On a New Low-Rank Kalman-Bucy Filter and its Convergence Property

Abstract

In this paper, we propose a new low-rank Kalman-Bucy filter. We approximate the Riccati equation associated with the Kalman-Bucy filter by low-rank matrices and discuss its convergence property. Furthermore, a condition under which the proposed low rank Kalman-Bucy filter becomes stable is derived. The performance between the proposed and previous approximations are shown numerically.