Comparison of estimation error between two different low-rank Kalman-Bucy filters

This paper analyzes the estimation error of a low-rank Kalman-Bucy filter proposed by the authors. Recently the authors proposed a low-rank approximation of the Kalman filter and showed some properties like the stability condition of the estimation error dynamics. However, the estimation accuracy was only shown by numerical examples. In this paper, the estimation accuracy is analyzed and compared with another low-rank Kalman-Bucy filter introduced by another work, and we show when our proposed filter is superior to the prior one.