Kernelbasierte implizite Datenassoziation für große Mengen von ungelabelten, verrauschten Daten
Zusammenfassung der Projektergebnisse
The objective of this proposal was to develop new methods for data association that can efficiently handle large data sets. Data association is a fundamental problem with many applications such as multiple object tracking (MOT), extended object tracking (EOT), and Simultaneous Localization and Mapping (SLAM). One of the key challenges in estimation problems that involve data association uncertainties is that all feasible associations have to be considered due to stochastic noise in the data, e.g., from the sensor. As the number of feasible associations grows significantly with the size of the data set, efficient approximations have to be applied to reduce the computational complexity. A focus of this project was to investigate how a (usually nonlinear) transformation of the measurements can be employed to facilitate estimation in the presence of data association uncertainties. First, we considered measurement transformations that are composed of kernel functions (i.e., a sum of Gaussians) in order to obtain a measurement equation that does not contain any unknown data associations. As this approach requires a discretization of the state space and results in a highly nonlinear measurement equation, we additionally proposed a novel approach that works with a distance metric on sets in order to create a measurement equation without unknown data association. Second, we employed the concept of state transformations for EOT. In EOT, the goal is to compute both the position and spatial extent of a target object given measurements stemming from the object surface. Hereby, the measurement origin on the object is unknown, i.e., it is unclear, which point on the object caused the reflection. By means of modeling the measurement origin with a spatial probability distribution, one can avoid the explicit modeling of measurement origins, however, a nonlinear estimation problem is obtained instead. It turned out that a quadratic state transformation is the key for deriving compact expressions for estimating the center and semi-axes lengths of an elliptical shaped extended object. Third, we considered a state-of-the-art method for MOT called Probability Hypothesis Density (PHD) filter. The PHD filter does not require a computationally expensive enumeration of measurement-to-object assignments, however, it does not maintain object labels (in its original version). In this context, we proposed a new efficient method for maintaining labels in the PHD filter, which is based on solving a minimum-cost flow problem. Finally, we derived a novel method for multiple extended object tracking (MEOT), which incorporates multiple measurements per object. The underlying idea is to determine the marginal association probabilities of single measurements for conducting a weighted measurement update. In this way, an extremely efficient method for MEOT is obtained that incorporates false and missing measurements as well as track initiation and termination. In this project, it turned out that transforming measurements can be a powerful techniques for solving tracking problems. It can not only remove the data association uncertainty from the problem but it also helps to derive nonlinear estimators. In the future, we will further investigate efficient methods for data association, where we will focus on directly optimizing a distance metric on sets.
Projektbezogene Publikationen (Auswahl)
- “Extended Kalman Filter for Extended Object Tracking”, in Proceedings of the 42nd IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), New Orleans, USA, Mar. 2017
S. Yang and M. Baum
(Siehe online unter https://doi.org/10.1109/ICASSP.2017.7952985) - “Symmetrizing Measurement Equations for Association-free Multi-target Tracking via Point Set Distances”, in SPIE - Signal Processing, Sensor/Information Fusion, and Target Recognition XXVI, Anaheim, California, USA, Apr. 2017
U. D. Hanebeck, M. Baum, and P. Willett
(Siehe online unter https://doi.org/10.1117/12.2266988) - “Linear-Time Joint Probabilistic Data Association for Multiple Extended Object Tracking”, in 2018 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2018), Sheffield, United Kingdom, Jul. 2018
S. Yang, K. Thormann, and M. Baum
(Siehe online unter https://doi.org/10.1109/SAM.2018.8448430) - “Network flow labeling for extended target tracking phd filters”, IEEE Transactions on Industrial Informatics, pp. 1–1, 2019
S. Yang, F. Teich, and M. Baum
(Siehe online unter https://doi.org/10.1109/TII.2019.2898992) - “Tracking the orientation and axes lengths of an elliptical extended object”, IEEE Transactions on Signal Processing, vol. 67, no. 18, pp. 4720– 4729, Sep. 2019
S. Yang and M. Baum
(Siehe online unter https://doi.org/10.1109/TSP.2019.2929462) - “Marginal Association Probabilities for Multiple Extended Objects without Enumeration of Measurement Partitions”, in Proceedings of the 23rd International Conference on Information Fusion (Fusion 2020), Virtual, Jul. 2020
S. Yang, L. M. Wolf, and M. Baum
(Siehe online unter https://doi.org/10.23919/FUSION45008.2020.9190500)
