Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 515

forward in time using the heading rate information), can usually be used to screen
gross errors induced by magnetic disturbances.
9.3.3 Sensor Integration Principles
9.3.3.1 Position Versus Measurement Domain Integration
Integration of GPS with any of the systems and sensors discussed in the previous sec-
tion can generally be done by either position or measurement domain integration.
Position domain integration means that GPS positions and velocities are processed
by the navigation filter, along with data from additional sensors. Measurement
domain integration means that individual GPS satellite pseudorange and Doppler
measurements are processed by the navigation filter, along with data from addi-
tional sensors. Generally speaking, measurement domain processing is preferred,
but it is not necessarily required for acceptable performance (see [54] for a descrip-
tion of a gyro-based DR system that uses position domain integration). The mea-
surement domain approach enables “partial” updates of the DR system using less
than the number of satellites required for a position fix (i.e., three for a two-dimen-
sional fix or four for a three-dimensional fix); thus, performance should be
improved. However, this improvement comes at a cost. The cost is the requirement
for the integration filter to either compute the satellite positions and velocities from
the ephemeris data decoded by the GPS receiver or request this from the GPS
receiver. If the integration filter shares a processor with the GPS receiver, the cost is
zero.
A commonly held myth by newcomers to GPS integration with inertial or auto-
motive sensors is that a measurement domain integration is needed for sensor cali-
bration. In fact, both integration approaches enable calibration of the DR sensors.
For example, GPS heading and speed information (derived from the GPS-
determined velocity), as well as individual Doppler measurements, can be used to
calibrate the gyros, accelerometers, and wheel sensors of the DR system.
9.3.3.2 The Ubiquitous Kalman Filter
The Kalman filter remains the most widely used tool in integrated navigation sys-
tems. In this section, the key aspects of Kalman filter designs for three of the inte-
grated systems identified in the previous section will be provided. It is assumed that
the reader is familiar with Kalman filters or can consult one of the many excellent
textbooks on the subject [5, 55] as well as the overview in Section 9.2.3. The three
systems that will be examined in detail include an INS with GPS, three gyros, and
two accelerometers; a system with GPS, a single gyro, and an odometer; and a sys-
tem with GPS and differential odometers using an ABS.
Two-Accelerometer INS Kalman Filter Model
The error equations for an INS are well known and will not be repeated here [56].
Suitable error models for automotive quality sensors should, of course, include the
basic nine error states associated with the unforced error dynamics of any INS,
excepting the two states specific to the vertical axis (i.e., two INS position errors,
two INS velocity errors, non-INS altitude and vertical velocity errors, and three atti-