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 our model 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 in W. 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.