The Blade Tip Clearance (BTC) measurement method based on Blade Tip Timing (BTT) suffers from poor accuracy under changing speed conditions and in the determination of blade-by-blade tip clearance. To address these challenges, this paper presents the Time of Arrival Polynomial Fitting (ToA-PF) method for achieving high-precision tip clearance measurements under variable speed conditions. Additionally, a correction method is introduced to effectively mitigate measurement errors in blade-by-blade tip clearance. Experimental validation on an academic test rig demonstrates significant improvements. The ToA-PF method enhances clearance measurement accuracy by 77% compared to traditional methods under low and rapidly changing rotational speeds. Furthermore, the correction method for blade-by-blade tip clearance notably enhances measurement accuracy, particularly for the shortest blade, by over 50%. These proposed methods show promise in enhancing the accuracy and practicality of the BTC measurement method based on BTT, offering substantial value for turbine blade health monitoring and predictive maintenance applications.