Online Probabilistic Model Identification using Adaptive Recursive MCMC

The Bayesian paradigm provides a rigorous framework for estimating the whole probability distribution over unknown parameters, but due to high computational costs, its online application can be difficult. We propose the Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, which calculates the complete probability density function of model parameters while alleviating the drawbacks of traditional online methods. These flaws include being limited to Gaussian noise, being solely applicable to linear in the parameters (LIP) systems, and having persisting excitation requirements (PE). A variable jump distribution based on a temporal forgetting factor (TFF) is proposed in ARMCMC. The TFF can be utilized in many dynamical systems as an effective way to adaptively present the forgetting factor instead of a constant hyperparameter. The particular jump distribution has tailored towards hybrid/multi-modal systems that enables inferences among modes by providing a trade-off between exploitation and exploration. These trade-off are adjusted based on parameter evolution rate. In comparison to traditional MCMC techniques, we show that ARMCMC requires fewer samples to obtain the same accuracy and reliability. We show our method on two challenging benchmarks: parameter estimation in a soft bending actuator and the Hunt-Crossley dynamic model. We also compare our method with recursive least squares and the particle filter, and show that our technique has significantly more accurate point estimates as well as a decrease in tracking error of the value of interest.