Efficient factorisation-based Gaussian process approaches for online tracking

Target tracking often relies on complex models with non-stationary parameters. Gaussian process (GP) is a model-free 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 factorisation-based 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.