# A Method for UWB Localization Based on CNN-SVM and Hybrid Locating Algorithm

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## Abstract

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## 1. Introduction

- (i)
- A complete method is proposed for NLOS/LOS classification and NLOS identification and mitigation, and a final accurate UWB coordinate solution is proposed through the integration of two machine learning algorithms and a hybrid localization algorithm, which can effectively mitigate signal propagation errors in indoor positioning and communication under strong NLOS interference. We call this innovative algorithm the C-T-CNN-SVM algorithm, which consists of three basic processes: an LOS/NLOS signal classification method based on SVM, an NLOS signal recognition and error elimination method based on CNN, and an accurate coordinate solution based on the hybrid weighting of the Chan–Taylor method.
- (ii)
- After LOS/NLOS signal classification based on SVM and the CNN-based method for NLOS signal recognition and error elimination, using the testing data set and focusing on four main prediction errors (range measurements, maxNoise, stdNoise and rangeError), the standard deviation decreases from 13.65 cm to 4.35 cm, while the mean error decreases from 3.65 cm to 0.27 cm, and the errors are practically distributed normally, which demonstrates that after training a CNN for NLOS recognition and performing NLOS mitigation, the accuracy of UWB range measurements may be greatly increased.
- (iii)
- During the final accurate UWB coordinate solution based on the hybrid weighting of the Chan and Taylor algorithms, using a total number of 648 testing data sets that vary in the percentage of LOS and NLOS signals, after target positioning, this method can realize a one-dimensional X-axis and Y-axis accuracy within 175 mm and a Z-axis accuracy within 200 mm; a 2D ($X,Y$) accuracy within 200 mm; and a 3D accuracy within 200 mm, most of which fall within (100 mm, 100 mm, 100 mm).
- (iv)
- Compared with the traditional Chan algorithm, Taylor algorithm, and intersection algorithm error, the proposed C-T-CNN-SVM algorithm performs better in location accuracy, cumulative error probability (CDF), and root-mean-square difference (RMSE): the 1D, 2D, and 3D accuracy of the proposed method is 2.5 times that of the traditional methods; when the location error is less than 10 cm, the CDF of the proposed algorithm only reaches $0.17$, while that of the four-side intersection algorithm is as high as $0.85$. When the positioning error reaches 30 cm, only the CDF of the proposed algorithm remains in an acceptable range; the RMSE of the proposed algorithm remains ideal when the distance error is greater than 30 cm, while that of the traditional algorithms grow very large when the distance error exceeds 10 cm.
- (v)
- The research result of this paper and the idea of a combination of machine learning methods with the classical locating algorithms for an improved UWB positioning under NLOS interference could meet the growing need for wireless indoor locating and communication, which indicates the possibility for the practical deployment of such a method in the future.

- (i)
- As stated in Section 2, we first create the UWB positioning model. From there, we investigate the NLOS error in the model and introduce standard UWB algorithms as well as the SVM and CNN technology that will be used in our method.
- (ii)
- The C-T-CNN-SVM algorithm, a particular UWB positioning technique, is described in detail in Section 3. It is separated into three sections: LOS/NLOS signal classification based on SVM, NLOS signal recognition and classification based on CNN, and final accurate UWB localization based on a hybrid locating algorithm.
- (iii)
- In Section 4, performance analysis and experimental findings are presented.
- (iv)
- Final remarks can be found in Section 5.

## 2. System Model, Assumptions and Notations

#### 2.1. The Overall Model of Accurate UWB Localization

#### 2.2. UWB Model Studied in This Paper

**transmitter**is the component that sends the TOF ranging signal, while the

**receiving end**is the component that receives the ranging signal and requires the UWB location. The arrows in the diagram merely show the general direction of sending and returning TOF signals, not their exact directions.

#### 2.3. The NLOS Propogation Error Model in UWB

**NLOS error**. Additionally, the true linear path between nodes will not be followed by the signal propagation path. In order to fully study the pattern characteristics of anomalous data in the TOF range data set, NLOS error is briefly examined in this paper.

#### 2.4. Traditional UWB Ranging Method of Quadrilateral Location Algorithm

**N edge location algorithm**(N is the number of anchors) is typically used in the conventional geometric location procedure. The target node position is determined by the intersection of the radius of the measured distance between the anchor node and the target node and the centers of K anchor nodes.

#### 2.5. UWB Ranging Method of Chan and Taylor Algorithm

#### 2.6. Machine Learning-Based Ideas for UWB Localization

#### 2.6.1. Technology of SVM

#### 2.6.2. Technology of CNN

#### 2.7. Assumptions

- (i)
- There is no other interference in the collected data other than that stated in the paper;
- (ii)
- Only the TOF-based ranging principle is considered;
- (iii)
- It is assumed that all interferences in the experimental design are of the same prototype;
- (iv)
- The effect of all interferences in the experimental design on the collected data remains stable.

#### 2.8. Notations

## 3. Methods

#### 3.1. Total Flow of C-T-CNN-SVM Algorithm

**LOS/NLOS signal classification method based on SVM**, an

**NLOS signal recognition and error elimination method based on CNN**, and an

**accurate coordinate solution based on C-T hybrid weighting**. The following section of this study refers to this innovative algorithm as the

**C-T-CNN-SVM algorithm**, which is based on the primary procedures and techniques we use.

- (i)
- Firstly, SVM-based signal classification is used to distinguish between LOS and NLOS signals. The following stage for NLOS signal detection and error eradication will use the results as input.
- (ii)
- Next, a CNN-based approach for recognizing and mitigating NLOS signals is proposed, which draws on the concept of neural network pattern recognition.
- (iii)
- Following error correction, the UWB signal data will be sent into the following hybrid weighting algorithm, which uses the Chan algorithm to calculate the initial coordinates and the Taylor algorithm to calculate the final coordinates. The specific coordinates of the target point are solved by dividing the weights of these two algorithms.

#### 3.2. LOS/NLOS Signal Classification Based on SVM

#### 3.3. CNN-Based Method for NLOS Signal Recognition and Error Elimination

**convolutional neural network (CNN)**. Our CNN will first adequately learn data sets of recognized UWB signal patterns (known as

**LOS, NLOS, and mixed NLOS-LOS**). Following training, the CNN will identify patterns in the input data set utilized for precise UWB positioning before performing error reduction.

**sigmoid hidden neurons**and

**softmax output neurons**. The

**proportional conjugate gradient back propagation function**will train the neural network.

#### 3.3.1. NLOS Signal Recognition

**Step 1: Selection of training and recognition data sets.**

**Step 2: Setting up the training, validation, and test data sets.**

**Step 3: Building a neural network.**

**Step 4: Training neural networks.**

**Step 5: Evaluation of the neural network.**

**Step 6: Recognizing NLOS signal patterns for target data sets.**

#### 3.3.2. NLOS Error Mitigation

#### 3.4. Final Accurate UWB Coordinate Solution Based on Hybrid Weighting of Chan and Taylor Algorithm

#### 3.4.1. Target Coordinate Preliminary Solution Using Chan Algorithm

**Step 1**

**Step 2**

**Chan algorithm-based preliminary solution of the target coordinates**is finished.

#### 3.4.2. Taylor Series-Based Technique for the Accurate Coordinate Solution of the Anchor Point

#### 3.4.3. Final Determination of Anchor Coordinates Based on Chan–Taylor Mixed Weighting Method

## 4. Experiment and Analysis

#### 4.1. Analysis of NLOS Mitigation Performance

#### 4.2. Accuracy Analysis of the Algorithms

#### 4.2.1. 1D Accuracy Analysis of the Algorithms

- (i)
- It can be seen from Figure 10 that, under the model in this paper, the one-dimensional error after target positioning is within 175 mm on the X-axis and Y-axis. The X-axis error of normal data sets is generally less than 60 mm, and the Y-axis error is generally less than 75 mm. The error of the X-axis and Y-axis of an abnormal data set is generally less than 100 mm. The Z-axis error is larger than that of the X-axis and Y-axis, but generally less than 200 mm.
- (ii)
- For comparison, although the coordinate error obtained by the traditional model is within 200 mm under most data sets, it has an abnormal error as high as 600 mm. In terms of Y-axis error, compared with the C-T-CNN-SVM model, although the error of the traditional model is within 500 mm under most data sets, there exists an abnormal result of 1000 mm. In terms of Z-axis error, the coordinate errors obtained by the traditional model are all within 200 mm under most data sets, though there remains an error of 500 mm.

#### 4.2.2. 2D Accuracy Analysis of the Algorithms

#### 4.2.3. 3D Accuracy Analysis of the Algorithms

#### 4.3. Validity Analysis of the Algorithms

#### 4.3.1. Cumulative Error Probability Analysis of the Algorithms

#### 4.3.2. Root-Mean-Square Difference Analysis of the Algorithms

#### 4.4. Complexity Analysis of the Proposed Algorithm

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**NLOS problem: In the absence of LOS in TOF-based ranging between MN and AP, the estimated range is larger than the true distance.

**Figure 9.**Comparison of NLOS mitigation performance between the proposed and other state-of-the-art algorithms.

**Figure 19.**Relation curve between root-mean-square distribution and location error of each algorithm.

Symbols | Description |
---|---|

c | The electromagnetic wave propagation speed |

${T}_{f}$ | One-way flight time for TOF ranging |

${A}_{\mathrm{i}-1}({x}_{i},{y}_{i},{z}_{i})(i=1,2,3,4)$ | Anchor point |

e | Error threshold |

$d\_Assemble$ | Data set to be processed |

${d}_{i}(i=1,2,3,4)$ | Distance measurements of anchor to target |

X | Set of machine learning samples |

$\Phi $ | Non-linear mapping |

${X}_{i}$ | Input vectors for machine learning samples |

$(x,y,z)$ | Coordinates of the target point to be located |

${Z}_{p}=\phantom{\rule{3.33333pt}{0ex}}{[x,y,z]}^{T}$ | Position of the target to be located in the hybrid weighting algorithm |

$\psi $ | Error vector of the hybrid weighting algorithm |

Q | Covariance matrix of TOF range values |

$\left(x\right(k),y(k),z(k\left)\right)$ | Coordinates of the target point calculated using the kth method |

${r}_{i,1}\left(k\right)$ | Difference between coordinates of target point to anchor point i and 1 |

$\Delta r$ | Square of the difference between true and measured values |

$\lambda \left(k\right)$ | Weighting factor |

SVM | CNN | C-T | C-T-CNN-SVM | |
---|---|---|---|---|

Time (FLOPS) | 20 G | 133.4 G | 15 G | 168.4 G |

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## Share and Cite

**MDPI and ACS Style**

Gao, Z.; Jiao, Y.; Yang, W.; Li, X.; Wang, Y.
A Method for UWB Localization Based on CNN-SVM and Hybrid Locating Algorithm. *Information* **2023**, *14*, 46.
https://doi.org/10.3390/info14010046

**AMA Style**

Gao Z, Jiao Y, Yang W, Li X, Wang Y.
A Method for UWB Localization Based on CNN-SVM and Hybrid Locating Algorithm. *Information*. 2023; 14(1):46.
https://doi.org/10.3390/info14010046

**Chicago/Turabian Style**

Gao, Zefu, Yiwen Jiao, Wenge Yang, Xuejian Li, and Yuxin Wang.
2023. "A Method for UWB Localization Based on CNN-SVM and Hybrid Locating Algorithm" *Information* 14, no. 1: 46.
https://doi.org/10.3390/info14010046