  Although the Bayesian paradigm offers a formal framework for estimating the
entire probability distribution over uncertain parameters, its online
implementation can be challenging due to high computational costs. We suggest
the Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, which
eliminates the shortcomings of conventional online techniques while computing
the entire probability density function of model parameters. The limitations to
Gaussian noise, the application to only linear in the parameters (LIP) systems,
and the persistent excitation (PE) needs are some of these drawbacks. In
ARMCMC, a temporal forgetting factor (TFF)-based variable jump distribution is
proposed. The forgetting factor can be presented adaptively using the TFF in
many dynamical systems as an alternative to a constant hyperparameter. By
offering a trade-off between exploitation and exploration, the specific jump
distribution has been optimised towards hybrid/multi-modal systems that permit
inferences among modes. These trade-off are adjusted based on parameter
evolution rate. We demonstrate that ARMCMC requires fewer samples than
conventional MCMC methods to achieve the same precision and reliability. We
demonstrate our approach using parameter estimation in a soft bending actuator
and the Hunt-Crossley dynamic model, two challenging hybrid/multi-modal
benchmarks. Additionally, we 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.
