Global Positioning System Reference
In-Depth Information
2. Methodology
2.1 Reduced inertial sensor system
In addition to MEMS-based sensors, the concept of RISS is used in a navigation scheme for
a full-sized vehicle (Iqbal et al., 2008) in order to further lower the cost of the positioning
solution. The RISS used in (Iqbal et al., 2008) involves a single-axis gyroscope and two-axis
accelerometer together with a built-in vehicle speed sensor to provide a 2-D navigation
solution in denied GPS environments. With the assumption that the vehicle remains mostly in
the horizontal plane, the vehicles speed sensor is used with heading information obtained
from the vertically-aligned gyroscope to determine the velocities along the East and North
directions. Consequently, the vehicles longitude and latitude are determined. If pitch and
roll angles are needed the two accelerometers pointing towards the forward and transverse
directions are used together with odometer-derived speed and a reliable gravity model to
determine these angles independently of the integration filter. In (Iqbal et al., 2009), 2-D
RISS/GPS integration were presented using Kalman filter (KF) for a full-sized vehicle.
In this work a low-cost navigation system using a KF to integrate MEMS-based RISS with GPS
in a loosely-coupled scheme is described. The RISS used herein is 3-D: it includes a three-axis
accelerometer and a single-axis gyroscope aligned with the vertical axis of the body frame
of the robot together with two wheel encoders. Here accelerometers are used to calculate
3-D velocity and position while the vertical gyroscope is used to calculate the azimuth angle
(i.e. the heading of the robot). Pitch and roll are calculated based on the idea presented in
(Noureldin et al., 2002)(Noureldin et al., 2004) using the two horizontal accelerometers and
the forward velocity obtained from wheel encoders. This constitutes the RISS mechanization.
The benefits of eliminating the other two gyroscopes in this RISS mechanization scheme
are as follows: (1) further decreases in system costs and (2) improvements in positioning
accuracy by employing fewer inertial sensors and thus less contribution of sensor errors
towards positional errors. Of particular importance is the reduction in error in pitch and
roll calculations. Whereas full mechanization of pitch and roll from gyroscopes involves
integration, their calculation in RISS mechanization using accelerometers does not. This last
fact decreases the portion of positional error originating from pitch and roll errors.
2.2 Coordinate transformation from local level lram (LLF) to body frame (B-F)
The local level frame (LLF) serves to represent mobile robot attitude and velocity for operation
on or near the surface of the earth and is defined as an origin, x, y and z-axis. The origin
coincides with the center of the sensor frame (origin of inertial sensor triad). The y-axis
points to true north. The x-axis points to east. Finally, the z-axis completes the right-handed
coordinate systems pointing up, perpendicular to the reference ellipsoid.
One of the important direction cosine matrices for specifying rotation between one coordinate
frame to another is
l
b
which transforms a vector from
b
-frame to LLF, a requirement during
the mechanization process.
R
l
b
R
is expressed in terms of yaw, pitch and roll Euler angles is
defined as:
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