# Track Segment Association Method Based on Bidirectional Track Prediction and Fuzzy Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Holt-Winters Method

#### 2.2. Fuzzy Track Association Algorithm

#### 2.3. Fuzzy Track Segment Association Algorithm

#### 2.4. Holt-Winters Prediction and Fuzzy Analysis Model

- Track segment judgment: real-time judgment of incoming track points, if the latest track point is not received after the set time, it is considered that the current track is in an interrupted state, and the procedure goes to the next step;
- Track segment data processing: convert the pre-interruption track data into the format required by the program and use the processed pre-interruption track data to train the Holt-Winters forward model while waiting for the recovery of the track point. If the point data are considered to be in an interrupted state at the end of the track, the program goes to the next step;
- Track segment data prediction: the processed track data before the interruption and the track data after the interruption are processed and sent to the Holt-Winters model, and the Holt-Winters method is used to predict from two directions. After the prediction is completed, the program goes to the next step;
- Track segment association: a fuzzy track association algorithm is used to correlate data before and after interruption. If the association fails and the number of repeated associations does not exceed the preset maximum number of times, end the program. If the association fails, perform the secondary association: first jump to step 3 to update the prediction result and then replace the Equation (7) of the algorithm with Equation (9) in the fourth step of the program, and then perform the fuzzy track. The association algorithm is shown below.

## 3. Results

#### 3.1. Data Set

#### 3.2. Experimental Setup

#### 3.3. Prediction Experiment

- TCN [23]: The input step is 10, the learning rate is 1 × 10
^{−3}; epoch: 300. - Prophet [29]: Parameters: default; the prediction frequency is 10 s.
- Holt-Winters: “Trend” is set to “add”. Except that, the three feature parameters x, and vx are slightly different, the “damped trend” of other feature column parameters is set to “true” and “seasonal” is set to “add”.

#### 3.4. Track Association Experiment

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The results of track association experiment: (

**a**) Influence of a different number of predicted points on the association accuracy; (

**b**) Influence of a different number of predicted points on the association accuracy (The baseline is the method that does not make predictions); (

**c**) Influence of different breakage periods on the association accuracy.

Error | Method | ||||
---|---|---|---|---|---|

LSTM | TCN | ARIMA | Prophet | Holt-Winters | |

x (m) | 0.01031226 | 0.00847442 | 0.00343247 | 0.000282 | 0.00036811 |

y (m) | 0.01457218 | 0.01379722 | 0.00490498 | 0.000393 | 0.00097181 |

z (m) | 0.0500951 | 0.04427563 | 0.02846062 | 0.005334 | 0.0077661 |

v_{x} (m/s) | 0.00623551 | 0.0041277 | 0.00063828 | 0.00068 | 0.000844625 |

v_{y} (m/s) | 0.0060439 | 0.00399427 | 0.00035111 | 0.000383 | 0.001006425 |

v_{z} (m/s) | 0.00608286 | 0.00376995 | 0.00048802 | 0.000474 | 0.00061313 |

a_{x} (m/s^{2}) | 0.00612628 | 0.0041475 | 0.00063779 | 0.000683 | 0.00148328 |

a_{y} (m/s^{2}) | 0.00591117 | 0.00409016 | 0.00034982 | 0.000384 | 0.001005105 |

a_{z} (m/s^{2}) | 0.00600928 | 0.00384299 | 0.00048726 | 0.000473 | 0.000612425 |

Time (min) | 120 | 480 | 15 | 15 | 10 |

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**MDPI and ACS Style**

Cao, Y.; Cao, J.; Zhou, Z.
Track Segment Association Method Based on Bidirectional Track Prediction and Fuzzy Analysis. *Aerospace* **2022**, *9*, 274.
https://doi.org/10.3390/aerospace9050274

**AMA Style**

Cao Y, Cao J, Zhou Z.
Track Segment Association Method Based on Bidirectional Track Prediction and Fuzzy Analysis. *Aerospace*. 2022; 9(5):274.
https://doi.org/10.3390/aerospace9050274

**Chicago/Turabian Style**

Cao, Yupeng, Jiangwei Cao, and Zhiguo Zhou.
2022. "Track Segment Association Method Based on Bidirectional Track Prediction and Fuzzy Analysis" *Aerospace* 9, no. 5: 274.
https://doi.org/10.3390/aerospace9050274