# A Low-Cost Collaborative Location Scheme with GNSS and RFID for the Internet of Things

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Radio Frequency Identification (RFID)-Based Location

#### 2.2. Low-Cost Location Scheme

#### 2.3. Deployment Method and Pattern

## 3. Collaborative Scheme with Global Navigation Satellite System (GNSS) and RFID Location

#### 3.1. System Overview

- The RFID reader measures the distance (d
_{i}) between the reader and the RFID tag attached to the target object when the RFID reader is moving, where i denotes the i-th location in RFID reader trajectory. - The RFID reader position (p
_{i}) is measured by the GNSS receiver, which is expressed as (x_{i}, y_{i}) for the coordinate values. - When the RFID reader is moving, two tuples (p
_{i}, d_{i}) are ready. When three or more tuples are prepared, the exact location of the target tag can be estimated according to the method shown in the following section.

_{1}, the RFID reader gets the distance d

_{1}and its position p

_{1}, then the tuple is (t

_{1}, p

_{1}, d

_{1}). When the reader is moving, the other tuples are obtained, such as (t

_{2}, p

_{2}, d

_{2}) and (t

_{3}, p

_{3}, d

_{3}). Finally, the coordinates of the tag are calculated based on these tuples.

#### 3.2. Tag-Location Principle

_{i}, p

_{i}, d

_{i}), where t

_{i}represents the locating time; p

_{i}is the position of the mobile RFID reader, using (x

_{i}, y

_{i}) denotes the coordinates value of the position p

_{i}at time t

_{i}. d

_{i}is measured by the RFID reader under the RFID ranging principle, which records the distance between the reader and the tag. The effective ranging distance is about 160 m, which may change with the surrounding conditions. Given the coordinates of the target tag as (x

_{p}, y

_{p}), this satisfies the following equation, where n denotes the n-th location:

_{1}shown in Figure 3a, which is a conflict of the reality that it has only one target tag at point p.

_{i}(i = 1, 2, 3,…), in which point P is ideally in the same position while the p

_{i}is different mainly for all triangles (as shown in Figure 3a). Therefore, p is the unique value of the target tag. As the mobile reader moves, we will obtain more numbers of the triangles, along with the coordinates of the target tag. However, due to measurement error, we will get a suite of possible positions of point p, as P, P’, and P’’ in Figure 3a. A simple arithmetic mean value is then taken to achieve the estimated position of p with Equation (3), wherein (x

_{p}, y

_{p}) denotes the coordinates of point p. The pseudo code of the tag localization algorithm is shown in Algorithm 1.

Algorithm 1. Tag localization algorithm | |

Input: reader location, distanceOutput: coordinate of target tag | |

1 | For each point in saved reader location points set do |

2 | set p_{i} = point coordinate of points set |

3 | set p_{i+1} = reader location |

4 | set d_{1} = distance between p_{i} and tag |

5 | set d = distance between p_{2}_{i} and p_{i+1} |

6 | set d_{3} = distance between p_{i+1} and tag |

7 | if (p_{i}, p_{i+1}, d_{1}, d_{2}, d_{3}) can build a triangle then |

8 | calculate the coordinate of target tag |

9 | add the coordinate to a candidate points set |

10 | else |

11 | continuous the next loop |

12 | end if |

13 | End for |

14 | Add (p_{i+1,} d_{3}) to reader location points set for next reader location calculate |

15 | For each coordinate of candidate points set do |

16 | Calculate the mean value of all points |

17 | End for |

#### 3.3. Optimization

Algorithm 2. Linear interpolation algorithm for reader location | |

Input: reader location, time, distance detection times arrayOutput: synchronous reader location array | |

1 | Set p_{s} = reader location started, t_{s} = start time |

2 | Set p_{d} = reader location ended, t_{d} = end time |

3 | # find the closest time from the distance points |

4 | Set deltaTstart = t_{0} − t_{s}, iIndexStart = 0 |

5 | Set deltaTend = t_{d} − t_{0}, iIndexEnd = 0 |

6 | For each time t_{i} of distance detection times array do |

7 | if t_{i} − t_{s} < deltaTstart then |

8 | set deltaTstart = t_{i} − t_{s} |

9 | set iIndexStart = i |

10 | end if |

11 | if t_{d} − t_{i} < deltaTend then |

12 | set deltaTend = t_{d} − t_{i} |

13 | set iIndexEnd = i |

14 | end if |

15 | End for |

16 | # Calculate the synchronous points |

17 | For each time t_{i} of distance detection times array do |

18 | p_{i} = p_{s} + (t_{i} − t_{s})/(t_{d} − t_{s}) × (p_{d} − p_{s}) |

19 | add p_{i} to synchronous reader location array |

20 | End for |

## 4. Experiment and Result

_{r}, y

_{r}) is the ground truth coordinates of the target object; (x

_{i}, y

_{i}) is the estimated coordinates; n is the triangle number; and ε represents the RME error. The smaller the ε is, the better the performance of the location scheme:

## 5. Discussion

#### 5.1. Low-Cost and Easy Deployment

#### 5.2. Location Determination Methods

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The hardware of the location system. (

**a**) Global Navigation Satellite System (GNSS) receiver; (

**b**) radio frequency identification (RFID) reader; (

**c**) RFID tags.

**Figure 3.**Proposed location algorithm. (

**a**) One triangle composed of three points, practical model of triangulation. Where, A, B, C, D are RFID reader position; P, P’, P” are candidate target tag location; the arc represents the mobile reader trajectory. (

**b**) Candidate points and estimated point.

**Figure 4.**Experimental devices and area. (

**a**) Overview of experimental area; (

**b**) overview of target object; (

**c**) experimental devices; (

**d**) detail of target object.

**Table 1.**The result of the experiment (where x

_{c}and y

_{c}denote the coordinates of this paper, for the concise description of the table, the digital prefix number is shown in the table headline).

Triangle Group ID | Triangle Number | x_{c} (m) | y_{c} (m) | Root Mean Error (m) | Triangle Group ID | Triangle Number | x_{c} (m) | y_{c} (m) | Root Mean Error (m) |
---|---|---|---|---|---|---|---|---|---|

b1 | 15 | 494,125.50 | 286,449.52 | 1.8215 | b26 | 184 | 494,126.21 | 286,449.35 | 1.1016 |

b2 | 24 | 494,125.47 | 286,449.52 | 1.8545 | b27 | 258 | 494,126.27 | 286,449.40 | 1.0447 |

b3 | 24 | 494,125.51 | 286,449.51 | 1.8205 | b28 | 192 | 494,126.39 | 286,449.44 | 0.9349 |

b4 | 42 | 494,125.60 | 286,449.49 | 1.7216 | b29 | 259 | 494,126.96 | 286,449.68 | 0.5216 |

b5 | 78 | 494,125.84 | 286,449.37 | 1.4762 | b30 | 174 | 494,127.61 | 286,450.28 | 1.0269 |

b6 | 67 | 494,125.88 | 286,449.32 | 1.4303 | b31 | 112 | 494,127.03 | 286,449.79 | 0.5772 |

b7 | 93 | 494,125.96 | 286,449.29 | 1.3482 | b32 | 200 | 494,126.97 | 286,449.69 | 0.5259 |

b8 | 96 | 494,126.33 | 286,449.20 | 0.9850 | b33 | 246 | 494,127.70 | 286,450.64 | 1.4010 |

b9 | 28 | 494,126.72 | 286,449.26 | 0.5963 | b34 | 203 | 494,127.63 | 286,450.65 | 1.3932 |

b10 | 84 | 494,126.93 | 286,449.27 | 0.3788 | b35 | 173 | 494,127.74 | 286,451.07 | 1.8299 |

b11 | 140 | 494,127.06 | 286,449.28 | 0.2500 | b36 | 268 | 494,127.60 | 286,451.29 | 2.0181 |

b12 | 144 | 494,127.27 | 286,449.32 | 0.0532 | b37 | 205 | 494,127.66 | 286,451.65 | 2.3832 |

b13 | 108 | 494,127.48 | 286,449.38 | 0.1929 | b38 | 73 | 494,127.99 | 286,452.10 | 2.8866 |

b14 | 129 | 494,127.80 | 286,449.52 | 0.5338 | b39 | 293 | 494,127.84 | 286,451.64 | 2.4099 |

b15 | 37 | 494,127.98 | 286,449.62 | 0.7472 | b40 | 184 | 494,128.07 | 286,451.53 | 2.3650 |

b16 | 72 | 494,127.97 | 286,449.73 | 0.7879 | b41 | 482 | 494,128.07 | 286,451.57 | 2.4019 |

b17 | 74 | 494,127.58 | 286,449.77 | 0.5453 | b42 | 93 | 494,128.05 | 286,451.66 | 2.4760 |

b18 | 156 | 494,127.48 | 286,449.74 | 0.4792 | b43 | 188 | 494,127.86 | 286,451.88 | 2.6478 |

b19 | 86 | 494,127.22 | 286,449.66 | 0.3827 | b44 | 258 | 494,127.86 | 286,451.88 | 2.6478 |

b20 | 40 | 494,126.96 | 286,449.58 | 0.4542 | b45 | 196 | 494,127.60 | 286,451.99 | 2.7157 |

b21 | 86 | 494,126.86 | 286,449.54 | 0.5181 | b46 | 450 | 494,127.59 | 286,451.97 | 2.6938 |

b22 | 86 | 494,126.60 | 286,449.46 | 0.7336 | b47 | 294 | 494,127.48 | 286,452.01 | 2.7256 |

b23 | 92 | 494,126.41 | 286,449.41 | 0.9043 | b48 | 188 | 494,127.28 | 286,451.93 | 2.6417 |

b24 | 123 | 494,126.35 | 286,449.39 | 0.9713 | b49 | 564 | 494,127.12 | 286,452.01 | 2.7276 |

b25 | 46 | 494,126.27 | 286,449.37 | 1.0478 | - | - | - | - | - |

Group number = 49; Average = 1.3904 m; maximum = 2.8866 m; minimum = 0.0532 m |

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## Share and Cite

**MDPI and ACS Style**

Jing, C.; Wang, S.; Wang, M.; Du, M.; Zhou, L.; Sun, T.; Wang, J.
A Low-Cost Collaborative Location Scheme with GNSS and RFID for the Internet of Things. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 180.
https://doi.org/10.3390/ijgi7050180

**AMA Style**

Jing C, Wang S, Wang M, Du M, Zhou L, Sun T, Wang J.
A Low-Cost Collaborative Location Scheme with GNSS and RFID for the Internet of Things. *ISPRS International Journal of Geo-Information*. 2018; 7(5):180.
https://doi.org/10.3390/ijgi7050180

**Chicago/Turabian Style**

Jing, Changfeng, Shouqing Wang, Mingshu Wang, Mingyi Du, Lei Zhou, Tiancheng Sun, and Jian Wang.
2018. "A Low-Cost Collaborative Location Scheme with GNSS and RFID for the Internet of Things" *ISPRS International Journal of Geo-Information* 7, no. 5: 180.
https://doi.org/10.3390/ijgi7050180