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Although the Bayesian paradigm offers a formal framework for estimating theentire probability distribution over uncertain parameters, its onlineimplementation can be challenging due to high computational costs. We suggestthe Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, whicheliminates the shortcomings of conventional online techniques while computingthe entire probability density function of model parameters. The limitations toGaussian noise, the application to only linear in the parameters (LIP) systems,and the persistent excitation (PE) needs are some of these drawbacks. InARMCMC, a temporal forgetting factor (TFF)-based variable jump distribution isproposed. The forgetting factor can be presented adaptively using the TFF inmany dynamical systems as an alternative to a constant hyperparameter. Byoffering a trade-off between exploitation and exploration, the specific jumpdistribution has been optimised towards hybrid/multi-modal systems that permitinferences among modes. These trade-off are adjusted based on parameterevolution rate. We demonstrate that ARMCMC requires fewer samples thanconventional MCMC methods to achieve the same precision and reliability. Wedemonstrate our approach using parameter estimation in a soft bending actuatorand the Hunt-Crossley dynamic model, two challenging hybrid/multi-modalbenchmarks. Additionally, we compare our method with recursive least squaresand the particle filter, and show that our technique has significantly moreaccurate point estimates as well as a decrease in tracking error of the valueof interest.

Online Probabilistic Model Identification using Adaptive Recursive MCMC