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Data Fusion via Kalman Filter 135

the vector of position errors are correlated. For the EKF estimation of the
INS error, the position error correlation matrix R x (t) must be available and
due to the cross-correlation scalar measurement processing cannot be used.
Typically, GPS receivers will not provide R x (t) along with the estimated
position.
Nonwhite measurement error processes: As shown in Examples 3.3 and 3.4
the GPS position error processes are not white, but may have significant time
correlation. The time correlation may come from nonwhite GPS measurement
errors such as multipath or from the GPS solution method. In particular, when
the GPS receiver position solution incorporates a KF [45], then the time correl-
ation of the GPS position errors is increased. The designer of a loosely coupled
GPS aided INS approach should ensure that the GPS receiver is configured to
determine epoch-wise position and velocity solutions.
Doppler: The GPS “Doppler” measurement is typically not a true Doppler
measurement. Typically, the Doppler measurement is the change of the phase
of the carrier signal over some interval of time [40]. The interval of time is
often 1.0 sec. Because of this, the GPS velocity output computed from the
Doppler measurement is not the instantaneous velocity at some specific time-
of-applicability.
Lever arm: The INS computes the position of the IMU effective center
location. The GPS computes the position of the antenna phase center. These
two positions are not the same. The vector offset is referred to as the lever arm
and should be compensated for the EKF data fusion procedure.
The main motivation for the use of a loosely coupled approach, instead
of a tightly coupled approach, is that the former is simpler. A loosely coupled
approach can be implemented with an off-the-shelf GPS receiver and an off-the-
shelf INS. The designer need not work with clock models, GPS ephemeris data,
ephemeris calculations, or GPS basic measurements. Note that this approach
does attempt to estimate IMU calibration parameters (e.g., biases). As those
errors are calibrated, the rate of growth of the INS errors will decrease. However,
depending on the extent of the simplifications made in implementing the EKF
and the extent to which the above issues are addressed, the INS errors may not
be correctly estimated.

3.5.2.2 Tightly coupled system
As illustrated in Figure 3.5, in a tightly coupled system, the EKF measurements
are the GPS range (or phase change) measurements. Residual measurements are
formed with the INS estimates of range (or phase change). The INS estimates
the range using Equation (3.44) with ε i = 0. To utilize that equation, the
satellite position is computed using ephemeris data downloaded through the
GPS receiver. Similarly, the GPS pseudorange or carrier phase measurements
are output by the GPS receiver.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c003” — 2006/3/31 — 16:42 — page 135 — #37