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DIMM: Decoupled Multi-hierarchy Kalman Filter for 3D Object Tracking

Jirong Zha, Yuxuan Fan, Kai Li, Han Li, Chen Gao, Xinlei Chen, Yong Li

TL;DR

DIMM tackles 3D object tracking with unknown dynamics by decoupling state estimation across dimensions and learning adaptive fusion weights. The approach combines a 3D-decoupled multi-hierarchy filter bank (DHFB) with a differentiable adaptive fusion network (DAFN) trained via TD3 and a hierarchical reward, expanding the model-combination space to a 3D hypercube and producing per-dimension fusion weights. Empirical results across multiple datasets show substantial improvements in MSE/MAE over state-of-the-art methods, with strong real-time inference performance and interpretability through transformation matrices. The work offers a practical, hybrid framework that balances model-based structure and learning-based adaptability for robust 3D tracking in dynamic environments, with potential for real-world autonomous systems.

Abstract

State estimation is challenging for 3D object tracking with high maneuverability, as the target's state transition function changes rapidly, irregularly, and is unknown to the estimator. Existing work based on interacting multiple model (IMM) achieves more accurate estimation than single-filter approaches through model combination, aligning appropriate models for different motion modes of the target object over time. However, two limitations of conventional IMM remain unsolved. First, the solution space of the model combination is constrained as the target's diverse kinematic properties in different directions are ignored. Second, the model combination weights calculated by the observation likelihood are not accurate enough due to the measurement uncertainty. In this paper, we propose a novel framework, DIMM, to effectively combine estimates from different motion models in each direction, thus increasing the 3D object tracking accuracy. First, DIMM extends the model combination solution space of conventional IMM from a hyperplane to a hypercube by designing a 3D-decoupled multi-hierarchy filter bank, which describes the target's motion with various-order linear models. Second, DIMM generates more reliable combination weight matrices through a differentiable adaptive fusion network for importance allocation rather than solely relying on the observation likelihood; it contains an attention-based twin delayed deep deterministic policy gradient (TD3) method with a hierarchical reward. Experiments demonstrate that DIMM significantly improves the tracking accuracy of existing state estimation methods by 31.61%~99.23%.

DIMM: Decoupled Multi-hierarchy Kalman Filter for 3D Object Tracking

TL;DR

DIMM tackles 3D object tracking with unknown dynamics by decoupling state estimation across dimensions and learning adaptive fusion weights. The approach combines a 3D-decoupled multi-hierarchy filter bank (DHFB) with a differentiable adaptive fusion network (DAFN) trained via TD3 and a hierarchical reward, expanding the model-combination space to a 3D hypercube and producing per-dimension fusion weights. Empirical results across multiple datasets show substantial improvements in MSE/MAE over state-of-the-art methods, with strong real-time inference performance and interpretability through transformation matrices. The work offers a practical, hybrid framework that balances model-based structure and learning-based adaptability for robust 3D tracking in dynamic environments, with potential for real-world autonomous systems.

Abstract

State estimation is challenging for 3D object tracking with high maneuverability, as the target's state transition function changes rapidly, irregularly, and is unknown to the estimator. Existing work based on interacting multiple model (IMM) achieves more accurate estimation than single-filter approaches through model combination, aligning appropriate models for different motion modes of the target object over time. However, two limitations of conventional IMM remain unsolved. First, the solution space of the model combination is constrained as the target's diverse kinematic properties in different directions are ignored. Second, the model combination weights calculated by the observation likelihood are not accurate enough due to the measurement uncertainty. In this paper, we propose a novel framework, DIMM, to effectively combine estimates from different motion models in each direction, thus increasing the 3D object tracking accuracy. First, DIMM extends the model combination solution space of conventional IMM from a hyperplane to a hypercube by designing a 3D-decoupled multi-hierarchy filter bank, which describes the target's motion with various-order linear models. Second, DIMM generates more reliable combination weight matrices through a differentiable adaptive fusion network for importance allocation rather than solely relying on the observation likelihood; it contains an attention-based twin delayed deep deterministic policy gradient (TD3) method with a hierarchical reward. Experiments demonstrate that DIMM significantly improves the tracking accuracy of existing state estimation methods by 31.61%~99.23%.
Paper Structure (26 sections, 1 theorem, 8 equations, 8 figures, 4 tables)

This paper contains 26 sections, 1 theorem, 8 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem formulation
  4. Methodology
  5. Revisiting interacting multiple model
  6. Planar solution space constraint
  7. Observation-dependent weight instability
  8. Overview of our DIMM approach
  9. Decoupled multi-hierarchical filter bank
  10. Differentiable adaptive fusion network
  11. Environment definition
  12. Attention-based network structure
  13. Transformation matrix construction
  14. Hierarchical reward design
  15. Experiment
  16. ...and 11 more sections

Key Result

Proposition 1

The solution space of IMM's estimate combination is a hyperplane, while the solution space of 3D model combination weights is a hypercube.

Figures (8)

  • Figure 1: Illustration of 3D object tracking with unknown dynamics. We aim to improve the estimation accuracy by determining what type of motion model to employ and how to select and fuse the models independently of each dimension.
  • Figure 2: Relationship between three kinds of methods.
  • Figure 3: Extend the combination solution space by converting the weighting object from state vectors to variables in each direction.
  • Figure 4: Overview of DIMM. Some critical technical contributions are highlighted in red.
  • Figure 5: Network structure of the DAFN module.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof