Partitioned Gaussian Process Regression for Online Trajectory Planning for Autonomous Vehicles

Gaussian process regression and ordinary kriging are effective methods for spatial estimation, but are generally not used in online trajectory-planning applications for autonomous vehicles. A common use for kriging is spatial estimation for exploration. Kriging is limited by the necessary covariance matrix inversion and its computational complexity of O(n3), where $n$ represents the number of measurements taken in a sparsely-sampled field. Using the Sherman-Morison matrix inversion lemma, the complexity can be reduced to O(n2). This work focuses on further improving the computational time required to conduct spatial estimation with partitioned ordinary kriging (POK) for online trajectory-planning. A recursive algorithm is introduced to quickly subdivide a field for local kriging, reducing the computation time. We show computational time decreases between ordinary kriging with a regular inverse (OK), the iterative inverse ordinary kriging (IIOK), and POK with the iterative inverse method. Computation times are also compared between OK, IIOK, and POK methods for trajectory planning using a highest variance criterion and linear trajectory segments.