Online Probabilistic Model Identification using Adaptive Recursive MCMC

TL;DR

The paper introduces ARMCMC, an adaptive recursive MCMC method that efficiently estimates entire probability distributions of model parameters in real-time, overcoming computational challenges of traditional Bayesian online techniques.

Contribution

The paper presents ARMCMC with a TFF-based adaptive jump distribution, improving online Bayesian parameter estimation for hybrid/multi-modal systems with fewer samples and higher accuracy.

Findings

Requires fewer samples than conventional MCMC

Achieves higher accuracy in parameter estimates

Reduces tracking error compared to recursive least squares and particle filter

Abstract

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.