Learning generative models and inferring latent trajectories have shown to be challenging for time series due to the intractable marginal likelihoods of flexible generative models. It can be addressed by surrogate objectives for optimization. We propose Monte Carlo filtering objectives (MCFOs), a family of variational objectives for jointly learning parametric generative models and amortized adaptive importance proposals of time series. MCFOs extend the choices of likelihood estimators beyond Sequential Monte Carlo in state-of-the-art objectives, possess important properties revealing the factors for the tightness of objectives, and allow for less biased and variant gradient estimates. We demonstrate that the proposed MCFOs and gradient estimations lead to efficient and stable model learning, and learned generative models well explain data and importance proposals are more sample efficient on various kinds of time series data. 

Road friction estimation concerns inference of the coefficient between the tire and road surface to facilitate active safety features. Current state-of-the-art methods lack generalization capability to cope with different tire characteristics and models are restricted when using Bayesian inference in estimation while recent supervised learning methods lack uncertainty prediction on estimates. This paper introduces variational inference to approximate intractable posterior of friction estimates and learns an amortized variational inference model from tire measurement data to facilitate probabilistic estimation while sustaining the flexibility of tire models. As a by-product, a probabilistic tire model can be learned jointly with friction estimator model. Experiments on simulated and field test data show that the learned friction estimator provides accurate estimates with robust uncertainty measures in a wide range of tire excitation levels. Meanwhile, the learned tire model reflects well-studied tire characteristics from field test data.