Bias introduced due to noisy point estimates being propagated through deterministic nonlinear mappings is a reoccurring problem in high-fidelity tracking and classification systems. This paper proves that it is a misconception that such bias is reduced when computing the expected value of the nonlinear output that follows when treating the input as a random vector with expectation equal to the provided estimate. Instead, this doubles the bias. An approximately unbiased estimator and an estimate of its covariance matrix are provided. The estimator can be calculated also in the case where the Hessian matrices associated with the nonlinear mapping are unavailable.

Date Published: 17 April 2008
PDF: 9 pages
Proc. SPIE 6969, Signal and Data Processing of Small Targets 2008, 69690G (17 April 2008); doi: 10.1117/12.777456

Published in SPIE Proceedings Vol. 6969:
Signal and Data Processing of Small Targets 2008
Oliver E. Drummond, Editor(s)