This paper explores the application of centralised and distributed Gaussian process algorithms to real-time target tracking and compares their performance. By embedding the algorithms into the Stone Soup, the focus is on the innovative implementation of Gaussian process methods with learning hyperparameters and implementation with a factorised variance of the Gaussian kernel. The performance of the methods with different kernels was evaluated, not only with the Gaussian kernel. Extensive experiments with various kernel configurations demonstrate their importance in enhancing prediction accuracy and efficiency, especially in real-time tracking. The case studies with manoeuvring targets show significant advancements in tracking capabilities, particularly in wireless sensor networks, using optimised Gaussian process methods. This work advances Stone Soup’s capabilities and lays the groundwork for future investigations into adaptive Gaussian Process applications in tracking and sensor data analysis.