  This work attempts to approximate a linear Gaussian system with a
finite-state hidden Markov model (HMM), which is found useful in solving
sophisticated event-based state estimation problems. An indirect modeling
approach is developed, wherein a state space model (SSM) is firstly identified
for a Gaussian system and the SSM is then used as an emulator for learning an
HMM. In the proposed method, the training data for the HMM are obtained from
the data generated by the SSM through building a quantization mapping.
Parameter learning algorithms are designed to learn the parameters of the HMM,
through exploiting the periodical structural characteristics of the HMM. The
convergence and asymptotic properties of the proposed algorithms are analyzed.
The HMM learned using the proposed algorithms is applied to event-triggered
state estimation, and numerical results on model learning and state estimation
demonstrate the validity of the proposed algorithms.
