The remote state estimation problem is considered for general non-Gaussian systems. The estimator runs particle filtering algorithm to track the non-Gaussian probability density function (PDF) of the target state. We are concerned with the reduction of sensor-to-estimator communication while maintaining acceptable estimation accuracy. For this purpose, a novel event-based transmission scheme is proposed where the Kullback-Leibler divergence is used to identify informative measurements. We develop a two-step approximation procedure to obtain a parametric form for the event generator function, thereby enabling each sensor to quantify the informativeness of its current measurement without running a copy of the estimator. Furthermore, a Monte Carlo method is proposed to evaluate the likelihood function of the set-valued measurements. Simulation results demonstrate the effectiveness of our scheme, especially when the predictive PDF of the measurement is strongly non-Gaussian. (C) 2019 Elsevier Ltd. All rights reserved.