ARMCMC: ONLINE MODEL PARAMETERS DENSITY ESTIMATION IN BAYESIAN PARADIGM

Although the Bayesian paradigm provides a rigorous framework to estimate the full probability distribution over unknown parameters, its online implementation can be challenging due to heavy computational cost. This paper proposes Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) which estimates full probability density of model parameters while alleviating shortcomings of conventional online approaches. These shortcomings include only being able to account for Gaussian noise, only being applicable to systems with linear in the parameters (LIP) constraint, and having requirements on persistence excitation (PE). In ARMCMC, we propose a variable jump distribution, which depends on a temporal forgetting factor. This allows one to adjust the trade off between exploitation and exploration, depending on whether there is an abrupt change to the parameter being estimated. We prove that ARMCMC requires fewer samples to achieve the same precision and reliability compared to conventional MCMC approaches. We demonstrate our approach on a challenging benchmark: estimation of parameters in the Hunt-Crossley dynamic model, which models both on/off contact forces applied to soft materials. Our method shows up to 75% improvement in parameter point estimation accuracy and approximately 40% reduction in tracking error compared with recursive least squares and conventional MCMC.