 This paper presents an efficient online algorithm for quantum state estimation using a matrix-exponentiated gradient method which is previously used in machine learning. The state update is governed by a learning rate that determines how much weight is given to new measurement results obtained in each step. The algorithm shows convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. To guarantee convergence beyond the noise threshold, the learning rate has to be chosen adaptively and decreasing. As a practical alternative, running averages of the measurement statistics and a constant learning rate are used to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum likelihood and least squares estimators, showing superior performance in terms of accuracy and runtime complexity. This article was authored by Akram Yassary, Christopher Ferry, and Marco Tomamical.