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On the modified Riccati equation and its application to target tracking
 

Summary: On the modified Riccati equation and its application to
target tracking
Yvo Boers
and Hans Driessen
THALES NEDERLAND
Haaksbergerstraat 49
7554 PA Hengelo
The Netherlands
Email: {yvo.boers,hans.driessen}@nl.thalesgroup.com
keywords: Target tracking, Kalman filter, Riccati equation, Cramer Rao lower bound, Lyapunov equation, Stability
Abstract
In this paper the modified Riccati equation is studied. This modified Riccati equation has already been associated
with tracking a target under measurement uncertainty. We 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 quite some attention
recently, especially in relationship with Cramer Rao bounds. In this paper some properties of the modified Riccati
equation will be derived and proven. 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.
1 Introduction
In this paper the modified Riccati equation, as it was originally formulated in [1] is revisited. This modified Riccati
equation plays a role in several target tracking related topics, such as: Cramer Rao Lower Bounds (CRLB's), see [2, 4, 3, 5]

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering