Quadrotor flight data

The quadrotor flight data has an approximately duration of 830 seconds, which is a period of about 13 – 14 minutes of flight. Here it is remarkable to see how the INAs’ estimations behave at the beginning. At the two other trajectories, this issue is not as notable because some minutes until the ride on the rollercoasters are left for calibration and alignment processes. But returning to the subject, the overall trajectory is shown subsequently:

Figure 7-13: Propagation and observer attitude estimation – Quadrotor flight.

Figure 7-14: RIEKF attitude estimation – Quadrotor flight.

As it is easily seen, the RIEKF estimates quite badly. Moreover, thanks to the Earth magnetic field measurement is perfectly estimated. This problem is not as pronounced for the observer and for the MEKF. It has to be remarked that it was not straightforward to select the covariance matrices for the KFs to estimate correctly as the trajectories have really sudden and abrupt changes difficult to predict.

Figure 7-15: MEKF attitude estimation – Quadrotor flight.

The MEKF is really better than the MEKF in this case; when the initial error is corrected and the algorithm has converged it always remains close to the measured values. It is highly important to remind that we are not comparing which estimation is closer to the measured attitude angles because they might not be perfect either. Then the question is: to what information should we compare the estimations? To solve this issue, amplified plots of the situation will be analysed in detail to try to conclude which one is the best estimation or the most suitable for our interests. Another aid added to the plots is the propagation of the attitude itself, which is a quite reliable source to compare the estimations with.

A closer examination can be performed with amplified plots. For instance, on the subsequent figure, there is a clearer example of how this should be interpreted to conclude on which one of the curves is closer to the real signal without any perturbation.

As it is seen, all three curves are accurate but paying attention to the second curve (pitch angle estimation) it is difficult to conclude which curve is better. The common sense leads us to the conclusion that the true/real attitude should be somewhere in between the three lines, and if we focus on the time period between 345 – 350 seconds, it is clear that the best estimation curve is the green line (or the observer estimation line). Moreover, even seeing that the green line is most of the time in between the other two lines, there are some parts of the plot where this is not accomplished.

To finish with this deduction, it is interesting to fix to the third plot of the previous figure. Here, a more evident conclusion can be extracted. As it is shown, the blue line (measured values line) is far from being the best of three, but there is a correlation between the green and red lines which seem to be following the same behaviour. The red line is updated every 5 seconds with the reference of the green line, but most of the 5 sec-period is not diverging that much. Thus, I am able to conclude that the observer estimation in this period is closer to the real values more time than the other evaluated curves.

After that, two amplified versions of the same plot in a different time period for the RIEKF and MEKF estimations are displayed:

From my point of view, it can be said that the MEKF estimation is better than the RIEKF, which seems to be more turbulent and not that accurate. Meanwhile, the MEKF is more similar to the observer estimation.

For comparing both of them, the initial part of the previous plots will be displayed to be able to evaluate the behaviour of the beginning in a better way:

Figure 7-19: Amplified initial observer attitude estimation – Quadrotor flight.

Figure 7-20: Amplified initial MEKF attitude estimation – Quadrotor flight.

The time scales are different but even being more turbulent at the beginning the MEKF is faster in converging to the desired measured values than the observer which lasts about 10 seconds to converge, while the MEKF only lasts 4 seconds. From another point of view, sometimes this is not an advantage as it is probably that the faster the convergence the more turbulent of noisy is the estimation. In this case, the observer overall estimation seems to be smoother than the MEKF one. This characteristic seems to be the result of the symmetry- preserving theory.

Evaluating the last sentence, our thoughts can lead us to the conclusion that the RIEKF should be, then, better than the observer. But probably what has happened is that the RIEKF parameters should be tuned in a different manner to adjust better the estimation. The issue is

that parameter configuration is far from being straightforward and no better configuration has been achieved regarding that the configuration should work in a more general case as the observer and the MEKF configurations do.

To finalize with this section it is also shown the velocity estimations without going more deep into them:

Figure 7-21: Observer velocity estimation – Quadrotor flight.

Figure 7-23: MEKF velocity estimation – Quadrotor flight.

For the velocity estimation is hard to conclude which of the algorithms is better. The MEKF seems to be better but for the z-axis. Then the observer is not really good for the x-axis, neither the RIEKF. But during the overall flight the RIEKF is more accurate from my point of view.

The reason why I was saying at the beginning of this chapter that the absolute truth of which of the algorithms is more accurate is difficult to know, can be observed in here where for the attitude estimation is better the observer or the MEKF but for the velocity is better the RIEKF. With real-time data is not straightforward to contrast the algorithms. It seems to be more reliable the evidences extracted from the previous section 7.1. More specific conclusions will be stated at section 8.