A novel iterative localization algorithm with high accuracy and low anchor node dependency for large-scale wireless sensor networks is proposed in this paper. At each iteration, blind nodes are located using a weighted linear least squares-based algorithm. To prevent errors in the blind nodes from propagating and accumulating throughout the network, an anchor geometric feature-based error control mechanism is used to select the nodes that participate in the localization and to estimate the localization confidence. The simulation results show that the algorithm can be used when only a few anchor nodes are involved. This algorithm is more advanced than traditional methods, which often require a large number of well-placed anchor nodes to operate appropriately. By optimizing the decision parameter

Wireless sensor networks (WSNs) are a basic component of the Internet of Things. Based on the development of mobile computing and embedded technologies, WSNs have been widely implemented in daily applications, such as health care monitoring, natural disaster prevention, and surveillance [

Various WSN localization approaches have been presented in the literature. Depending on the usage of the range information between nodes, node localization approaches can be classified into range-based localization and range-free localization. In a range-based localization method, the blind nodes estimate the distance to each anchor node and then estimate the location based on the distance to and position of the anchor nodes. Anchor nodes are a special type of sensor node with known locations, with the help of GPS, or are predeployed. Blind nodes are sensor nodes with unknown positions. To estimate distance, blind nodes use radio channel information, such as the received signal strength indicator (RSSI) [

Iterative node localization is a novel localization method that can decrease the dependence on anchor nodes by importing a blind node leveling-up scheme [

In this paper, we analyze the localization problem to reduce anchor node dependency in a large-scale WSN. A novel iterative localization algorithm with an anchor geometric feature-based error control mechanism is proposed. Compared with previous research that precisely modeled the localization error during each iteration, we formulate the error control problem as a classification problem. Based on node localization data under varying ratios of anchor nodes, RSSI variances, and radio communication ranges in a randomly deployed node environment, we characterize the localization condition by considering the number of anchor nodes, the anchor positions, the distance between the anchors and blind nodes, and the spatial distribution of anchors. Additionally, a one-class support vector decision-maker is trained based on the selected features. The simulation results show that the algorithm can be used when only a few anchor nodes are involved, which is more advanced than traditional methods that often require a large number of well-placed anchor nodes to work well. We evaluate the performance of our algorithm with different numbers of anchor nodes and RSSI variances. The results show that the algorithm efficiently solves the error propagation problem. The average localization error of the algorithm is approximately 0.43 meters when the percentage of anchor nodes is 1.25%, the RSSI variance is 8 dBm, and the radio range is 50 meters. The location accuracy is better than those of certain global localization methods, including MDS, SDP, and SPA. The efficiency of the proposed localization algorithm is evaluated in a real sensor network, and the accuracy is high and robust to radio channel variance.

The remainder of this paper is organized as follows. In Section

In this paper, we classify wireless sensor nodes as blind nodes, anchor nodes, pseudoanchor nodes, and reference nodes based on their localization duty. These names will be discussed in the following sections, and their respective duties are explained at the beginning of the paper. Anchor nodes are nodes that can access their absolute location at the beginning of the deployment. Blind nodes are nodes that do not know their location and attempt to estimate it based on the locations of the anchor nodes. A pseudoanchor node is a blind node that has an estimated location and is upgraded to an anchor node. The location of the pseudoanchor node always has an error, and the algorithm should be designed to stop the error from propagating throughout the network. The reference node is a node used by the blind node to locate itself. Both the anchor nodes and the pseudoanchor nodes can be used as reference nodes.

Many channel models have been proposed in the literature for indoor or outdoor localization applications [

RSSI model in the outdoor environment.

The distance

The localization problem finds the optimal

Searching methods require an initial estimate of the position, which is difficult in real environmental applications. Therefore, we prefer to translate the problem into a linear problem that can be solved with a least squares estimator. Based on the positions of the blind node and the references, the distance between them can be expressed as follows:

In a real RSSI-based localization system, the real distance between nodes is never obtained. Instead, a noisy distance estimation

Now, the position of the blind node is calculated as the least squares solution of (

The RSSI signal is sensitive to environmental interference. The linear least squares localization solution exhibits poor accuracy when the RSSI variance is increasing. To improve the localization accuracy, a weighted linear least squares estimator is introduced, in which the solution is weighted based on the variance of the distance estimation. The weighted linear least squares solution is expressed as follows:

The weighted linear least squares localization displays increased accuracy and robustness and less complexity than traditional methods.

Multilateration is infeasible when three references are collinear, and it is feasible when three references are not collinear [

Description of simulation parameters.

Parameter | Description | Default |
---|---|---|

Number of blind nodes | 380 | |

Number of anchor nodes | 20 | |

Number of initial pseudoanchors | 5 | |

Radio communication range | 30 m | |

RSSI variance | 1 dBm | |

Path loss at one meter | 32.6 dBm | |

Path loss exponent | 3.79 | |

OC-SVM kernel type | Linear | |

OC-SVM parameter nu | 0.1 | |

OC-SVM parameter epsilon | 0.001 |

Based on the localization results of the simulation, six typical localization situations for a single blind node with different numbers of anchor nodes are plotted in Figure

Estimation layouts for different anchor (neighbor) geometries. (a) Uncertain with 6 references; (b) uncertain with 10 references; (c) uncertain with 16 references; (d) stable with 6 references; (e) stable with 10 references; and (f) stable with 16 references.

As Figure

Localization error for different numbers of references.

Our observations show that the number of references and the reference geometric pattern significantly affect the localization accuracy. When the references are not evenly distributed around the blind node or when the number of references is less than the threshold, the localization results will exhibit considerable uncertainty. Therefore, we believe that the localization error can be predicted by characterizing the reference geometry.

The uncertain locations of the references, the distance estimation errors, and the reference geometry are the factors that affect the localization accuracy. These features can be used to predict the localization accuracy and inform the decision-making in the blind upgrading process.

The covariance matrix is used to describe the data distribution in a higher dimension, which is an extension of the variance. In our implementation, we construct the covariance matrix based on the coordinates of the references in a 2-dimensional plane. Given a blind node, let

When the spatial location of a set of references is located on a line,

To describe the uniformity of the references, we define two features

In addition to the previously proposed features, several basic data features used in classification applications are shown in Table

Signal features from the literature.

Feature | Description |
---|---|

Len() | Number of references |

Mean() | Mean value |

Std() | Standard deviation |

Max() | Largest value in a series |

Min() | Smallest value in a series |

Sma() | Signal magnitude area |

Energy() | Sum of squares divided by the number of values |

Entropy() | Signal entropy |

In total, 25 features are extracted, but some are irrelevant or redundant features. Therefore, feature selection and feature ranking are applied to identify the important features in the feature space. Feature selection methods can be classified as the wrapper method, the embedded method, and the filter method. In this paper, we apply a two-stage feature selection procedure. First, the maximal information coefficient (MIC) is used to score each feature. Then, the 10 best features are selected to form a feature subset, and a recursive feature elimination (RFE) method is used to select the 4 best features from the subset. The MIC is a measure of the strength of the linear relationship between two variables

MIC scores for 25 different features.

The 10 best features with their corresponding ranks are shown in Table

Rank of the 10 best features.

Rank | 1 | 2 | 3 | 4 | 5 |

Name | ALR | ALS | pLen | ALC | dEng |

Rank | 6 | 7 | 8 | 9 | 10 |

Name | ySma | dEntr | yEng | xEng | yMin |

Classification accuracy for different feature combinations.

Accuracy | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

0.843 | × | × | × | × | ||||||

0.839 | × | × | × | × | ||||||

0.835 | × | × | × | × | ||||||

0.636 | × | × | × | × | ||||||

0.645 | × | × | × | × | ||||||

0.649 | × | × | × | × |

As previously noted, in a large-scale WSN localization problem, the percentage of anchor nodes is expected to be small, which results in a situation in which a small percentage of blind nodes can directly communicate with the anchor nodes. However, none of the blind nodes in the network may be able to find at least three anchor nodes to derive a location. To overcome this problem, a two-phase localization algorithm that includes the initialization phase and the error control phase is proposed.

Considering the small number of anchor nodes, the initialization algorithm will find a series of pseudoanchor nodes and estimate their positions based on a distance vector-hop (DV-hop) [

By determining the hop information associated with each anchor node, a blind node estimates the distances by multiplying the hop information by a shared average hop distance metric. The DV-hop distance estimation suffers from large error compared with those of channel model-based methods because the localization error of the DV-hop estimation process is large. Therefore, multiple blind nodes are selected as pseudoanchor nodes in the initialization phase. The blind nodes in the one-hop range of each anchor node are the best choices of pseudoanchor nodes because one reference distance can be estimated based on the channel model. Given the one-hop neighbors of an anchor, the blind nodes are sorted by their distance to the anchor node, and the nearest

NeighborInfo Packet _{1}_{n_init}}

Neighbor RSSI List _{i}_{i}]

Neighbor Distance List _{i}_{i}]

1: send an

2:

3:

4: parse the

5: obtain the

6:

7: append

8: reset the timer

9:

10: pass

11:

12:

13: estimate _{i}_{i}

14: append _{i}_{i}]

15:

16: sort _{i}

17:

18: set

19:

20: set

21: send an

NeighborInfo Packet _{1}_{n_init}}

Anchor HopInfo List

_{i}_{i}_{i}]

Neighbor Distance List _{i}_{i}]

1:

2: parse the

3:

4:

5:

6:

7: append

8: send an

9:

10: record

11:

12: parse the

13:

14:

15: estimate _{i}

16: estimate the position of _{i}

17: change node type to pseudo-anchor

In an iterative localization scenario, the position of a pseudoanchor node is uncertain. This positional error may further affect the localization of the other nodes and increase the localization error, which represents the problem of error propagation in an iterative localization scenario. Therefore, an error control procedure must be implemented to improve the localization performance. In this paper, we use an error control method based on the neighboring geometric features of the target. The features used to estimate the localization confidence are discussed in Section

Blind node

After discovering the current geometric features, a one-class support vector classifier is used for the localization decision. Conventional binary classification methods require both positive and negative training samples. However, guaranteeing that most of the negative states are included in the training is difficult. The OC-SVM differs from traditional classifiers in that only one class of training samples is required. The OC-SVM has demonstrated good performance for anomaly and fault detection.

By detecting anomalies during location estimation, we treat the error control problem as a one-class classification problem in which the OC-SVM is used with a linear kernel to detect good reference geometries and reject the others. The OC-SVM maps the input samples to a high-dimensional feature space with a kernel function and then searches for a hyperplane to separate the mapping points from the origin (in this feature space) [

If

The node Type of current node

Location Packet

Reference List _{i}_{i}_{i}]

Localization Confidence Score

Estimated Position

Confidence List

Localization Decision

1: send an

2:

3: parse the

4: obtain the

5:

6: obtain distance estimation

7: append

8:

9: calculate current geometric features via Eqs. (

10: calculate the

11:

12: input the features to one-class SVM classifier to

obtain a decision result

13:

14: estimate the location of current node

Eq. (

15: change the type of current node to pseudo-anchor

16: append [

In this section, the localization algorithm described above is validated with a simulation experiment. First, we conduct a simulation in a grid sensor deployment that directly assesses the performance of the error control. Then, we further examine the algorithm performance in different environmental conditions for a randomly deployed sensor arrangement, including the number of anchor nodes, radio communication range, and RSSI variance. Finally, we compare the proposed algorithm to several global localization methods.

In the simulation, 400 sensor nodes are deployed in a 2D square environment with an edge length equal to 200 meters. The details of the simulation parameters are shown in Table

The localization error in a 2D plane is defined as follows:

The relative localization error is defined as follows:

The Cramer-Rao lower bound derived in [

Figure

Localization error heat map with four different numbers of anchor nodes: (a) 3 anchor nodes are set and (b) 10 anchor nodes are set.

3 anchor nodes

10 anchor nodes

As the figure shows, in the 100% stage, all the blind nodes in the network are located for each scheme, and the localization error is less than two meters, with the exception of a node in the corner of scheme (a). The localization starts from the neighborhood of the anchor nodes and then spreads all over the network. Certain blind nodes that have large localization error in the early stage exhibit a good localization result by the end of the localization. During the localization, a blind node with a bad localization result can be found and relocated with a better reference combination, thereby representing the effect of the proposed error control method. This method recognizes a bad localization condition based on the geometric features of the anchor node and improves the localization result by selecting a good reference combination.

The localization results shown in Section

Performance of parameter

Figure

CDF for different numbers of anchor nodes when error control is used or not used.

Equation (

Performance of RSSI variance

Finally, we compare the proposed algorithm with several global localization algorithms for varying numbers of anchor nodes. These localization algorithms are MDS [

Comparison of the performance of different algorithms with different numbers of anchor nodes.

Accuracy of the different localization algorithms.

In this section, we conduct some experimental analyses to evaluate the efficiency of the proposed localization algorithm based on a real WSN deployed in an outdoor football field. There are two stages in the experiment. In the first stage, we deploy a sensor network with only one blind node to test the efficiency of the weighted least squares position estimator. In the second stage, a multihop sensor network is deployed to test the efficiency of the proposed localization algorithm with error control.

The sensor nodes are based on a TI CC2650 wireless radio transceiver, which runs a TI-RTOS real-time embedded system and is powered by a 4800 mAh battery bank. A 2.4 GHz whip antenna is attached to the sensor nodes, and the nodes are synchronized by an FTSP time synchronization algorithm.

In this experiment, four sensor nodes working as anchor nodes are deployed at the vertexes of a square, which are indicated by the blue circles in Figure

Deployment area in the position estimation experiment.

Figure

Average localization error for each test point with different estimation methods.

Figures

Average localization error for different values of

Average localization error for different values of

In the second experiment, we deploy 16 sensor nodes in a 4 × 4 square grid area, as shown in Figure

Deployment area in the iterative localization experiment.

Experimental schemes.

Scheme | Anchor ID | Anchor ID | Anchor ID | Anchor ID |
---|---|---|---|---|

T1 | 1 | 2 | 5 | × |

T2 | 1 | 2 | 3 | × |

T3 | 1 | 4 | 13 | × |

T4 | 1 | 10 | 16 | × |

T5 | 7 | 10 | 11 | × |

F1 | 1 | 2 | 5 | 6 |

F2 | 1 | 4 | 13 | 16 |

F3 | 1 | 2 | 3 | 4 |

F4 | 1 | 7 | 10 | 16 |

F5 | 6 | 7 | 10 | 11 |

During the experiments, the sensor nodes run the localization algorithm introduced in Section

The distance estimation accuracy is important for the proposed localization algorithm. For the given deployments of the sensor network, the real distances between sensor nodes are 10 m, 14 m, 20 m, 22 m, 28 m, 30 m, 32 m, 36 m, and 42 m. During the experiment, the distance estimation results of the sensor nodes are collected, and the estimation errors are shown in Figure

Average distance estimation error.

The localization errors of all the schemes listed in Table

Localization results for different schemes.

Scheme | Average error | Error variance |
---|---|---|

T1 | 0.62 | 0.38 |

T2 | 2.31 | 1.41 |

T3 | 1.43 | 0.6 |

T4 | 1.83 | 1.24 |

T5 | 0.67 | 0.43 |

F1 | 0.61 | 0.36 |

F2 | 0.47 | 0.35 |

F3 | 2.38 | 1.28 |

F4 | 1.71 | 1.11 |

F5 | 0.8 | 0.41 |

Total | 0.8 | 0.41 |

In some applications of WSNs, the computational ability is constrained, which requires the localization to be performed on chip. Computational complexity, which is defined as the number of operations performed by the algorithm, is used to evaluate the possibility of chip implementation.

The proposed localization algorithm has three parts, which are presented in Algorithms

This paper presents a novel iterative localization algorithm that mitigates the effects of error propagation with an anchor geometric feature-based error control mechanism. The advantage of this approach is that it can be used when only a few anchor nodes are involved. Traditional methods often require a large number of well-placed anchor nodes to work well; this limitation is overcome by using a combination of DV-hop localization and a novel error control mechanism. First, we analyze the geometric relationships between the blind node and the anchor nodes. Several features are proposed to describe the geometric features. Then, an OC-SVM-based decision machine is trained to select a good localization condition for the blind node. The performance of the algorithm is assessed by simulation experiments as well as real-life outdoor experiments, and the results show that the localization accuracy is improved compared with that of several global localization methods.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (11402121).