Retinal blood vessels structure analysis is an important step in the detection of ocular diseases such as diabetic retinopathy and retinopathy of prematurity. Accurate tracking and estimation of retinal blood vessels in terms of their diameter remains a major challenge in retinal structure analysis. In this research, we develop a rider-based Gaussian approach for accurate tracking and diameter estimation of retinal blood vessels. The diameter and curvature of the blood vessel are assumed as the Gaussian processes. The features are determined for training the Gaussian process using Radon transform. The kernel hyperparameter of Gaussian processes is optimized using Rider Optimization Algorithm for evaluating the direction of the vessel. Multiple Gaussian processes are used for detecting the bifurcations and the difference in the prediction direction is quantified. The performance of the proposed Rider-based Gaussian process is evaluated with mean and standard deviation. Our method achieved high performance with the standard deviation of 0.2499 and mean average of 0.0147, which outperformed the state-of-the-art method by 6.32%. Although the proposed model outperformed the state-of-the-art method in normal blood vessels, in future research, one can include tortuous blood vessels of different retinopathy patients, which would be more challenging due to large angle variations. We used Rider-based Gaussian process for tracking blood vessels to obtain the diameter of retinal blood vessels, and the method performed well on the "STrutred Analysis of the REtina (STARE) Database" accessed on Oct. 2020 (https://cecas.clemson.edu/~ahoover/stare/). To the best of our knowledge, this experiment is one of the most recent analysis using this type of algorithm.