Deep Learning Aided State Estimation for Guarded Semi-Markov Switching Systems with Soft Constraints

This article investigates the problem of state estimation for guarded semi-Markov switching systems with soft constraints. We first construct the switching system in a multiple model manner and derive the recursive Bayesian filter compatible with the sojourn time and base state dependent mode transitions. To solve the intractable conditioned mode transition probabilities, we develop deep learning based classifiers with long short-Term memory networks capturing the temporal dependencies. Various network structures are designed to handle different situations where knowledge of the transition probability matrix is available or deficient. Furthermore, we incorporate sequential Monte Carlo techniques into the multiple model framework to resolve the local filtering task. A novel particle refinement procedure exploiting the constraint information is proposed to improve the efficiency of particle propagation and prevent the exponential increase of particle number simultaneously. Simulations on a robotic manipulator and an autonomous vehicle tracking task validate the effectiveness of the proposed state estimation method.