In the remote detection of the rotational velocity of a target, the vortex beam is easily affected by the random atmospheric turbulence, which causes the phase distortion of the beam and the dispersion of OAM spectrum, resulting in the deterioration of the performance of rotational velocity measurement. Since Wirtinger flow algorithm was proposed, its remarkable feature is that it can complete iterative convergence without any prior information and only one input, without falling into local optimal solutions. Relevant studies have theoretically shown that Wirtinger Flow algorithm has the ability of high precision and absolute convergence to the global optimal solution. The current research has improved the performance of the algorithm by enhancing the traditional WF algorithm. However, the analysis of improving the rotational velocity measurement metrics through compensating the beam distortion in complex environments is still insufficient.To solve this problem, this work enhances the traditional WF algorithm by improving the initialization and gradient descent rules, and proposes Truncated Weighted Wirtinger Flow (TWWF) algorithm. In this algorithm, the median value of the sample is introduced into the truncation rule in the initialization stage to make the initial estimation closer to the global optimal. The weight adjustment strategy of the weighted gradient descent algorithm is used to calculate the weight coefficient according to the results of adjacent iterations, and the distorted vortex beam is compensated to improve the optical field and the rotating Doppler frequency shift characteristics.Firstly, a vortex light field recovery and rotation velocimeter performance improvement system based on TWWF algorithm is designed. The input is simplified into one path. The probe beam then passes through the coded aperture of a programmable LCD screen, simulating a coded diffraction pattern, and then the CCD measures the light intensity for algorithm calculation, and finally the generated compensated phase screen is loaded on the spatial light modulator. The results show that when the atmospheric turbulence intensity Cn2 is 1×10^-14 m^-2/3, the purity, RDS peak-to-maximum sideband ratio and velocity measurement accuracy can reach 0.99, 2.18, 0.80 rad/s. When Cn2 is 1×10^-12 m^-2/3, it can reach 0.74, 2.09, 0.83 rad/s, and the phase relative error can reach the order of 3×10^-16, which demonstrates the powerful compensation ability of TWWF algorithm. In addition, the influence of mask number, superposition state of optical field and other factors on the algorithm metrics is discussed. More masks can provide more phase information, accelerate the convergence speed and prevent the algorithm from falling into the local minimum, improve the global search ability of the algorithm, make the algorithm more accurate and reliable phase recovery, and improve the stability and accuracy of phase recovery. Considering that more masks increase the computational complexity and time cost, it is appropriate to choose L=40, it balances these factors effectively, the purity is 25 times that of L=5, and the velocity measurement error is 57.76% of that of L=5. For vortex beam superposition state, TWWF algorithm also shows excellent compensation ability, P, SMSR, σ can be stable at 0.49, 3.19, 0.54 rad/s. This study further broadens the application of WF type algorithm in the direction of turbulence distortion compensation, and provides a method to improve the remote velocity measurement performance of vortex beams.