Comparison of LAAS B-Values to the Linear Model Optimum B-values

Robert J. Kelly

Abstract:	The accuracy of the GPS Local Area Augmentation System (LAAS) is achieved by using pseudorange corrections in the LAAS ground reference system to form estimates of the signal-in-space portion of the navigation system error (NSE). The LAAS integrity monitor ensures that these pseudorange correction error do not exceed a given value. These pseudorange correction error estimates are called B-values. The entire integrity of the landing system guidance centers on the truth of the B-values. Integrity is maintained by testing the B-values using the LAAS integrity monitor. Since the B-values are so important, how are they derived? Are they optimum estimates of the pseudorange correction errors? In fact the LAAS B-values are not derived from first principles. They are ad-hoc estimates based upon the idea that one of M receivers can be assumed to be the reference receiver that estimates the pseudorange correction error. The remaining M-1 receivers are viewed as the monitors that compare this estimate to a predetermined ground station alert limit. Using this procedure, M equations are formed in terms of the pseudorange corrections. The solution of these equations is the LAAS B-values. The purpose of this paper is to derive the B-values from first principles. What we do is determine a linear model for the ground reference station. From this linear model the optimum estimates and optimum tests are derived. The optimum estimates are called the linear model B-values. A linear model has a measurement equation and a covariance matrix. The linear model applies to the LAAS ground station because the pseudor&ge corrections are the measurements and the measurement equation is linear. We show that the linear model B-values are identical to the LAAS B-values when there are no reference receiver failures. When there are reference receiver failures the variance or error of the LAAS B-values are slightly more than the optimum linear model B-values over an ensemble of trials. Thus the linear model suuuorts the choice of the LAAS B-value algorithm. The expectation of the mean square E(MS) errors (or variance) of the linear model B-values are a lower bound on the E(MS) of the LAM B-values. Most surprisingly, the LAM B-value algorithm is identical to the residuals test statistics used by the RAIM algorithm in the unaugmented GPS.
Published in:	Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999) June 27 - 30, 1999 Royal Sonesta Hotel Cambridge, MA
Pages:	191 - 198
Cite this article:	Kelly, Robert J., "Comparison of LAAS B-Values to the Linear Model Optimum B-values," Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999), Cambridge, MA, June 1999, pp. 191-198.
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