2.3 Results analysis
The results of the comparison between TruRover track and
double frequency receiver one are not satisfying; indeed
receivers utilized in experiments show some problems in
curves, where the estimated track is larger than the exact one.
This bad performance may be due to the presence of a Kalman
filter inside the system, that is not optimized for the specific
application. Probably at each epoch this filter uses previous
estimated positions in order to anticipate the future one on a
constant velocity, linear trajectory assumption. In that way
when vehicle curves the filter understand it as a mistake and
modify the position; this behaviour causes a delay in curving
and consequently a shift in positioning. Figure 1 shows this
orderly problem on curve.
Higher precision for agricultural applications is not required in
curves but in straight directions, where farmers make their main
activities on yield. However curves have a great importance
mainly at their end because there it is necessary for the vehicle
trajectory to be parallel to the previous one. The main reason
for that is to economize input products spread about field.
Kinematic trajectory is considered the exact one, the reference
for a comparison between pseudo-range and kinematic tracks.
The results show distances greater than 1 meter (the target
aimed) but always inside the method precision (10 meters).
Statistical parameters, as means and standard deviations,
confirm the same things. Table 2 and 3 relate these statistical
valuers. At the beginning the idea was that Kalman filter needs
a period of assessment time to work better; on the contrary,
with the elapsed time the differences increase with a worrying
time drift.
Figure 1. Shift between postprocessed track and TruRover
track.
Statistical
parameters
First
track
Second
track
[m] [m]
σ∆E 0.7816 0.7555
σ∆N 1.1183 1.2799
Mean ∆E 0.169 -0.175
Mean ∆N 1.948 1.573
Max distance 5.733 7.742
Min distance 0.091 0.080
Table 2. Statistical parameters, means and standard deviations,
in kinematic paths..
Statistical
parameters
First
stop
Second
stop
Third
stop
[m] [m] [m]
σ∆E 0.4743 0.3018 0.3163
σ∆N 0.7210 0.5001 0.3907
Mean ∆E 0.221 -0.725 -0.848
Mean ∆N 0.534 2.081 1.086
Max distance 2.022 3.184 2.138
Min distance 0.007 1.262 0.476
Table 3. Statistical parameters, means and standard deviations,
in static stops.
3. DEVELOPMENT OF A NEW ALGORITHM BASED
ON KALMAN FILTERING
The reason for problems in curve is probably the presence of a
Kalman filtering inside TruRover, not especially studied for
farming applications. Thereof the need of trying a kind of
TruRover performances improvement pursued by means of the
development and the implementation of a new algorithm based
on Kalman filtering and, at the same time, optimized for
agricultural requirements.
The first problem was the choice of the process modelling to
put in Kalman equations. In particular two trials have been done
and described in the following: the constant velocity model and
the constant acceleration model. Before the models description,
it will be shortly illustrated Kalman filter principles.