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Data Fusion via Kalman Filter 133

performance that is superior to which either system could attain on its own.
This section will discuss different approaches for GPS/INS integration. The
main objective is to compare the relative advantages and disadvantages between
the alternative approaches.

3.5.1 INS with GPS Resetting

In this approach, the INS is integrated to provide its state estimate between
the GPS measurement epochs. At a GPS measurement epoch, the methods
of Section 3.3 are used to compute the position and velocity based only on
the GPS measurement data. The GPS position and velocity estimates are
used as the initial conditions for the INS state during the next period of
integration.
Often, the reason that this approach is proposed is its extreme simplicity.
For example, GPS receivers directly output user position and velocity. In this
approach, where the designer treats the position and velocity computed by the
GPS receiver as measurements for the state estimation process, the designer of
the integrated system need not solve the GPS system equations. In addition, the
design of this approach does not involve a KF (outside of the receiver). However,
the disadvantage of this simplicity is a low level of performance relative to the
level that could be achieved by a more advanced approach. Note, for example,
that the IMU errors are not estimated or compensated. Therefore, the rate of
growth of the INS error state does not decrease over time. Also, additional
sensors or multiple GPS antennae and additional processing are required to
maintain the attitude accuracy.
Various ad hoc procedures can be defined to improve performance of the
resettingapproach, butperformanceanalysisistypicallynotpossible. Thereset-
ting approach is not a recommended approach. Note that this approach does
not involve any advanced form of data fusion. The only point at which inform-
ation is exchanged is after the GPS measurement, when the INS state is reset.
Significantly better performance can be obtained by the methods described in
the following section.

3.5.2 GPS Aided INS

The following two sections discuss the EKF as a tool to use GPS measurements
to calibrate INS errors. In both approaches, the INS integrates the vehicle state
based on IMU measurements. In Step 1 of the EKF algorithm of Section 3.2.3,
∗
the INS state is represented by x and the IMU input is represented by u. The
linearized F matrix is given by Equation (3.68). The matrix Q k represents the
covariance of the integrated accelerometer and gyro measurement noise pro-
cesses. The matrix Q k can be computed accurately (see Example 3.1) and
is determined by the quality of the IMU. The only remaining quantities that

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c003” — 2006/3/31 — 16:42 — page 133 — #35