A new conditional posterior Cramér-Rao lower bound for a class of nonlinear systems

ABSTRACT

In this paper, a new conditional posterior Cramér-Rao lower bound (CPCRLB) is proposed for a class of nonlinear systems, in which current measurement is dependent on current state as well as one step previous state. In order to compute the proposed CPCRLB recursively, a new particle filter for such class of nonlinear systems is designed, based on which a general formulation of the proposed CPCRLB can be derived. To facilitate practical engineering applications, CPCRLBs for special cases of such class of nonlinear systems, including nonlinear systems with coloured measurement noises and nonlinear systems with correlated noises at one epoch apart, are developed, respectively. Simulation results show the efficiency and superiority of the proposed CPCRLB as compared with existing CPCRLB.

Keywords:

• Conditional posterior Cramér-Rao lower bound
• coloured measurement noises
• correlated noises at one epoch apart
• particle filter
• nonlinear system

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61001154], [grant number 61201409], [grant number 61371173]; China Postdoctoral Science Foundation [grant number 2013M530147], [grant number 2014T70309]; Heilongjiang Postdoctoral Fund [grant number LBH-Z13052], [grant number LBH-TZ0505]; Fundamental Research Funds for the Central Universities of Harbin Engineering University [grant number HEUCFQ20150407].

Notes on contributors

Yulong Huang

Yulong Huang received his BS degree from the Department of Automation, Harbin Engineering University, Harbin, China, in 2012, and is currently working towards a PhD degree in control science and engineering. His current research interests include state estimation, system identification and information fusion.

Yonggang Zhang

Yonggang Zhang received his BS and MS degrees from the Department of Automation, Harbin Engineering University, Harbin, China, in 2002 and 2004, respectively. He received his PhD degree in Electronic Engineering from Cardiff University, UK in 2007 and worked as a post-doctoral fellow at Loughborough University, UK from 2007 to 2008 in the area of adaptive signal processing. Currently, he is a professor of navigation, guidance, and control in Harbin Engineering University (HEU) in China. His current research interests include signal processing, information fusion and their applications in navigation technology, such as fiber optical gyroscope, inertial navigation and integrated navigation.