用神经网络模型实现精准状态估计与平滑，提升控制性能。
Assumed Density Filtering and Smoothing with Neural Network Surrogate Models
- 基于神经网络的解析均值与协方差传播方法
- 在随机Lorenz系统和Wiener系统上表现优于传统方法
- 提出交叉熵更适合作为滤波器评估指标
卡尔曼滤波器和Rauch-Tung-Striebel（RTS）平滑器在线性动态系统中是最优的状态估计方法。对于非线性系统，核心挑战在于如何将不确定性通过状态转移和输出函数进行传播。针对神经网络模型，本文利用一种最新的解析公式，精确计算深度神经网络在高斯输入下的均值与协方差，实现准确的不确定性传播。我们主张，相比均方根误差（RMSE），交叉熵更适合作为滤波器与平滑器的评估指标。实验在随机Lorenz系统和Wiener系统上验证了该方法在状态估计上的优越性，并发现当使用该状态估计进行反馈时，能实现更优的线性二次调节（LQR）性能。代码已开源：https://github.com/simontheflutist/analytic-moments。
原文摘要 · Abstract (English)
The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output function. For the case of a neural network model, we enable accurate uncertainty propagation using a recent state-of-the-art analytic formula for computing the mean and covariance of a deep neural network with Gaussian input. We argue that cross entropy is a more appropriate performance metric than RMSE for evaluating the accuracy of filters and smoothers. We demonstrate the superiority of our method for state estimation on a stochastic Lorenz system and a Wiener system, and find that our method enables more optimal linear quadratic regulation when the state estimate is used for feedback. Code available at https: //github.com/simontheflutist/analytic-moments.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。