ARMCMC: Bayesian Online Full Density Estimation of Model Parameters
The Bayesian paradigm provides a rigorous framework for estimating the whole probability distribution over unknown parameters, but due to high processing costs, its online application can be difficult.
The Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method is proposed in this study, which calculates the complete probability density of model parameters while avoiding the drawbacks of traditional online methods. These flaws include being limited to Gaussian noise, being solely applicable to systems with a linear in the parameters (LIP), and having persisting excitation requirements (PE).
A variable jump distribution based on a temporal forgetting factor is proposed in ARMCMC.
This enables the trade-off between exploitation and exploration to be adjusted based on whether the parameter being evaluated changes abruptly or smoothly. In comparison to traditional MCMC techniques, we show that ARMCMC requires less 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. Our findings are compared to those obtained using pure MCMC and two efficient online estimators, recursive least square and particle filter. Our technique exhibits a significant improvement in parameter point estimate accuracy as well as a decrease in tracking error of the value of interest.
