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A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1
Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
* Author to whom correspondence should be addressed.
Received: 8 October 2012; in revised form: 6 December 2012 / Accepted: 7 December 2012 / Published: 14 December 2012
Abstract: Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds.
Keywords: posterior Cramer-Rao lower bound (PCRLB); detection probability; target state estimation; random finite set (RFS); information reduction factor (IRF)
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Cite This Article
MDPI and ACS Style
Tong, H.; Zhang, H.; Meng, H.; Wang, X. A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1. Sensors 2012, 12, 17390-17413.
Tong H, Zhang H, Meng H, Wang X. A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1. Sensors. 2012; 12(12):17390-17413.
Tong, Huisi; Zhang, Hao; Meng, Huadong; Wang, Xiqin. 2012. "A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1." Sensors 12, no. 12: 17390-17413.