EM wave is scattered to all directions if it encounters small molecules of the air, known as the _{r}_{r}_{s}

According to the descriptions given above, we suppose that any existing interface in the natural environment functions as an action on the polarization vector (_{r}_{p}_{i}_{p}_{i}_{i}_{inc}_{i}_{i}_{i}_{ref}_{inc}_{a⃗r, a⃗′r} is the angle between _{r}_{r}_{a⃗r, a⃗′r} can be obtained as:

With the aforementioned formulation, we assume that an EM wave with the electric field _{0} is emitted from an antenna of a reference node. The antenna is horizontal oriented with a polarization vector parallel to the horizontal plane. All interfaces are randomly presented in the pseudo-space with random orientations. The EM wave uniformly propagates through the air and encounters a random number of interfaces. Assume here that there will be between 1 to 100 random incidence vectors. By performing a computer simulation, the amplitude of the electric field of the EM wave that its polarization vector (denoted by
_{h}_{0}. Since the antenna of the sensor node is vertically oriented, it can receive the multi-reflected EM wave with the polarization vector
^{−5} _{0}.

With the derivation given above, we assume that the orientations of incident surfaces existing in the natural environment are randomly oriented, the term
_{s}_{r}_{s}_{a}

Regarding the reflection coefficients Γ_{r}_{s}_{r}_{s}_{r}^{2}) · (1 – |Γ_{s}^{2}) in _{Γ}. In addition, the mediums in the path of signal propagation are mainly air. The attenuation coefficient ^{−1} according to [^{−αd〈r,s〉} can be completely reduced to a constant _{α}

The signal wavelength _{s}_{s}_{s}_{s}_{s}_{r}_{<r, s>} and _{r}

Therefore, the variables that are able to manipulate _{s}_{<r, s>} and _{r}_{s}_{Γ}·_{a}_{α}^{2}, and _{s}_{<r, s>}, _{r}_{r}_{s}_{<r, s>}, _{r}_{r}_{s}_{r}_{r}_{<r, s>} and _{r}

While the antenna of the reference node _{r}_{g}_{c}_{g}_{c}_{<}_{r}_{,} _{s}_{>}(_{r}_{r}_{r}_{<r, s>} + log

For an example given in _{r}_{<r, s>} = 10 m, and _{c}_{g}_{c}_{r}_{<}_{r}_{,} _{s}_{>}(_{<}_{r}_{,} _{s}_{>}(_{<r, s>} and

Assume that the RSSI patterns of any given paired nodes _{r}_{r}_{r}_{r}_{r}_{<}_{r}_{,} _{s}_{>}(_{r}

Given an unknown distance between _{<}_{r}_{,} _{s}_{>}(_{<}_{r}_{,} _{s}_{>}(_{r}_{r}_{<}_{r}_{,} _{s}_{>}(

Many well-known metrics (e.g., Euclidian distance, Pearson correlation) have been proposed for pattern matching. These metrics are proven effective in solving linear problems, but they do not work well in nonlinear cases, nor do they in handling data with outliers. While the distance between _{r}_{<}_{r}_{,} _{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(

First, we need to recognize that the RSSI patterns Ψ_{r}_{<}_{r}_{,}_{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(

Furthermore, we use a linear regression model to fit ▿Ψ_{r}_{<}_{r}_{,} _{s}_{>}(_{0}, _{1}, _{0} and _{1} are the intercept and slope of the regression line, respectively. Since the first-order derivative step neutralizes the baseline shift effect, the intercept _{0} can be removed from _{1}, ^{*} based on the Cauchy-Lorentz distribution function, the data points that fit well to the model in ^{*}, and the data points that do not fit well to the model give lower ^{*}. Consequently, the optimal slope _{1}(^{*}, iteratively. The goal of the robust correlation estimator is to estimate _{1} by maximizing the sum of ^{*}(_{1}, _{1} can be formulated as:

Since the value of _{1}(_{r}_{<}_{r}_{,} _{s}_{>}(_{1}(^{*}(▿Ψ_{r}_{<}_{r}_{,} _{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(_{r}_{<}_{r}_{,} _{s}_{>}(_{<}_{r}_{,} _{s}_{>}(_{r}

The localization problem now can be formulated by a maximum function as:
_{<}_{r}_{,} _{s}_{>} is the predicted distance between _{<}_{r}_{,} _{s}_{>} is the predicted angular direction of _{r}_{r}_{s}_{s}_{s}_{s}_{r}_{<}_{r}_{,} _{s}_{>}cos(_{<}_{r}_{,} _{s}_{>}), _{r}_{<}_{r}_{,} _{s}_{>}sin(_{<}_{r}_{,} _{s}_{>})). The robust correlation estimator proposed in this section can be used to analyze the similarity or dissimilarity of RSSI patterns in multidimensional space. It allows the network to locate the position of a sensor node through a fixed reference node.

The localization method proposed in Section 3 directly converts the problem into the framework of collaborative localization when multiple reference nodes are considered. Based on the result in

Suppose that there is a sensor node _{1}, _{2}, …, and _{n}_{i}_{i}_{i}_{〈ri, s〉}(_{i}, ω̂_{i}

We set the initial values in an overall solution space ℑ(_{ri}, _{ri}) is the coordinate of the reference node _{i}_{r}

After the overall solution space is obtained, we can determine the highest possible position of the sensor node _{s}_{s}

In this section, we evaluate the performance of the proposed RSS-based cooperative localization method using two examinations, computer simulations in MATLAB and real-world field experiments. In the computer simulation case, we compare the performance of the proposed method with the results published in [_{L}_{r}_{s}_{0} is the path loss at the reference distance when _{0} = 1, _{<r, s>} is the measured distance between _{g}

However, given the antenna configuration proposed in this study, the ordinary log-distance path loss model is insufficient to model the behavior of wave propagation between reference nodes and sensor nodes. Therefore, we modify the path loss model in _{〈ri, s〉} is formulated by Gaussian noise controlled by envelop amplitudes _{r}_{ri}), which is given as below:

Therefore, the interference model in _{ri}) of distinct reference nodes into consideration during the simulation study, which provides a more accurate channel-model than using Gaussian model as in [

In real world scenarios, the results yielded by the proposed algorithm are merely conducted from field measurements of RSSI patterns. Thereby, the actual parameter values in real-world scenarios are not required for the localization process using the proposed algorithm.

The radiation pattern of the antenna of _{r}_{<}_{r}_{,} _{s}_{>}(_{g}

For each sensor node, the reference node performs a complete measurement of the RSSI pattern by rotating the antenna, counterclockwise. The results yielded by the proposed algorithm are shown in

To further compare the performance of the proposed method with other quantitative techniques, multidimensional scaling (MDS), maximum-likelihood estimator (MLE), and hybrid of MDS and MLE (MDS-MLE) were applied to the same deployment structure. The results yielded by the proposed algorithm and different weighting methods in [

From the simulation results shown in

In this subsection, we apply the proposed algorithm to real-world scenarios using a WSN platform. The sensor nodes used in this study are Octopus II-A [

In order to simplify the problem, we connected an external antenna to each sensor node. The antenna is an omnidirectional 5 dBi high gain antenna (Maxim AN-05DW-S [

It is designed to support 2.4 GHz RF signals and the most popular protocols defined by IEEE 802.11b and 802.11g. The radiation patterns of the antenna in the H-plane and E-plane are depicted in

In real-world scenarios, it is impossible to construct a reference standard pattern for a reference node under all of the possible distances and orientations of the external antenna. We measured the values of RSSI when a sensor node is moved away from the reference node by five individual distances (1.8 m, 5 m, 10 m, 13 m, and 18 m).

In order to save electric energy of all sensor nodes, we measured the RSSIs when the azimuths of the external antennas of the reference node is 0°, 30°, 60°, …, and 330°. The cubic spline interpolation technique is used to predict the RSSI values at unmeasured azimuths. Base on these results, we used a 2nd order polynomial curve fitting model to identify the RSSI values at unmeasured distances. The constructed RSSI pattern is depicted in

First, we used the proposed algorithm to localize a sensor node in a single reference node scenario. The deployment arrangement is depicted in

In the two-reference nodes scenario, two reference nodes are deployed at individual coordinates (7.8, 0) and (−7.2, −5). The true position of the sensor node is at (3.5, 2.5). The deployment arrangement is depicted in

In addition, due to unknown environment conditions (e.g., standing electromagnetic waves, and electromagnetic absorption or interference), the reference standard RSSI pattern, as shown in

If we want to improve the localization accuracy obtained in two-reference nodes scenario, another reference node may be added at the coordinate (–1.5, 2.5). This leads a three-reference nodes scenario, as shown in

The association between the angular bias and the number of antenna rotation has been also examined. We have conducted the same experiments 50 times to estimate the average angular bias under different number of antenna rotations. The experimental results are depicted in

An RSSI-based collaborative localization method that makes use of the irregularity of the EM wave is proposed. First, we coupled external low-cost omnidirectional antennas with sensor nodes and reference nodes using specific antenna configurations. The antenna of the reference node rotates in the horizontal plane to measure the RSSI pattern between the sensor node and the reference node. A robust estimation technique is also presented to analyze the RSSI patterns obtained by the reference node. The RSSI pattern might involve some noise caused either by antenna specification or by environmental conditions. By using the proposed antenna configuration to generate multiple RSSI measurements, the signal-to-noise ratio of the RSSI pattern can be increased. The proposed algorithm is thus able to provide the localization results with higher precision. In addition, a collaborative localization scheme is presented to integrate the information obtained by multiple reference nodes.

The proposed algorithm has been evaluated through computer simulations and real-world experiments. Several algorithms (including MDS, MLE, and MDS-MLE) that use different weighting schemes are also applied to the same simulation cases. The simulation results show that the proposed algorithm outperforms these algorithms with estimation bias smaller than 1 m. The proposed algorithm is also examined in real-world scenarios using different number of reference nodes. The estimation bias is around 0.1 m, 1.14 m, and 0.2 m, respectively. Averaged estimation biases are also analyzed and reported.

Both computer simulations and real-world experiments have confirmed that the proposed algorithm is not perfect but it is a significantly advanced method than other ones. The proposed algorithm uses low-cost omnidirectional antennas to achieve accurate localization, and it does not require special information that can only be measured by special instruments (e.g., ultrasound devices, directional antennas) in order to localize a sensor node in the network. Finally, how to determine the speeds and 3-D locations of the moving sensor nodes and how to perform localization in the presence of security threats in WSNs, are left as our future works.

The authors are deeply grateful to Cheng-Shiou Ouyang for his great help in computer graphics. We are grateful to three anonymous referees for their invaluable suggestions to improve the paper. This work was financially supported in part by the President of National Taiwan University, the National Science Council of the Executive Yuan, and the Council of Agriculture of the Executive Yuan, Taiwan, under grants No.: 97R0533-2, NSC 96-2628-E-002-252-MY3, NSC 97-2218-E-002-006, NSC 97-3114-E-002-005, NSC 98-2218-E-002-039 and 98AS-6.1.5-FD-Z1, respectively.

Architecture of a given sample network _{1}, _{2}, _{3}}, _{1}, _{2}}, and _{1}, _{1}>, <_{1}, _{2}>, <_{2}, _{2}>, <_{2}, _{3}>}.

Schematic diagrams of the configurations used to couple external antennas and other peripheral circuits with (a) a sensor node and (b) a reference node.

Example of alteration of polarization state of an EM wave.

An example of RSSI measurement. (a) A pseudo scenario that consists of a sensor node

Examples of RSSI patterns. (a) Reference standard RSSI patterns Ψ_{r}_{<}_{r}_{,} _{s}_{>}(_{<}_{r}_{,} _{s}_{>}(_{r}

The radiation pattern of the antenna of

Actual locations of the deployed sensor nodes and the reference nodes, as compared to the estimated locations of the sensor nodes with (a) one rotation cycle and (b) two cycles of the antenna on the reference nodes.

Bias performance of the proposed algorithm and previously proposed methods (a) versus the number of grids and (b) versus the number of reference nodes.

Octopus II-A sensor node utilized in this study.

Specification of the omnidirectional antenna utilized in this study. (a) Maxim AN-05DW-S Antenna [

Testing environment of the experiment located on the campus of the National Taiwan University.

Reference standard RSSI pattern measured from the experiment in a real-world scenario, where the dash lines are obtained by 1,000 repeated experiments.

Experimental result for single reference node scenario. (a) Deployment arrangement of the sensor node and reference node in the scenario for single reference node. (b) Estimation result using the proposed robust correlation. The estimated coordinate of the sensor node is annotated by black cross (×).

Experimental result for two reference nodes scenario. (a) Deployment arrangements of the sensor node and the reference node in a scenario for two-reference nodes. (b) Overall solution space with coordinates of reference nodes (red circles

Experimental result for three reference nodes scenario. (a) Deployment arrangement of the sensor node and reference node in the scenario for three-reference nodes. (b) Overall solution space with coordinates of reference nodes (red circles ○) and estimated coordinate (white cross ×) of the sensor node.

(a) Average angular biases and (b) averaged distance errors yielded by the proposed algorithm versus different number of antenna rotations (cycle).

Simulation parameters.

Size of sensor field | 80 m × 80 m |

Number of grids | 8 |

Number of reference nodes | 4 |

Path-loss exponent |
3 |

Standard deviation of noise in Ω_{<}_{r}_{,} _{s}_{>}( |
6 dB |

First meter (_{0} = 1) RSS _{0} |
−30 dBm |

RSS detection threshold | −80 dBm |

Neighborhood selection threshold | −75 dBm |

Performance statistics of the proposed algorithm and different methods using previous proposed weighting schemes^{*}

MDS(W1) | 8.40 | 15.26 | 17.41 |

MDS(W2) | 12.23 | 10.96 | 16.42 |

MDS(W3) | 9.18 | 10.97 | 14.30 |

MDS(W4) | 9.03 | 12.8 | 15.67 |

MLE | 6.81 | 13.56 | 15.18 |

MDS(W1)-MLE | 5.93 | 12.39 | 13.73 |

MDS(W2)-MLE | 5.44 | 9.06 | 10.57 |

MDS(W3)-MLE | 4.68 | 8.89 | 10.05 |

MDS(W4)-MLE | 5.19 | 9.96 | 11.24 |

Proposed Method (1 cycle) | 1.89 | 1.31 | 3.75 |

Proposed Method (2 cycle) | 1.30 | 0.66 | 2.43 |

Results of the previous studies were reported in [