For a parametric inversion of standard or global rainbow signals， this study proposes a local minima-based general inversion algorithm， establishes a nonlinear optimized objective function with inequality constraints based on the complex angular momentum theory theory with correction coefficients and iteratively solves the function using sequential quadratic programming. Before the inversion， a different signal preprocessing， including the removal of the high-frequency structure and the inversion parameter range estimation， was performed for the standard and global rainbow signal. The rainbow signals of the droplets with different refractive indices and droplet size distributions （logarithmic and normal distributions） were numerically simulated based on the Lorenz-Mie theory. The proposed inversions with or without the size distribution were performed to verify the algorithm's effectiveness. The results show that the maximum absolute error of the refractive index of the standard rainbow signal inversion is less than 3×10^-4， and the maximum relative error of the droplet size is 1.3%. Under various conditions， the error of the refractive index of the global rainbow signal inversion is less than 1×10^-4， and the relative error of the mean droplet size is less than 1.67%. Finally， the algorithm was verified via the experimental standard and global rainbow data.