In this paper, a sequential analytic center approach for bounded error parameter estimation is proposed. The authors show that the analytic center minimizes the logarithmic average output error among all the estimates within the membership set and is a maximum likelihood estimator for a class of noise density functions which include parabolic densities and approximations of truncated Gaussian. They also show that the analytic center is easily computable for both offline and online problems with a sequential algorithm. The convergence proof of this sequential algorithm is obtained and, moreover, it is shown that the complexity in terms of the maximum number of Newton iterations is linear in the number of observed data points.