对比神经滤波与经典滤波在非线性系统中的表现,发现状态空间模型更优。
Model-Free Neural Filtering: A Comparison with Classical Filters in Nonlinear Systems
- 用Transformer、RNN和状态空间模型做无模型神经滤波,对比粒子滤波与卡尔曼滤波。
- 状态空间模型(如Mamba)在多个非线性系统中接近经典滤波性能,推理速度更快。
- 适合无系统模型但需高效实时估计的场景,尤其关注结构化建模优势。
神经网络在控制与决策中的状态估计算法中日益普及,但其在非线性动态系统中作为规范滤波器的表现仍不明确。与依赖显式动力学和噪声模型的经典滤波不同,神经估计器可仅从数据训练。本文系统比较了无模型神经估计器与经典滤波方法在多种非线性场景下的表现。神经方法评估了基于Transformer的模型、循环神经网络及状态空间模型(SSMs);经典方法则对比粒子滤波(PF)与非线性卡尔曼滤波(UKF)。结果表明,在神经方法中,结构化状态空间模型(特别是Mamba和Mamba-2)始终表现强劲,能在多个非线性系统中逼近强基线经典滤波性能,并在未获系统模型情况下优于较弱经典基线。同时,所评估的神经实现方案在测试硬件上推理吞吐量显著更高。当模型假设匹配时,精确的模型基滤波仍占主导。我们归因于状态空间模型的过滤对齐归纳偏置:在固定参数预算、有限数据及长时程评估下,递归隐状态更新使其结构更接近经典滤波。
原文摘要 · Abstract (English)
Neural network models are increasingly used for state estimation in control and decision-making, yet it remains unclear to what extent they behave as principled filters in nonlinear dynamical systems. Unlike classical filters, which rely on explicit dynamics and noise models, neural estimators can be trained purely from data. We present a systematic comparison between model-free neural estimators and classical filtering methods across multiple nonlinear scenarios. On the neural side, we evaluate Transformer-based models, recurrent neural networks, and state-space models; on the classical side, we compare against particle filters and nonlinear Kalman filters. Results show that structured state-space models (SSMs), in particular Mamba and Mamba-2, are consistently strong among neural estimators. They approach strong classical filters in several nonlinear systems and outperform weaker classical baselines without access to system models, while the evaluated neural implementations achieve substantially higher inference throughput on the tested hardware. Accurate model-based filters can still dominate when their assumptions are well matched. We attribute the relative strength of SSMs to filtering-aligned inductive bias: recursive latent-state updates make them structurally closer to classical filters under fixed parameter budgets, finite data, and long-horizon evaluation.
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