3DM-GX4
™
-45
™
Inertial Navigation System
User Manual
Performance Optimization
44
when attempting to navigate between geographic way- points expressed in latitude and
longitude. This error is due to the difference between detecting magnetic north, which is output
by the AHRS sensor, and true north, which is used to define lines of longitude. If the AHRS is
always used in one geographical location, the user can correct for this difference using a
constant offset. If the AHRS is used over a wide range of longitude, the magnetic declination
must be calculated from a magnetic model or obtained from GPS subsystem which outputs this
data. The greatest problem with an AHRS is that it is an attitude-only device and requires a
GPS for position and velocity.
As a first attempt at an improved navigation solution, a user could get position and velocity from
a GPS receiver and attitude from an AHRS. This is an acceptable solution for many navigation
problems, but is susceptible to most of the errors described above. A more accurate estimation
of position, velocity, and attitude can be found by fusing the data from these two independent
systems using a Kalman filter.
The 3DM-GX4-45
™
runs a loosely-coupled Extended Kalman Filter. In a loosely-coupled filter,
the inertial sensors in the IMU are used to propagate the state estimation at a high rate (100
Hz); whereas, the GPS position and velocity measurements are used to periodically correct the
state (4 Hz.) This form of Kalman filter is called a sensor fusion filter as it is combining similar
information from multiple sources in a complementary way. This combination takes into
account the statistical properties of the sensors used, providing a better estimate of the true
state than either system individually. The 3DM-GX4-45
™
has a full-state dynamics model. The
state propagation utilizes Newton’s and Euler’s equations of motion with the acceleration and
angular rate treated as control inputs. In addition to the GPS measurement, the IMU
magnetometer is available to correct heading mis-alignments which occur during periods of low
dynamics. The magnetometer corrections can be disabled for applications where large, non-
constant magnetic interference sources exist, which would impair their use (such as when
mounting the 3DM-GX4-45
™
on a gimbal close to the frame of a ground vehicle).
The Kalman filter estimates the full states of position, velocity, and attitude for a total of 25
states: 3 position, 3 velocity, 4 attitude (quaternion), 3 accel bias, 3 gyro bias, 3 accel scale
factor, 3 gyro scale factor, and 3 GPS antenna offset error states. The bias states are
estimated in order to compensate for the time- varying biases inherent in MEMS inertial
sensors, which are the largest error sources for these devices. The bias states are subtracted
from the gyro inputs, thus providing more accurate inertial data to the propagation stage of the
filter. This enhances overall accuracy and is especially useful during GPS outage conditions.
The Kalman filter also provides statistical information about the quality of the estimated states
described in a covariance matrix. The diagonal terms of the matrix are the variance of each