<p>The convergence rate of the online quantum state fliter (OQSF) algorithm for quantum state estimation in the presence of Gaussian measurement noise and sparse disturbance is investigated in this paper. For the OQSF algorithm, by defining the average loss function of the optimization function and constraint conditions during <i>T</i> iterations, we derive and prove the convergence rate theorem for two loss functions. The theorem leads to the convergence rate of the normalized distance in the quantum state density matrix for the OQSF algorithm. Finally, in numerical simulations, we employ the algorithm for online estimation of a 4-qubit quantum system, using the normalized distance of the density matrix as a metric. The algorithm is compared with two existing theoretical studies on online quantum state estimation, validating the derived convergence rate performance and the superiority of the OQSF algorithm.</p>