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Data Fusion via Kalman Filter 143

preconditions is the integration of GPS and INS. We have presented an analytic
overview of a few of the existing uses of the EKF in this application. Many other
alternatives have been suggested in the literature. We have used a 2D example
to work through various design issues and to illustrate various implementation
issues.
While the theory of this chapter has reviewed GPS aided INS in standard
vector form, four of the examples have utilized a fictional 2D world. There-
fore, it is useful to briefly consider how the conclusions of those examples
generalized to the 3D world in which an actual system must function. The
objectives of Example 3.2 were to illustrate the standard method of solution
of the GPS positioning problem and to demonstrate that the components of
the position estimate error vector were correlated (i.e., R x is not diagonal).
The objectives of Examples 3.3 and 3.4 were to illustrate the use of the Q
matrix as a tuning parameter, to reinforce the fact that such tuning removes
the optimal stochastic properties from the KF, and to illustrate the fact that
there are not optimal settings of the tuning parameters that apply in all user
situations. In addition, that example demonstrates that the position estimate
error vector is not white, but has significant time correlation. The objectives of
Example 3.6 were to illustrate the error state modeling approach which allows a
2
proper stochastic interpretation of KF implementations, to illustrate the state
augmentation process used for instrument calibration, to illustrate that in this
approach the Q and R matrices are not tuning parameters but are physically
determined, to illustrate that the observability of certain subspaces of the error
state are dependent on the vehicle motion, and to illustrate that the state estim-
ation error is uncorrelated with the vehicle motion due to the IMU and INS. All
these issues were more convenient to illustrate in a 2D example, but are equally
applicable to our 3D world.
Another implementation approach, referred to in the literature as Deep
or Ultratight integration, feeds information from the INS back into the GPS
receiver [46–48]. We have not discussed these methods in this chapter as their
implementation requires access to GPS receiver source code, which is not avail-
able to most GPS users. The objective of these techniques is to use the INS
estimates of the GPS receiver position and velocity to aid the receiver in acquir-
ing and tracking the GPS satellite signals. This would be especially beneficial
in low signal-to-noise ratio situations.

ACKNOWLEDGMENTS
The authors gratefully thank California PATH and CalTrans for their contin-
ued interest in and support of related research at the University of California
Riverside. Specifically, this chapter was written with support from CalTrans
2
It is only proper to first order for EKF implementations.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c003” — 2006/3/31 — 16:42 — page 143 — #45