Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking Over Wireless Sensor Networks

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Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking Over Wireless Sensor Networks

Xingchi Liu; Lyudmila Mihaylova; Jemin George; Tien Pham

Uncertainty quantification plays a key role in the development of autonomous systems, decision-making, and tracking over wireless sensor networks (WSNs). However, there is a need of providing uncertainty confidence bounds, especially for distributed machine learning-based tracking, dealing with different volumes of data collected by sensors. This paper aims to fill in this gap and proposes a distributed Gaussian process (DGP) approach for point target tracking and derives upper confidence bounds (UCBs) of the state estimates. A unique contribution of this paper includes the derived theoretical guarantees on the proposed approach and its maximum accuracy for tracking with and without clutter measurements. Particularly, the developed approaches with uncertainty bounds are generic and can provide trustworthy solutions with an increased level of reliability. A novel hybrid Bayesian filtering method is proposed to enhance the DGP approach by adopting a Poisson measurement likelihood model. The proposed approaches are validated over a WSN case study, where sensors have limited sensing ranges. Numerical results demonstrate the tracking accuracy and robustness of the proposed approaches. The derived UCBs constitute a tool for trustworthiness evaluation of DGP approaches. The simulation results reveal that the proposed UCBs successfully encompass the true target states with 88% and 42% higher probability in X and Y coordinates, respectively, when compared to the confidence interval-based method.


Target tracking in wireless sensor networks (WSNs) is a fundamental task for various applications including sea surveillance, autonomous vehicles, and traffic monitoring. The objective is to collect sensor measurements from one or multiple targets to estimate their current and future states [1]. However, the measurements may not only originate from the targets but also from the environmental interference (e.g. from ground and rain), which is referred to as the clutter [2]. To achieve reliable performance, a tracker should be able to distinguish between target measurements and clutter measurements, and also decide which measurement is associated with which target, which is called the data association problem [3].

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