# Tracking of Maneuvering Complex Extended Object with Coupled Motion Kinematics and Extension Dynamics Using Range Extent Measurements

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## Abstract

**:**

## 1. Introduction

- (a)
- MCEOT using measurements of target’s range extent is first considered explicitly, our approach characterizes not only the evolution of the kinematic state over time, but also the object extension dynamics. More importantly, the coupling between the centroid kinematics and extension evolution (e.g., the close relationship between the turn maneuver of the centroid and the abrupt change of extension) is also explicitly involved.
- (b)
- The new model has a concise and unified form and it can accurately describe an MCEO with a turn maneuver in both the extension dynamics and the centroid kinematics, i.e., the maneuver model of a complex extended object can be obtained and directly represented by that of several simple sub-objects (decomposed using the Minkowski sum) jointly. In particular, the elliptical maneuvering object model is obtained in this paper, which is a by-product of the proposed approach.
- (c)
- Based on the Minkowski sum, different parameterizations can be adopted in our unified modeling framework if they are efficient to describe sub-objects’ extension dynamics. This does not affect the generality of the proposed approaches for solving MCEOT.
- (d)
- Due to the concise linear form, the proposed modeling is easily incorporated into a general tracking architecture, in which the exchange of information between centroid kinematics and extension dynamics are sufficiently utilized. This largely facilitates the derivation and design of an MCEOT algorithm for achieving much better estimation performance.

## 2. Problem Formulation

- (a)
- how to accurately describe the extension dynamics (change in size, shape, orientation, e.g., rotation) of an MCEO over time,
- (b)
- how to deal with the close coupling between the centroid kinematics and extension evolution, and how to embody it in the MCEO modeling.

**Remark**

**1.**

## 3. MCEO Modeling Using Range Extent Measurements

#### 3.1. The Unified Complex Extension Dynamics Based on Minkowski Sum

**Remark**

**2.**

**Remark**

**3.**

#### 3.2. The Minkowski-Sum-Based Modeling and Estimation for CT Maneuvers with Known Turn Rates

**Remark**

**4.**

#### 3.3. The Minkowski-Sum-Based Modeling and Estimation for CT Maneuvers with Unknown Turn Rates

#### 3.4. Complexity Analysis

## 4. Simulation Results and Performance Evaluation

- (a)
- MCEOT-1: The proposed approach based on Minkowski sum considering the highly coupled dynamics of both the state and the extension.
- (b)
- MCEOT-2: The approach considering only the centroid state dynamics.

#### 4.1. Tracking Performance Using Minkowski-Sum-Based CT Model with Known Rates

#### 4.2. Tracking Performance Using Minkowski-Sum-Based CT Model with Unknown Rates

#### 4.3. Performance Comparison and Complexity Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**The complex object extension dynamics based on Minkowski sum, (

**a**) illustrative example; (

**b**) extension dynamics of complex object; (

**c**) extension dynamics of sub-object 1; (

**d**) extension dynamics of sub-object 2.

**Figure 3.**Trajectory of the complex extended object in scenario A (the blue solid line is for the true object, the red solid line and black dash line are for MCEOT-1 and MCEOT-2, respectively).

**Figure 4.**Trajectory of the complex extended object in scenario B (the blue solid line is for the true object, the red solid line and black dash line are for MCEOT-1 and MCEOT-2, respectively).

**Figure 5.**Performance comparison for scenario A. (

**a**) position RMSE; (

**b**) velocity RMSE; (

**c**) Hausdorff distance; (

**d**) average probability of MCEOT-1.

**Figure 6.**Performance comparison for scenario B. (

**a**) position RMSE; (

**b**) velocity RMSE; (

**c**) Hausdorff distance; (

**d**) average probability of MCEOT-1.

**Figure 7.**Simulation results in scenario C. (

**a**) the object trajectory; (

**b**) position RMSE; (

**c**) velocity RMSE; (

**d**) Hausdorff distance.

**Table 1.**Averaged computation time (seconds) for one run (90 steps) of two approaches in scenario A.

MCOET-1 | MEOT-1 |
---|---|

0.2971 | 0.1103 |

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**MDPI and ACS Style**

Sun, L.; Ji, B.; Lan, J.; He, Z.; Pu, J.
Tracking of Maneuvering Complex Extended Object with Coupled Motion Kinematics and Extension Dynamics Using Range Extent Measurements. *Sensors* **2017**, *17*, 2184.
https://doi.org/10.3390/s17102184

**AMA Style**

Sun L, Ji B, Lan J, He Z, Pu J.
Tracking of Maneuvering Complex Extended Object with Coupled Motion Kinematics and Extension Dynamics Using Range Extent Measurements. *Sensors*. 2017; 17(10):2184.
https://doi.org/10.3390/s17102184

**Chicago/Turabian Style**

Sun, Lifan, Baofeng Ji, Jian Lan, Zishu He, and Jiexin Pu.
2017. "Tracking of Maneuvering Complex Extended Object with Coupled Motion Kinematics and Extension Dynamics Using Range Extent Measurements" *Sensors* 17, no. 10: 2184.
https://doi.org/10.3390/s17102184