VSE: Variational state estimation of complex model-free process
Gustav Norén, Anubhab Ghosh, Fredrik Cumlin, Saikat Chatterjee
TL;DR
The paper tackles Bayesian state estimation for complex model-free dynamics using nonlinear measurements. It introduces Variational State Estimation (VSE), which employs two RNNs (RNN_post for inference and RNN_prior for learning) to learn a Gaussian posterior q(x_t|y_{1:t}) via variational inference, yielding a closed-form, sampling-free posterior during inference. Training maximizes a variational lower bound that couples the learned prior and posterior and uses the reparameterization trick for efficient gradient-based optimization. The method is demonstrated on a stochastic Lorenz system observed by a 2-D camera, showing VSE to be faster than pDANSE and competitive with a model-aware PF, highlighting its potential for real-time, model-free tracking in imaging-based sensing scenarios.
Abstract
We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have a suitable physics-based model characterizing the temporal evolution of the process state. The closed-form Gaussian posterior is provided by a recurrent neural network (RNN). The use of RNN is computationally simple in the inference phase. For learning the RNN, an additional RNN is used in the learning phase. Both RNNs help each other learn better based on variational inference principles. The VSE is demonstrated for a tracking application - state estimation of a stochastic Lorenz system (a benchmark process) using a 2-D camera measurement model. The VSE is shown to be competitive against a particle filter that knows the Lorenz system model and a recently proposed data-driven state estimation method that does not know the Lorenz system model.