The Statistical Estimation of Navigation Errors

W. A. Poor

Abstract:	A big problem for both the designer and the user of a navigation system is to determine how well the system is doing. Among other things, the system’s designers need statistical information to see if the system will meet design goals, and to integrate it with other systems. Navigators also perform a simple filtering function when they combine position estimates from several systems to produce a “most probable position”; this requires some prior information on relative system accuracies. Finally, navigators would like to detect and correct system problems before they make navigation unsafe. Traditional methods for assessing a system’s accuracy have relied on comparisons of positions reported by the system with external reference data. The external data source is usually assumed to be perfect, and is often referred to as “ground auth”. For example, a system designer may check a system on a well-instrumented test range, and a ship’s navigator may use radar to check system accuracy against geographic points on a coastline. Checking a system against ground truth data has several disadvantages. For example, it only provides information in a limited geographical setting and for relatively short periods of time. In particular, although a test on a range may provide detailed quantitative information, a ground truth check of a system in service often yields only rudimentary information. Finally, the assumption of perfect ground truth data attributes the errors in the ground truth reference data to the system under test. This paper presents an algorithm for estimating system accuracy without the use of ground truth data; at least three systems must be available. The estimates are expressed in terms of system covariance matrices and relative bias vectors; if one of the systems is a dead-reckoning or inertial system, the algorithm also estimates a drift rate parameter. An unclassified summary of tests with more than 20 U.S. Navy ships backs up the results of Monte Carlo testing.
Published in:	Proceedings of the 1991 National Technical Meeting of The Institute of Navigation January 22 - 24, 1991 Sheraton San Marcos Hotel Phoenix, AZ
Pages:	361 - 369
Cite this article:	Poor, W. A., "The Statistical Estimation of Navigation Errors," Proceedings of the 1991 National Technical Meeting of The Institute of Navigation, Phoenix, AZ, January 1991, pp. 361-369.
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