Title :
A comparison of two Crame´r-Rao bounds for nonlinear filtering with Pd<1
Author :
Hernandez, Marcel ; Ristic, Branko ; Farina, Alfonso ; Timmoneri, Luca
Author_Institution :
Integration Dept., QinetiQ Ltd., Malvern, UK
Abstract :
The paper presents a comparative study of two recently reported Crame´r-Rao lower bounds (CRLBs) for nonlinear filtering, both applicable when the probability of detection is less than unity. The first bound is the information reduction factor CRLB; the second is the enumeration method CRLB. The enumeration method is accurate but computationally expensive. We prove in the paper that the information reduction factor bound is overoptimistic, being always less than the enumeration CRLB. The theory is illustrated by two target tracking applications: ballistic object tracking and bearings-only tracking. The simulations studies confirm the theory and reveal that the information reduction factor CRLB rapidly approaches the enumeration CRLB as the scan number increases.
Keywords :
direction-of-arrival estimation; filtering theory; nonlinear filters; probability; state estimation; target tracking; Cramer-Rao lower bounds; ballistic object tracking; detection probability; enumeration method CRLB; information reduction CRLB; nonlinear filtering; target tracking; Closed-form solution; Covariance matrix; Filtering; Jacobian matrices; Navigation; Nonlinear equations; Radar tracking; State estimation; Target tracking; Time measurement; Ballistic object tracking; Cramér–Rao lower bound; bearings-only tracking; detection probability; information reduction factor; target state estimation;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2004.831906