Abstract
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. In order to account for the lack of information about the different aspects of this type of complex system, an alternative representation of uncertainty based on possibility theory is considered. It is shown how analogues of usual concepts such as Markov chains and hidden Markov models (HMMs) can be introduced in this context. In particular, the considered statistical model for multiple dynamical objects can be formulated as a hierarchical model consisting of conditionally independent HMMs. This structure is leveraged to propose an efficient method in the context of Markov chain Monte Carlo (MCMC) by relying on an approximate solution to the corresponding filtering problem, in a similar fashion to particle MCMC. This approach is shown to outperform existing algorithms in a range of scenarios.
Highlights
We consider the problem of performing inference for multiobject dynamical systems under partial, corrupted and noisy observations
This class of problems, known as multi-target tracking in the engineering literature (Fortmann et al 1980; Mahler 2003; Vo et al 2014), arises in many applications, e.g. bio-imaging (Chenouard 2014), robotics (Mullane et al 2011) and surveillance (Benfold and Reid 2011), which can all benefit from principled inference solutions in different ways: i) when the number of objects is too large to be treated by hand, ii) when the phenomena of interest take place on extended periods of time or, when an immediate response is needed, iii) when the data available about
It would be possible to extend our approach in order to make it suitable for online estimation, e.g. by running the proposed Markov chain Monte Carlo (MCMC) chain over a fixed lag for some or all iterations of a suitable online estimation algorithm in order to further explore the set of data associations; this extension is kept for future work
Summary
We consider the problem of performing inference for multiobject dynamical systems under partial, corrupted and noisy observations. This class of problems, known as multi-target tracking in the engineering literature (Fortmann et al 1980; Mahler 2003; Vo et al 2014), arises in many applications, e.g. bio-imaging (Chenouard 2014), robotics (Mullane et al 2011) and surveillance (Benfold and Reid 2011), which can all benefit from principled inference solutions in different ways: i) when the number of objects is too large to be treated by hand, ii) when the phenomena of interest take place on extended periods of time or, when an immediate response is needed, iii) when the data available about.
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