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.

翻译：我们设计了一种变分状态估计（VSE）方法，该方法能从（含噪声的）非线性测量中为底层复杂动态过程提供闭式高斯后验分布。该复杂过程是无模型的，即我们没有一个合适的基于物理的模型来描述过程状态的时间演化。该闭式高斯后验由一个循环神经网络（RNN）提供。在推理阶段，使用RNN在计算上较为简单。为了学习该RNN，在学习阶段使用了另一个RNN。基于变分推断原理，两个RNN相互辅助以实现更好的学习。VSE在一个跟踪应用中得到验证——使用二维相机测量模型对一个随机Lorenz系统（一个基准过程）进行状态估计。结果表明，VSE与已知Lorenz系统模型的粒子滤波器以及最近提出的、未知Lorenz系统模型的数据驱动状态估计方法相比具有竞争力。