On Difference Variances as Residual Error Measures in Geolocation

Victor S. Reinhardt

Abstract:	Two types of random error measures are utilized by the navigation community. Observable residual error (R) variances are used in geolocation to characterize the mean square (MS) error of data from a trajectory estimate generated from the data itself. On the other hand, Mth order difference (Ä) variances, such as Allan and Hadamard variances, are used in time and frequency (T&F) source characterization to determine the MS of the Mth order difference of data over a separation interval ô. Ä-variances are used in this capacity because they have excellent convergence properties for the negative power law (neg-p) noise present in T&F sources, while Rvariances are not known for such properties. When neg-p noise is present in geolocation problems, it would be desirable to use Ä-variances as measures of residual error. This paper shows that Ä-variances can indeed be used in this capacity under certain conditions, principally when the model function used estimate the trajectory is an th ) 1 M ( . order polynomial. It is also shown that Rvariances share the good convergence properties of Ä- variances when neg-p noise is present, even when the Ä- variances can’t be used to represent residual error. It is further shown that the convergence properties of Rvariances are a function of the complexity of the model function used. Therefore, R-variances are guaranteed to converge in the presence of neg-p noise if one is free to choose the model function.
Published in:	Proceedings of the 2008 National Technical Meeting of The Institute of Navigation January 28 - 30, 2008 The Catamaran Resort Hotel San Diego, CA
Pages:	763 - 772
Cite this article:	Reinhardt, Victor S., "On Difference Variances as Residual Error Measures in Geolocation," Proceedings of the 2008 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2008, pp. 763-772.
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