Likelihood functions evaluated using particle filters are typically noisy, computationally expensive, and non-differentiable due to Monte Carlo variability. These characteristics make conventional optimization methods difficult to apply directly or potentially unreliable. This paper investigates the use of Bayesian optimization for maximizing log-likelihood functions estimated by particle filters. By modeling the noisy log-likelihood surface with a Gaussian process surrogate and employing an acquisition function that balances exploration and exploitation, the proposed approach identifies the maximizer using a limited number of likelihood evaluations. Through numerical experiments, we demonstrate that Bayesian optimization provides robust and stable estimation in the presence of observation noise. The results suggest that Bayesian optimization is a promising alternative for likelihood maximization problems where exhaustive search or gradient-based methods are impractical. The estimation accuracy is quantitatively assessed using mean squared error metrics by comparison with the exact maximum likelihood solution obtained via the Kalman filter.

翻译：使用粒子滤波评估的似然函数通常具有噪声、计算成本高昂且因蒙特卡洛变异性而不可微。这些特性使得传统优化方法难以直接应用或可能不可靠。本文研究了利用贝叶斯优化来最大化由粒子滤波估计的对数似然函数。该方法通过高斯过程代理模型对噪声对数似然曲面进行建模，并采用平衡探索与利用的采集函数，从而仅需有限次数的似然评估即可识别出最大化点。通过数值实验，我们证明贝叶斯优化在存在观测噪声的情况下能够提供稳健且稳定的估计。结果表明，在穷举搜索或基于梯度的方法不切实际的情况下，贝叶斯优化是似然最大化问题的一种有前景的替代方案。通过与卡尔曼滤波器获得的精确最大似然解进行比较，使用均方误差指标对估计精度进行了定量评估。