基于非高斯滤波器的状态空间模型极大似然与贝叶斯估计
Maximum Likelihood and Bayesian Estimation for State-Space Models Using the Non-Gaussian Filter
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中文总结 AI 辅助
本文重新研究非高斯滤波器，将其用于状态空间模型的极大似然估计与贝叶斯推断，实验显示其对数似然平滑可优化，实用价值因计算技术进步重获提升。
中文摘要 AI 辅助
非高斯滤波器为非线性及非高斯状态空间模型提供了确定性数值方法，但其应用长期受限于数值积分的计算成本。计算能力与内存容量的进步已大幅降低低、中维度模型的该限制。本文重新研究非高斯滤波器，证明其对极大似然估计与贝叶斯推断的实用性。针对线性、非线性及雷达跟踪模型的数值实验显示，非高斯滤波器得到的对数似然是平滑的，可被可靠优化，而粒子滤波器得到的对数似然即便使用大量粒子，也会受蒙特卡洛变异性强烈影响。贝叶斯估计采用自组织状态空间模型，其中未知参数被纳入状态向量，与潜状态联合估计。这些结果表明，当前计算技术已让确定性滤波在状态空间模型统计推断中的实用价值重获新生。
英文摘要
The non-Gaussian filter provides a deterministic numerical method for nonlinear and non-Gaussian state-space models, but its application has long been limited due to the computational cost of numerical integration. Advances in computing power and memory capacity have substantially reduced this limitation for low and moderate dimensional models. This paper re-examines the non-Gaussian filter and demonstrates its usefulness for maximum likelihood estimation and Bayesian inference. Numerical experiments with linear, nonlinear and radar-tracking models show that log-likelihood obtained by non-Gaussian filter is smooth and can be optimized reliably, whereas the ones obtained by particle filter are affected strongly by Monte Carlo variability even with many particles. Bayesian estimation is performed using a self-organizing state-space model, in which unknown parameters are incorporated into the state vector and estimated jointly with the latent states. These results demonstrate that the current computing technology has renewed the practical value of deterministic filtering for statistical inference in state-space models.
