<p>This paper considers the zonotopic set-membership estimation problem of discrete-time systems disturbed by process noises and measurement noises. The noises are supposed to be unknown but bounded. The systems’ measurements are quantized by a logarithmic quantizer. The zonotope that contains the systems’ state is obtained. The estimation procedure is divided into three steps: prediction, measurement and correction. How to minimize the Frobenius radius of the zonotopic estimation set and the upper boundedness of the zonotope’s Frobenius radius are both analyzed. A numerical example is given to display the theoretical results in the end.</p>