Blade tip timing (BTT) has become the most promising online monitoring method for turbine blade health. Current BTT data analysis algorithms are extremely sensitive to the number of BTT probes installed and the accuracy of prior information, limiting the practical application of BTT. In this article, a BTT data analysis algorithm is proposed based on a sparse Bayesian learning framework. It requires fewer BTT probes and less prior information than previous algorithms. Different degrees of noise were added to the numerically simulated BTT signal, and the results show that the method has high accuracy and reliability under high-noise conditions. The experimental results demonstrate the feasibility of the method with a single BTT probe without any prior information. Furthermore, the characteristics of the signal of a single BTT probe were investigated from a theoretical perspective.