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When an agent, person, vehicle or robot is moving through an unknown environment without GNSS signals, online mapping of nonlinear terrains can be used to improve position estimates when the agent returns to a previously mapped area. Mapping algorithms using online Gaussian process (GP) regression are commonly integrated in algorithms for simultaneous localisation and mapping (SLAM). However, GP mapping algorithms have increasing computational demands as the mapped area expands relative to spatial field variations. This is due to the need for estimating an increasing amount of map parameters as the area of the map grows. Contrary to this, we propose a recursive GP mapping estimation algorithm which uses local basis functions in an information filter to achieve spatial scalability. Our proposed approximation employs a global grid of finite support basis functions but restricts computations to a localized subset around each prediction point. As our proposed algorithm is recursive, it can naturally be incorporated into existing algorithms that uses Gaussian process maps for SLAM. Incorporating our proposed algorithm into an extended Kalman filter (EKF) for magnetic field SLAM reduces the overall computational complexity of the algorithm. We show experimentally that our algorithm is faster than existing methods when the mapped area is large and the map is based on many measurements, both for recursive mapping tasks and for magnetic field SLAM.