A Deep Learning Approach To Estimation Using Measurements Received Over a Network

Abstract

We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are received over a communication network. The measurements are communicated over a network as packets, at a rate unknown to the estimator. Packets may suffer drops and need retransmission. They may suffer waiting delays as they traverse a network path. Works on estimation often assume knowledge of the dynamic model of the measured system, which may not be available in practice. The DNN estimator doesn't assume knowledge of the dynamic system model or the communication network. It doesn't require a history of measurements, often used by other works. The DNN estimator results in significantly smaller average estimation error than the commonly used Time-varying Kalman Filter and the Unscented Kalman Filter, in simulations of linear and nonlinear dynamic systems. The DNN need not be trained separately for different communications network settings. It is robust to errors in estimation of network delays that occur due to imperfect time synchronization between the measurement source and the estimator. Last but not the least, our simulations shed light on the rate of updates that result in low estimation error.