^{1,2}

^{1,2}

^{1,2}

^{1,3}

^{1,3}

^{1}

^{2}

^{3}

In the wireless sensor network (WSN) localization methods based on Received Signal Strength Indicator (RSSI), it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.

Generally, two steps are needed for the wireless sensor networks (WSN) localization algorithm to estimate the location of an unknown node based on the Received Signal Strength Indicator (RSSI) [

However, the preliminary environmental test is a very complicated process that requires large amounts of experimental works. Besides, the preliminary test must be taken in a fixed localization environment. In case of any changes in the communication environment, the parameters in the radio signal propagation model would change along location information which plays an important role in location-based service application system, leading to error increment to the distance estimated upon RSSI value or the original model becoming not applicable any more. The factors affecting the environment usually include temperature, humidity, interference, and non-line-of-sight (NLOS) [

In consideration of this, an analysis was given to the working process of self-adaptive localization algorithm. It was found that the propagation parameters in the radio signal propagation model became linear after the model was taken from the logarithm, and the computational amount could be reduced significantly using the least square method. Hence, this paper proposes the least square-based self-adaptive WSN localization method.

In this section, the system flow of the least square-based self-adaptive localization method is presented before every part is elaborated.

In the proposed self-adaptive localization algorithm, initialization is given firstly, including parameter initialization and representation of RSSI in probability density, before self-adaptive localization is performed iteratively. It is divided into two steps. The first step is to estimate the location of the unknown node and the second step is to estimate the parameter in the propagation model. Graphically, the workflow of the proposed least square-based self-adaptive localization method is illustrated in Figure

Workflow of least square-based self-adaptive localization method.

The parameter initialization in Figure

In the traditional RSSI-based localization method, a path loss model is established for mapping between RSSI and distance

Make a transformation to (

Now, the mean received signal strength

If the communication distance

And then, it is required to work out the joint probability corresponding to the total signal strength at the unknown node receiving from

If every unknown node is estimated separately, then different nodes might give different

If the joint probability density is expressed with likelihood function

When the log likelihood function

We work out (

To obtain the values of

With least square optimization criterion, we can obtain the optimal solution shown as (

The calculated values of

Where the least square optimization criterion is different from maximum likelihood criterion, as in maximum likelihood criterion, the

Computational complexity is an average measurement of calculated quantity of processing method via pseudocode. And from analysis, the computational complexity of least square-based self-adaptive localization method is

If we equate

In this section, the performance of the least square-based WSN self-adaptive localization algorithm will be evaluated and analyzed in comparison with that of the maximum likelihood-based self-adaptive localization algorithm [

The simulation environment is a 3.2 m × 3.2 m area, where 4 anchor nodes are positioned at the four vertexes and unknown nodes move horizontally and vertically at intervals of 0.8 m to establish a total of 25 fixed points, as shown in Figure

The localization field.

The computation platform used in the process of evaluation is parameterized as follows: CPU, i7 720QM@1.6 GHz, RAM, 4 GB, operating system, Windows XP Professional SP3, and evaluation software, Matlab 7.5.

Use the

Firstly, the proposed self-adaptive localization algorithm will be evaluated in terms of localization accuracy and convergence, and a performance analysis will be given to the proposed algorithm in comparison with other algorithms; finally, different self-adaptive localization algorithms will be compared in terms of processing time.

Use both the maximum likelihood-based self-adaptive localization algorithm [^{−3} and 1 × 10^{−3}, respectively. The iteration times are set to 10, 20, 30, 200, and 1000, respectively, and the distribution model of the background white noise is set to variance

Localization errors using maximum likelihood-based self-adaptive localization method.

Error/m | 10 times | 20 times | 30 times | 200 times | 1000 times |
---|---|---|---|---|---|

Variance |
1.30 m | 1.28 m | 1.25 m | 0.93 m | 0.82 m |

Variance |
1.33 m | 1.30 m | 1.28 m | 1.11 m | 0.98 m |

Localization errors using the least square-based self-adaptive localization method (proposed).

Error/m | 10 times | 20 times | 30 times | 200 times | 1000 times |
---|---|---|---|---|---|

Variance |
0.97 m | 0.94 m | 0.90 m | 0.29 m | 0.33 m |

Variance |
0.65 m | 0.34 m | 0.31 m | 0.56 m | 0.56 m |

As shown in Tables

After iterating 1000 times with the maximum likelihood-based self-adaptive localization method, the localization errors at all the fixed points are shown in Figures

Localization error of self-adaptive localization methods with (0, 0.2) noise.

Maximum likelihood-based self-adaptive localization

Least square-based self-adaptive localization

Localization error of self-adaptive localization methods with (0,

Maximum likelihood-based self-adaptive localization

Least square-based self-adaptive localization

As shown in Figures

Table

Localization errors of different localization methods.

Sample points | 10 | 20 | 30 | 200 | 1000 |
---|---|---|---|---|---|

MCL | 1.38 m | 1.21 m | 1.13 m | 0.93 m | 0.87 m |

MCLS | 1.19 m | 1.13 m | 1.08 m | 0.89 m | 0.82 m |

GPLA | 0.98 m | 0.97 m | 0.95 m | 0.31 m | 0.30 m |

Least square-based self-adaptive (proposed) | 0.65 m | 0.34 m | 0.31 m | 0.56 m | 0.56 m |

Table

To further evaluate the performance of the least square-based self-adaptive localization method, a comparison was given in terms of localization error after 1000 iteration times between the least square-based self-adaptive localization method and the original and modified Bound-box localization algorithms [

Comparison between least square-based adaptive localization method and Bounding-box-based localization methods.

Error/m | B-box | Weighted B-box | 3-point centroid B-box | 3-point weighted centroid B-box | Least square-based self-adaptive (proposed) |
---|---|---|---|---|---|

Variance |
0.35 m | 0.28 m | 0.45 m | 0.45 m | 0.33 m |

Variance |
0.34 m | 0.23 m | 0.44 m | 0.44 m | 0.56 m |

In Bounding-box (B-box for simplicity), the centroid of the overlap region among different communication ranges is treated as location estimation value. Considering different contributions of each distance estimation value, the weighted Bounding-box was proposed to improve the location accuracy, where the weighted values are the reciprocal of distance estimation values. In the 3-point centroid Bounding-box method, three anchor nodes are selected from four anchor nodes, and we get four groups of anchor nodes and their corresponding location estimation values; then we treat the mean of the four location estimation values as the final location estimation result. And the 3-point weighted centroid Bound-box is the weighted improved version of 3-point centroid Bound-box, where the weighted value is the reciprocal of the sum of the values of three distances in each group.

As shown in Table

Location error convergence is the property that location errors of different iteration stages have the same tendency to the zero end state; that is, with the increment of iteration number, the value of location error gets smaller and smaller. We conducted an analysis of location error convergence to evaluate the convergence speed of different location methods.

After iterating 1000 times with the maximum likelihood-based self-adaptive localization method, the convergence results of localization errors at the 25 fixed points within the localization area are shown in Tables

Localization error convergence graphs of different location method with (0,

Serial number of unknown node | Localization error convergence (iteration times) | |
---|---|---|

Maximum likelihood-based self-adaptive | Least square-based self-adaptive (proposed) | |

1 | 150 | 120 |

2 | 1200 | 300 |

3 | No convergence | 400 |

4 | 1100 | 270 |

5 | 160 | 150 |

6 | 1000 | 275 |

7 | 8000 | 180 |

8 | No convergence | No convergence |

9 | 8000 | 370 |

10 | 1100 | 250 |

11 | No convergence | 8000 |

12 | No convergence | No convergence |

13 | No convergence | No convergence |

14 | No convergence | 700 |

15 | No convergence | No convergence |

16 | 1100 | 200 |

17 | 8000 | 280 |

18 | No convergence | No convergence |

19 | 8000 | 300 |

20 | 1200 | 220 |

21 | 100 | 100 |

22 | 1100 | 200 |

23 | No convergence | 480 |

24 | 1200 | 200 |

25 | 130 | 120 |

Localization error convergence graphs of different location method with (0, 0.2) noise.

Serial number of unknown node | Localization error convergence (iteration times) | |
---|---|---|

Maximum likelihood-based self-adaptive | Least square-based self-adaptive (proposed) | |

1 | 15 | 20 |

2 | 400 | 30 |

3 | No convergence | 100 |

4 | 400 | 60 |

5 | 15 | 5 |

6 | 4000 | 40 |

7 | 8000 | 60 |

8 | No convergence | 100 |

9 | 8000 | 90 |

10 | 400 | 15 |

11 | 15 | 90 |

12 | 15 | 100 |

13 | 15 | No convergence |

14 | No convergence | 100 |

15 | 15 | 60 |

16 | 4000 | 50 |

17 | 6000 | 60 |

18 | 6000 | 100 |

19 | 7000 | 100 |

20 | 400 | 40 |

21 | No convergence | 5 |

22 | 8000 | 20 |

23 | 15 | 100 |

24 | 5000 | 120 |

25 | 15 | 5 |

As shown in Tables

As the computational complexity of Monte Carlo-based localization method and self-adaptive localization method is the same, we analyze more detail; that is, we compare the processing times.

Tables

Processing time of maximum likelihood-based self-adaptive localization method.

Time/s | 10 times | 20 times | 30 times | 200 times | 1000 times |
---|---|---|---|---|---|

Variance |
12.75 s | 18.71 s | 23.15 s | 205.30 s | 1087.13 s |

Variance |
11.59 s | 22.97 s | 28.84 s | 212.64 s | 1058.04 s |

Processing time of the least square-based self-adaptive localization method (proposed).

Time/s | 10 times | 20 times | 30 times | 200 times | 1000 times |
---|---|---|---|---|---|

Variance |
3.04 s | 5.18 s | 7.21 s | 44.04 s | 134.77 s |

Variance |
4.17 s | 6.79 s | 9.43 s | 28.47 s | 28.64 s |

As shown in Tables

Table

Localization processing time of different localization methods.

Sample points | 10 | 20 | 30 | 200 | 1000 |
---|---|---|---|---|---|

MCL | 0.9 s | 1.7 s | 2.5 s | 17.3 s | 90.3 s |

MCLS | 1.1 s | 2.1 s | 3.4 s | 21.9 s | 112 s |

GPLA | 1.3 s | 2.5 s | 3.9 s | 25.1 s | 132 s |

Least square-based self-adaptive (proposed) | 4.17 s | 6.79 s | 9.43 s | 28.47 s | 28.64 s |

Table

To sum up, the simulation results show that the proposed least square-based self-adaptive localization algorithm has definite advantages over the maximum likelihood-based self-adaptive localization algorithm in terms of both localization accuracy and localization processing time. Considering the fact that the nodes in a wireless sensor network are still, the environment changes relatively slowly and the signal attenuation parameter varies slowly with time in the communication environment; it is believed that the proposed least square-based self-adaptive localization method is capable of satisfying the typical dynamic localization requirement.

The traditional WSN localization method requires a preliminary environmental test to determine the radio signal propagation parameters, leading to a complex localization process, highly experimental workload, and poor environment adaptability. In view of these weaknesses, this paper proposes a least square-based WSN self-adaptive localization method. Using least square technique and iteration strategy to estimate the radio parameters, this method not only reduces the computational amount in the localization process but also improves the localization accuracy. It provides methodological and technical means for the dynamic localization applications.

It is requisite for a self-adaptive localization method to be finally applied into an actual WSN localization system. For this reason, the proposed localization method is going to be demonstrated and evaluated in the true WSN localization environment.

The authors declare that they have no competing interests.

This work is funded by National Natural Science Foundation of China (61601142 and 61671174), space support technology fund projects (2014-HT-HGD5), Natural Science Foundation of Shandong Province of China (ZR2015FM027), State Key Laboratory of Geo-information Engineering (no. SKLGIE2014-M-2-4), State Key Laboratory of Satellite Navigation System and Equipment Technology, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ14205 and YQ15203), and Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.201721).