  This paper deals with the identification of piecewise affine state-space
models. These models are obtained by partitioning the state or input domain
into a finite number of regions and by considering affine submodels in each
region. The proposed framework uses the Expectation Maximization (EM) algorithm
to identify the parameters of the model. In most of the current literature, a
discrete random variable with a discrete transition density is introduced to
describe the transition between each submodel, leading to a further
approximation of the dynamical system by a jump Markov model. On the contrary,
we use the cumulative distribution function (CDF) to compute the probability of
each submodel given the measurement at that time step. Then, given the submodel
at each time step the latent state is estimated using the Kalman smoother.
Subsequently, the parameters are estimated by maximizing a surrogate function
for the likelihood. The performance of the proposed method is illustrated using
the simulated model of the JAS 39 Gripen aircraft.
