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.

翻译：尽管贝叶斯范式为估计不确定参数的完整概率分布提供了形式化框架，但其在线实现因计算成本高昂而极具挑战性。我们提出自适应递归马尔可夫链蒙特卡洛（ARMCMC）方法，该方法在计算模型参数完整概率密度函数的同时，克服了传统在线技术的缺陷。这些缺陷包括对高斯噪声的局限性、仅适用于参数线性（LIP）系统以及持续激励（PE）约束等。在ARMCMC中，我们提出了基于时变遗忘因子（TFF）的可变跳跃分布。作为常数超参数的替代方案，该遗忘因子可通过TFF在多种动态系统中自适应调整。通过平衡开发与探索，这种特定跳跃分布针对支持模式间推断的混合/多模态系统进行了优化，其权衡策略可根据参数演变速率动态调整。我们证明，ARMCMC在达到相同精度和可靠性时所需的样本量低于传统MCMC方法。通过柔性弯曲执行器和Hunt-Crossley动力学模型这两个具有挑战性的混合/多模态基准测试中的参数估计，验证了所提方法的有效性。此外，我们将该方法与递归最小二乘法和粒子滤波器进行对比，结果表明本文方法在点估计精度上显著更优，且感兴趣值的跟踪误差更低。