ARMCMC: Online Bayesian Density Estimation of Model Parameters

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 costs. 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: being solely able to account for Gaussian noise, being applicable to systems with linear in the parameters (LIP) constraint, or 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 two challenging benchmarks: the estimation of parameters in a soft bending actuator and the Hunt-Crossley dynamic model. Our method shows at-least 70\% improvement in parameter point estimation accuracy and approximately 55\% reduction in tracking error of the value of interest compared to recursive least squares and conventional MCMC.