# Application of Interactive Multiple Model Adaptive Five-Degree Cubature Kalman Algorithm Based on Fuzzy Logic in Target Tracking

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fuzzy Logic Algorithm

- (1)
- The domain of input variables and output variables:$$\{\begin{array}{c}{\mathrm{I}}_{1}:\left[0,\text{}1\right]\\ {\mathrm{I}}_{2}:\left[-1,\text{}1\right]\\ \mu :\left[0,\text{}1\right]\end{array}$$
- (2)
- Fuzzy set of input variables and output variables:$$\{\begin{array}{c}{\mathrm{I}}_{1}:\left\{Small\left(S\right),Medium\left(M\right),Big\left(B\right)\right\}\\ {\mathrm{I}}_{2}:\left\{Negative\left(N\right),Zero\left(Z\right),Positive\left(P\right)\right\}\\ \mu :\left\{Small\left(S\right),Medium\left(M\right),Big\left(B\right)\right\}\end{array}$$
- (3)
- Determining the membership function:

## 3. Adaptive Five-Degree Cubature Kalman

#### 3.1. Time Update

#### 3.2. Measurement Update

## 4. Algorithm Overall Framework

#### 4.1. Input Interaction

#### 4.2. Parallel Filtering

#### 4.3. Update Probability

#### 4.4. Output Data Fusion

## 5. Missile Dynamics Modeling

#### 5.1. Analysis of The Motion Characteristics of Missiles

#### 5.2. Snake-Like Maneuvering

## 6. Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Rule Number | ${\mathbf{I}}_{1}$ | ${\mathbf{I}}_{2}$ | $\mathbf{\mu}$ |
---|---|---|---|

1 | S | N | S |

2 | S | Z | S |

3 | S | P | M |

4 | M | N | S |

5 | M | Z | M |

6 | M | P | B |

7 | B | N | M |

8 | B | Z | B |

9 | B | P | B |

Max Error | IMMCKF | IMM5CKF | IMMA5CKF | FLIMMA5CKF |
---|---|---|---|---|

${P}_{x}$ | 265.62 | 258.53 | 39.81 | 26.65 |

${P}_{y}$ | 48.75 | 43.50 | 9.66 | 5.78 |

${P}_{z}$ | 38.80 | 38.81 | 45.82 | 50.25 |

${v}_{x}$ | 15.28 | 14.96 | 4.10 | 2.68 |

${v}_{y}$ | 7.24 | 6.21 | 2.03 | 1.47 |

${v}_{z}$ | 39.69 | 39.78 | 40.16 | 40.62 |

${a}_{x}$ | −0.87 | −0.85 | −0.45 | −0.42 |

${a}_{y}$ | 0.81 | 0.79 | 0.31 | 0.26 |

${a}_{z}$ | 19.62 | 19.65 | 19.70 | 19.89 |

time (s) | 8.253 | 17.356 | 18.031 | 28.311 |

RMSE | IMMCKF | IMM5CKF | IMMA5CKF | FLIMMA5CKF |
---|---|---|---|---|

${P}_{x}$ | 71.13 | 65.35 | 19.24 | 14.38 |

${P}_{y}$ | 15.09 | 14.29 | 7.19 | 6.26 |

${P}_{z}$ | 8.62 | 8.59 | 8.56 | 8.65 |

${v}_{x}$ | 6.86 | 6.35 | 2.41 | 1.67 |

${v}_{y}$ | 3.06 | 2.96 | 2.21 | 1.87 |

${v}_{z}$ | 6.08 | 5.96 | 5.93 | 5.89 |

${a}_{x}$ | 0.37 | 0.36 | 0.22 | 0.16 |

${a}_{y}$ | 0.58 | 0.57 | 0.49 | 0.39 |

${a}_{z}$ | 3.19 | 3.16 | 3.15 | 3.12 |

time (s) | 8.253 | 17.356 | 18.031 | 28.311 |

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**MDPI and ACS Style**

Wan, J.; Ren, P.; Guo, Q.
Application of Interactive Multiple Model Adaptive Five-Degree Cubature Kalman Algorithm Based on Fuzzy Logic in Target Tracking. *Symmetry* **2019**, *11*, 767.
https://doi.org/10.3390/sym11060767

**AMA Style**

Wan J, Ren P, Guo Q.
Application of Interactive Multiple Model Adaptive Five-Degree Cubature Kalman Algorithm Based on Fuzzy Logic in Target Tracking. *Symmetry*. 2019; 11(6):767.
https://doi.org/10.3390/sym11060767

**Chicago/Turabian Style**

Wan, Jian, Peiwen Ren, and Qiang Guo.
2019. "Application of Interactive Multiple Model Adaptive Five-Degree Cubature Kalman Algorithm Based on Fuzzy Logic in Target Tracking" *Symmetry* 11, no. 6: 767.
https://doi.org/10.3390/sym11060767