Kernel-based implicit data association for large amounts of unlabeled noisy data

• Applicant: Professor Dr.-Ing. Marcus Baum
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 253954122

This proposal is concerned with the general problem of state estimation based on unlabeled noisy measurement data. Unlabeled data arise in uncountable applications such as robotics, automotive safety, medicine, and surveillance. For example, in robotics, multiple objects have to be localized and tracked over time by sensors such as laser ranger finders that do not provide labels for the object measurements, i.e., the association between measurements and objects is not available.Existing association methods maintain a set of possible association hypotheses. However, as the number of possible association hypotheses grows exponentially with the number of data, only a strongly reduced set can be maintained, which results in a significant loss of precision. As a consequence, existing methods are either infeasible for a large number of highly noisy data (>>10) or suffer from a low estimation quality.The objective of this proposal is to establish a fundamentally new data association approach that can efficiently deal with a large data volume while providing a high estimation quality. This framework then allows the systematic and mathematically sound treatment of large data association problems for which currently no suitable methods exist. The basic idea is to reformulate the original estimation problem by transforming the measurement data by means of a kernel mixture function. The resulting modified estimation problem is nonlinear but does not contain any data association uncertainties anymore. As the association is now performed implicitly, an enumeration of all association hypotheses is not necessary anymore, which results in a dramatic reduction of complexity. Furthermore, as the reformulation is exact and does not remove any information, it is still possible to derive precise state estimators.The following problems are addressed in this proposal: First, the theoretical foundations of the novel approach will be explored, i.e., different approaches for constructing a kernel mixture function will be investigated and nonlinear estimators are developed for the reformulated problem. Second, the approach will be extended for dealing with data not being related to the state of interest (spurious data) and objects for which no data is available (missing data). Third, in order to deal with multiple objects, a mechanism for the birth and death of objects will be developed and integrated into the proposed approach.

• DFG Programme: Research Grants
• Participating Person: Professor Dr.-Ing. Uwe D. Hanebeck