Zero Mean Noise Processes that Do Not Appear to be Zero Mean

Victor S. Reinhardt

Abstract:	This paper shows that correlated but random zero mean noise processes can cause estimation filters (such as Kalman and least squares filters) to generate anomalous results that are similar to those generated by unmodeled non-zero mean causal behavior. The paper discusses two types of such noise processes: stationary Poisson and Gauss-Markov processes and non-stationary negative power law (neg-p) processes. The paper shows that such anomalous results are due to two factors. First, it is shown that single ensemble members of such correlated noise processes exhibit non-ergodic-like behavior over a finite data collection interval T, if tc the correlation time of the noise process is an appreciable fraction of T, even if the process is strictly ergodic as T?8. This these causes practical realizations of such filters, which rely on ergodic-like behavior in a single ensemble member for their proper operation, to generate results that deviate from theoretically predicted behavior. Second, it is shown that the signatures over T of such individual ensemble members can mimic those of the desired signal being estimated. This causes the filter to treat such noise as part of the desired signal and leads to the underestimation of the true error generated by the noise. It is then shown that setting T >> tc allows one to properly separate the noise from the desired signal and to properly estimate the true error. It is further shown that tc ? 8 for neg-p noise, and thus one can never separate the correlated part of such noise from the desired signal, regardless of the value of T. This is shown to lead to infinite true errors for neg-p noise unless one introduces periodic calibration to bound the divergent effects of such noise. The paper concludes with a description of (causal) environmentally induced errors that mask their causal nature and exhibit behavior similar to correlated ZM noise processes.
Published in:	Proceedings of the 2009 International Technical Meeting of The Institute of Navigation January 26 - 28, 2009 Disney's Paradise Pier Hotel Anaheim, CA
Pages:	384 - 390
Cite this article:	Reinhardt, Victor S., "Zero Mean Noise Processes that Do Not Appear to be Zero Mean," Proceedings of the 2009 International Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2009, pp. 384-390.
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