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

Real-time Linear Operator Construction and State Estimation with Kalman Filter Tsuyoshi Ishizone 1 Graduate School of Advanced Mathematical Sciences, Meiji University and Kazuyuki Nakamura Department of Interdisciplinary Mathematical Sciences, Meiji University JST, PRESTO Abstract 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. Thus, we propose new method that can estimate the transition matrices and the states of the system in real-time. 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 spatiotemporal data. Moreover, this methodology has potential in areas such as weather forecast and vector field analysis. Keywords: state space model, noise reduction, flow analysis, online learning, weather forecast 1 INTRODUCTION A quick tool of noise reduction and short-term prediction is important for areas such as weather forecast and adjusting scanning probe microscope (SPM). In weather forecast, engineers need a speedy denoising method to utilize the result for instantaneous forecast.