Elliott, RobertMalcolm, W. P.2012-06-282012-06-282008R.J. Elliott and W. P. Malcolm. „Discrete Time Expectation Maximization Algorithms for Markov – Modulated Poisson Processes‟. IEEE Transactions on Automatic Control 53 (2008) 247-2560018-9286http://hdl.handle.net/1880/49072“© 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.” Doi: 10.1109/TAC.2007.914305 Article deposited according to the policy found on the IEEE website, http://www.ieee.org/publications_standards/publications/rights/rights_policies.html, June 28, 2012.In this paper, we consider parameter estimation Markov-modulated Poisson processes via robust filtering and smoothing techniques. Using the expectation maximization algorithm framework, our filters and smoothers can be applied to estimate the parameters of ourmodel in either an online configuration or an offline configuration. Further, our estimator dynamics do not involve stochastic integrals and our new formulas, in terms of time integrals, are easily discretized, and are written in numerically stable forms inW. P.Malcolm, R. J. Elliott, and J. van der Hoek, “On the numerical stability of time-discretized state estimation via clark transformations,” presented at the IEEE Conf. Decision Control, Mauii, HI, Dec. 2003.engChange of measurecounting processesexpectation maximization (EM) algorithmmartingalesjournal article10.11575/PRISM/34080