Talk
Abstract:
The Linear Model in GPS Integrity Monitoring
Robert J. Kelly
Ohio University
We discuss two topics: the notion of a "mixed" model and the application
of the linear model to the LAAS ground station. Engineers are
usually not familiar with the mixed model concept. The statistics
literature addresses three kinds of linear models: the "fixed
model, the "random effects" model and the "mixed" model. The mixed
model is a combination of fixed and random effects. In many aircraft
navigation systems the linear model is a fixed model. That is
the unknown parameters are fixed quantities over the measurement
period. In the navigation application the fixed parameter can
be the aircraft x,y,z positions. In a random effects model, the
unknown parameters are unobservable parameters that can only be
defined by variance components. In the LAAS application random
effects are selective availability and tropospheric errors. Both
models contain an unobservable model error. We emphasize that
random effects are not the model errors.
In the second topic we derive the B-values from first principles
and compare them to the GPS Local Area Augmentation System (LAAS)
B-values. We begin with the linear model for the reference receiver
architecture of the ground reference station. This model is
a mixed model. Using the mixed model we derive the optimum estimates
and optimum tests. The optimum B-values are the residuals of
the linear model. Using the minimum mean square error (MSE)
as the performance criteria, allows us to calculate the optimum
residuals. We call these optimum linear model residuals, the
linear model B-values. We also show that the difference in the
MSE between the linear model B-values and the LAAS B-values
is not significant. Thus the linear model B-values supports
the choice of the LAAS B-value algorithm. Most surprisingly,
the LAAS B-value algorithm for cov(e) = s2I is identical to
the residual test statistics used by the RAIM algorithm in the
unaugmented GPS. Thus there is a common integrity-monitoring
theme that connects unaugmented GPS, WAAS GOPS and LAAS GPS.
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