  This paper concerns the identification of continuous-time systems in
state-space form that are subject to Lebesgue sampling. Contrary to equidistant
(Riemann) sampling, Lebesgue sampling consists of taking measurements of a
continuous-time signal whenever it crosses fixed and regularly partitioned
thresholds. The knowledge of the intersample behavior of the output data is
exploited in this work to derive an expectation-maximization (EM) algorithm for
parameter estimation of the state-space and noise covariance matrices. For this
purpose, we use the incremental discrete-time equivalent of the system, which
leads to EM iterations of the continuous-time state-space matrices that can be
computed by standard filtering and smoothing procedures. The effectiveness of
the identification method is tested via Monte Carlo simulations.
