Modified Riccati equation and its application to target tracking

The modified Riccati equation is studied here. This modified Riccati equation has already been associated with tracking a target under measurement uncertainty. The authors consider the special case of tracking a target without clutter but with a probability of detection of less than one. This special case has received some attention recently, especially in relationship with Cramer-Rao bounds. Here, some properties of the modified Riccati equation are derived and proved. Also the relationship of the modified Riccati equation with two special suboptimal filters is shown. Furthermore, the relationship with the Cramer-Rao bound and other bounds is studied.