The process of integrating
the measurements form the experiment to obtain position and velocity is
achieved developing and executing a complex algorithm offline after the
flight. A
classical levelled mechanizations process was used, so that all the
measurements was projected into a reference frame NED (North-East-Down).
The results of the LowCoINS
experiment used as a pure inertial navigation system are briefly
reported hereafter:
As you can see, just
processing few minutes of data, the calculated position diverges
immediately. This is due to the bias of the gyros resulting in wrong
projection of the acceleration from the body frame to the navigation
frame that lead to a wrong velocity determination and in turn a wrong
position determination. Together with the bias of the gyros, also bias
of the accelerometers and low sensitivity of the IMU contribute to the
poor result. However this results were widely expected because inertial
sensor for navigation need to be order of magnitudes better than those
onboard LowCoINS.
The alternative is to
integrate the position and velocity determination from the IMU with that
from a GPS receiver, using a sensor fusion algorithm i.e a Kalman
Filter.
Kalman filtering is a
statistical technique that combines knowledge of the statistical nature
of system errors with knowledge of system dynamics, as represented as a
state space model, to arrive at an estimate of the state of a system.
The state estimate uses a weighting function, called the Kalman gain,
which is optimized to produce a minimum error variance. For this reason,
the Kalman filter is called an optimal filter.
Integration of GPS and INS
was made with a configuration known as loosely integrated or
loosely coupled. This configuration typically includes a GPS
receiver, which measurements are position and velocity form rather than
pseudorange and pseudorange rate, an IMU, navigation equations to
convert the gyros and accelerometer measurement from the IMU to platform
attitude, position and velocity.
In this way it is possible
to have a correction of the wrong position and velocity calculated by
the IMU with a more precise GPS data, but in the meanwhile, having an
estimate of the position and velocity of the Bexus 6 gondola in the time
lapse between two GPS fixes, because of the higher rate of the IMU.
The figure below show the
flight profile obtained used LowCoINS filtered data.
The quite poor performances
of the experiment used as a navigator are exclusively due to the poor
quality of the sensors that are not good enough for inertial navigation
purposes. However, they could be good enough to realize a low accuracy
Attitude and Heading Reference System (AHRS). The attitude of the
gondola can be very useful for a wide range of balloon borne
experiments, and it is an information that is not available from the
Bexus standard avionics. The working principle of the LowCoINS used as
AHRS is to integrate the angular velocity from the gyros to determine
the attitude, while bounding the unavoidable drift of the attitude,
mainly due to gyros biases, using the magnetometers and/or
accelerometers as an auxiliary system for the attitude determination.
The fusion of the attitude data computed from the integration of the
gyros output and from the manipulation of the information from
accelerometers and magnetometers is achieved using a sensor fusion
algorithm such as a Kalman filter.
Hereafter are reported some
flight phases. Below it is a graph showing the attitude of the gondola
at lift-off. It can be noticed that the gondola is tilted about 15 deg
about its pitch axis before returning in a levelled attitude at the
moment of liftoff. This is due to the oscillation of the gondola as
Hercules moves before the gondola is released. After the liftoff, the
gondola begins to oscillate about its vertical axis. Note that the
discontinuity in the yaw angle is due to the representation used for the
yaw: the yaw in our assumption is between +/-180 deg, meaning that the
solution jumps from 180 to -180 or vice-versa as the gondola points
toward south. Zero degree for yaw means North, +90° means East, -90°
means West.
During the ascent and float
phase no major oscillation have been recorded. The gondola remained
levelled with oscillation around its vertical axis.
The attitude determination at the cut-down as well as
at the landing, is uncertain and not reliable because of the large
dynamic accelerations sensed by our sensors in these moments. It is
noticeable a spike, particularly on the pitch and roll angles,
corresponding to the time instants of the cut-down and the landing.
Further tuning of the Kalman filter is required to have a better
estimate of the attitude in these phases.
The following graph shows the attitude at the
landing. Except for the spikes exactly at the touchdown, the attitude
estimation is meaningful, and can be noticed that the gondola remains a
little bit tilted after the landing, probably because of the terrain
under the gondola.
The following video shows the capabilities of LowCoINS as an Attitude
and Heading Reference System (AHRS).