Underwater DOA estimation generally uses sound waves as signal carriers, and the propagation speed of sound waves is constantly affected by various factors. Sound velocity errors can degrade the performance of conventional DOA estimation algorithms, becoming an important issue that cannot be ignored in underwater DOA estimation. The existing narrowband signal sound speed independent algorithms eliminate sound speed errors by adding an array and relying on the angle relationship between the two arrays. However, the sound speed search process performed to eliminate sound speed increases computational complexity, and the estimation accuracy is affected by the search step size. Compared to narrowband signals, broadband signals usually contain more source angle feature information, so DOA estimation of broadband signals receives greater attention. The ROOT-ISSM-VI-MUSIC algorithm, based on broadband signals and without the need for sound speed search, calculates multiple sets of polynomial roots containing information on the source angle and sound speed at each frequency point and averages them. Based on the array angle relationship, the expression of the actual sound speed related to the root mean is obtained, thus obtaining a sound speed independent DOA estimation value, avoiding the process of sound speed search. The simulation results show that under the same number of array elements, the ROOT-ISSM-VI-MUSIC algorithm has higher accuracy in joint estimation of sound velocity and DOA.