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Convolutional Unscented Kalman Filter for Multi-Object Tracking with Outliers

Shiqi Liu, Wenhan Cao, Chang Liu, Tianyi Zhang, Shengbo Eben Li

TL;DR

This work adopts a probabilistic perspective, regarding the generation of outliers as misspecification between the actual distribution of measurement data and the nominal measurement model used for filtering, and derives a variant of the UKF that is robust to outliers, called the convolutional UKF (ConvUKF).

Abstract

Multi-object tracking (MOT) is an essential technique for navigation in autonomous driving. In tracking-by-detection systems, biases, false positives, and misses, which are referred to as outliers, are inevitable due to complex traffic scenarios. Recent tracking methods are based on filtering algorithms that overlook these outliers, leading to reduced tracking accuracy or even loss of the objects trajectory. To handle this challenge, we adopt a probabilistic perspective, regarding the generation of outliers as misspecification between the actual distribution of measurement data and the nominal measurement model used for filtering. We further demonstrate that, by designing a convolutional operation, we can mitigate this misspecification. Incorporating this operation into the widely used unscented Kalman filter (UKF) in commonly adopted tracking algorithms, we derive a variant of the UKF that is robust to outliers, called the convolutional UKF (ConvUKF). We show that ConvUKF maintains the Gaussian conjugate property, thus allowing for real-time tracking. We also prove that ConvUKF has a bounded tracking error in the presence of outliers, which implies robust stability. The experimental results on the KITTI and nuScenes datasets show improved accuracy compared to representative baseline algorithms for MOT tasks.

Convolutional Unscented Kalman Filter for Multi-Object Tracking with Outliers

TL;DR

This work adopts a probabilistic perspective, regarding the generation of outliers as misspecification between the actual distribution of measurement data and the nominal measurement model used for filtering, and derives a variant of the UKF that is robust to outliers, called the convolutional UKF (ConvUKF).

Abstract

Multi-object tracking (MOT) is an essential technique for navigation in autonomous driving. In tracking-by-detection systems, biases, false positives, and misses, which are referred to as outliers, are inevitable due to complex traffic scenarios. Recent tracking methods are based on filtering algorithms that overlook these outliers, leading to reduced tracking accuracy or even loss of the objects trajectory. To handle this challenge, we adopt a probabilistic perspective, regarding the generation of outliers as misspecification between the actual distribution of measurement data and the nominal measurement model used for filtering. We further demonstrate that, by designing a convolutional operation, we can mitigate this misspecification. Incorporating this operation into the widely used unscented Kalman filter (UKF) in commonly adopted tracking algorithms, we derive a variant of the UKF that is robust to outliers, called the convolutional UKF (ConvUKF). We show that ConvUKF maintains the Gaussian conjugate property, thus allowing for real-time tracking. We also prove that ConvUKF has a bounded tracking error in the presence of outliers, which implies robust stability. The experimental results on the KITTI and nuScenes datasets show improved accuracy compared to representative baseline algorithms for MOT tasks.
Paper Structure (15 sections, 5 theorems, 27 equations, 8 figures, 5 tables)

This paper contains 15 sections, 5 theorems, 27 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Preliminaries
  4. Problem Formulation of Filtering
  5. Convolutional Unscented Kalman Filter
  6. Algorithm Design
  7. Stability Analysis
  8. Experiments
  9. Settings
  10. Results
  11. Visualization and Discussion
  12. Conclusion and Limitation
  13. Proof of Proposition 1
  14. Proof of Proposition 2
  15. Proof of Theorem 2

Key Result

Lemma 1

Consider the following nominal system model $p(\bar{y}_t|x_t) = \mathcal{N}(\bar{y}_t;h(x_t),R_t)$. If $d_y({y}, \bar{{y}}) = \|{y} - \bar{{y}} \|^2$ and ${\epsilon} \sim \mathrm{Exp}(\gamma)$ with $\gamma>0$ as the parameter of the exponential distribution, then we have $p_c(y_t|x_{t}) = \mathcal{N

Figures (8)

  • Figure 1:
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  • Figure 6: TBD framework. Firstly, the object detection module detects bounding boxes $\{D_t^1,D_t^2,\dots,D_t^{d_t}\}$ from the raw LiDAR point cloud, providing initial information about the objects in the environment. Next, the motion prediction in filtering module employs a motion model to predict the motions of detected objects, generating $\{\hat{x}_{t|t-1}^1,\hat{x}_{t|t-1}^2,\cdots,\hat{x}_{t|t-1}^{b_{t-1}}\}$. Subsequently, the data association module matches these predictions with the current detections for the continuous tracking of the same objects $\{(\hat{x}^i_{t|t-1},D^j_t)\}$. Finally, the estimation update in filtering module computes the motion estimation of objects $\{\hat{x}_{t}^{1},\hat{x}_{t}^{2},\cdots,\hat{x}_{t}^{b_{t}}\}$ at timestamp $t$. As the next frame, object detection will process the incoming sensor data again.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Remark 1
  • Lemma 1: cao2024convolutional
  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Remark 2
  • Lemma 2