In this work, a problem of energy-based event-triggered remote state estimation for systems described by discrete finite-state hidden Markov models is investigated. We consider energy harvesting sensors, which absorb power from the environment or other resources and convert it to electrical power. The event-triggering condition (ETC) considered depends on the sensor energy level, which evolves according to a Markov process. The reference measure approach is used to obtain the optimal estimates of the state based on event-triggered measurement information available at the remote estimator. By introducing a reference probability measure and a map from the "real-world" measure to the reference measure, we derive the recursive expression of the unnormalized state conditional distribution under the reference measure, which depends on the estimate of the energy level. Next, we propose a second level of reference probability measure, under which, the state, measurement, energy level and event-trigger are mutually independent, so that the recursive form of unnormalized estimate of the energy level under this reference measure can be obtained. With the help of the two reference measures, the state estimate in the "real-world" probability measure can be derived: The effectiveness of the proposed method is illustrated with simulation results for a linear Gaussian system quantized and parameterized into a hidden Markov model. (C) 2017 Elsevier Ltd. All rights reserved.