Real-time Linear Operator Construction and State Estimation with the Kalman Filter

Abstract

The Kalman filter has been shown to be the most powerful tool for estimating the states of a linear Gaussian system. With this method, an expectation maximization algorithm can be used to estimate the model's parameters. However, the algorithm is unable to function in real-time due to the enormous computation and memory costs for smoothing. We propose three methods by which to estimate the model's states and parameters in real-time. We have demonstrated that the method correctly estimates the states and the parameters for the damped oscillation model. In addition, by introducing localization and spatial uniformity to the proposed method, we have demonstrated that the methods effectively denoise and short-term forecast for high-dimensional spatio-temporal data. The results indicate that the proposed methods can be applied in various fields, such as weather forecasting and vector field analysis.