Target tracking often relies on complex models with non-stationary parameters. Gaussian process (GP) is a modelfree method that can achieve accurate performance. However, the inverse of the covariance matrix poses scalability challenges. Since the covariance matrix is typically dense, direct inversion and determinant evaluation methods suffer from cubic complexity to data size. This bottleneck limits the GP for long-term tracking or high-speed tracking. We present an efficient factorisationbased GP approach without any additional hyperparameters. The proposed approach reduces the computational complexity of the Cholesky decomposition by hierarchically factorising the covariance matrix into off-diagonal low-rank parts. Meanwhile, the resulting low-rank approximated Cholesky factor can also reduce the computation complexity of the inverse and the determinant operations. Numerical results based on offline and online tracking problems demonstrate the effectiveness of the proposed approach.

Tracking manoeuvring targets often relies on complex models with non-stationary parameters. Gaussian process (GP) based model-free methods can achieve accurate performance in a data-driven manner but face scalability challenges. Aiming to address such challenges, this paper proposes a distributed GP-based tracking approach able to learn the kernel hyperparameters in an online manner, to improve the tracking performance and scalability. It caters to the inherent distributed feature of sensor networks and does not need measurements to be transmitted among sensors for target states predictions. Theoretical upper confidence bounds about the tracking error are derived within the regret bound setting. Through this theoretical analysis, the tracking error per time step is upper bounded as a function of predictive variances from local sensors. The theoretical results are supported by simulation based ones over a case study for tracking over wireless sensor networks. With evaluation on challenging target trajectories, a comparison on state-of-theart centralised and distributed GP approaches, numerical results demonstrate that the proposed approach achieves competitively high and robust tracking performance.