Assumed Density Filtering and Smoothing with Neural Network Surrogate Models
This work addresses state estimation challenges in nonlinear systems for applications like control, but it is incremental as it builds on existing methods with neural network surrogates.
The paper tackled state estimation in nonlinear dynamic systems using neural network models by enabling accurate uncertainty propagation with an analytic formula for computing mean and covariance, and demonstrated superiority on stochastic Lorenz and Wiener systems, showing improved linear quadratic regulation with state estimates.
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.