# A Stochastic Characterization of the Capture Zone in Pursuit-Evasion Games

## Abstract

**:**

## 1. Introduction

## 2. Statement of the Problem

#### 2.1. Engagement Description

#### 2.2. Pursuit-Evasion Games

#### 2.3. Estimator in the Loop

## 3. Characterization of the Game Structure

#### 3.1. Mahalanobis Distance

#### 3.2. Cramér–Rao Bound

## 4. Numerical Example

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Parameter | Value | Parameter | Value |
---|---|---|---|

${v}_{P}$ | 3 km/s | ${v}_{E}$ | 1.2 km/s |

${a}_{P}^{max}$ | 30 g | ${a}_{E}^{max}$ | 10 g |

${R}_{0}$ | 10 km | ${\lambda}_{0}$ | ${5}^{\circ}$ |

${\gamma}_{{E}_{0}}$ | $\sim \mathcal{U}$ (${30}^{\circ}$, ${10}^{\circ}$) | g | 9.81 m/s${}^{2}$ |

${a}_{{P}_{0}}$ | 0 m/s${}^{2}$ | ${a}_{{E}_{0}}$ | 0 m/s${}^{2}$ |

${\tau}_{P}$ | 0.1 s | ${\tau}_{E}$ | 0.2 s |

$\psi $ | ${{a}_{E}^{max}}^{2}/{t}_{f}$ | ${\Delta}_{T}$ | 0.02 s |

${\sigma}_{{\nu}_{\lambda}}$ | 0.001 rad | ${\sigma}_{{\nu}_{r}}$ | 50 m |

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**MDPI and ACS Style**

Battistini, S. A Stochastic Characterization of the Capture Zone in Pursuit-Evasion Games. *Games* **2020**, *11*, 54.
https://doi.org/10.3390/g11040054

**AMA Style**

Battistini S. A Stochastic Characterization of the Capture Zone in Pursuit-Evasion Games. *Games*. 2020; 11(4):54.
https://doi.org/10.3390/g11040054

**Chicago/Turabian Style**

Battistini, Simone. 2020. "A Stochastic Characterization of the Capture Zone in Pursuit-Evasion Games" *Games* 11, no. 4: 54.
https://doi.org/10.3390/g11040054