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Three-Dimensional Extended Target Tracking and Shape Learning Based on Double Fourier Series and Expectation

Hongge Mao1,2, Xiaojun Yang1

  • 1School of Information Engineering, Chang'an University, Xi'an 710064, China.

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|August 14, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for tracking 3D objects with unknown star-convex shapes using point clouds. The approach estimates shape and motion directly, overcoming limitations of prior models for real-world applications.

Keywords:
axis-angledouble Fourier seriesexpectation conditional maximizationshape estimationtarget tracking

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Area of Science:

  • Robotics and Autonomous Systems
  • Computer Vision
  • Signal Processing

Background:

  • Target tracking with unknown shapes is challenging due to model uncertainties.
  • Existing methods often rely on predefined, potentially inaccurate, prior models for shape evolution.
  • Accurate estimation of 3D kinematics, extent, and orientation is crucial for many applications.

Purpose of the Study:

  • To develop a robust algorithm for tracking targets with unknown, fixed 3D star-convex shapes.
  • To jointly estimate target kinematics, extent, and orientation from point cloud measurements.
  • To circumvent limitations of prior models by directly optimizing shape parameters.

Main Methods:

  • Utilizing the Expectation Conditional Maximization (ECM) framework for joint parameter estimation.
  • Modeling 3D shape with a radial function via double Fourier series (DFS) expansion.
  • Representing orientation using the singularity-free axis-angle method.
  • Employing an Unscented Kalman Smoother for kinematic inference (E-step) and regularized cost minimization for shape and orientation estimation (M-step).

Main Results:

  • The proposed ECM-based algorithm effectively performs joint estimation of kinematics, extent, and orientation.
  • The method demonstrates robustness and smoothness in shape and orientation estimation.
  • Experimental evaluations validate the algorithm's effectiveness in tracking unknown 3D star-convex shapes.

Conclusions:

  • The developed ECM approach offers a significant advancement in tracking targets with unknown shapes.
  • Direct parameter optimization provides a more practical solution compared to methods relying on prior shape evolution models.
  • The algorithm shows promise for real-world applications requiring precise 3D target tracking.