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

Kalman filter is the most powerful tool for estimation of the states of the linear Gaussian system. In addition, used this method, expectation maximization algorithm can estimate the parameters of the model. However, this algorithm cannot function in real-time situation. Thus, we propose new method that can estimate the transition matrices and the states of the system in real-time. This method utilizes two ideas: estimation in observation space and online learning framework. Applied to damped oscillation model, we have obtained extraordinary performance to estimate the matrices. Also, introduced localization and spatially uniformity to the method, we have demonstrated that our methods could reduce noise in high-dimensional spatio-temporal data. Moreover, this methodology has potential in areas such as weather forecast and vector field analysis.