The performances of the complementary filter earlier described have been tested by means of both simulated and real world flights.
With references to off-line testing, the simulator values of the relevant variables have been assumed as real and compared with the values obtained from complementary filter and GPS. The values obtained from GPS are filtered through a first order low-pass filter, whose cut-off frequency has been chosen in order to reduce as much as possible the noise, but without attenuating the aircraft dynamic. Based on these requirements, the cut-off frequency used for GPS has been set to 1 Hz.
In order to emphasize the performances and the usefulness of the complementary filter, in the next some figures are shown which present a comparison among measures obtained by complimentary filter (red line), measures obtained by GPS (black line) and real value (blue line) of some inertial parameters of interest. The figures refer to an autonomous landing off-line simulation and are representative of the several off-line simulations performed in the validation stage of the autonomous guidance algorithms and, as a consequence, of the complementary filter too.

Figure 2 - Comparison among measures obtained by complimentary filter and GPS and real value of altitude during off-line simulated autonomous landing
In particular, Figure 2 shows the comparison among the above mentioned values with reference to the altitude measure during an autonomous landing, while Figure 3 shows this comparison regarding the vertical speed during the same manoeuvre.
Both figures show that by using the complementary filter here proposed two advantages can be obtained:
● complementary filter is able to attenuate the noise more than the first order low-pass filter;
● measures obtained from complementary filter have more accuracy than the ones obtained by filtering the GPS measures. For what concerns real world in-flight testing, in all flights performed in order
to validate advanced guidance algorithms developed in the framework of TECVOL project, as previously described, the behaviour of complementary filter fully confirmed results obtained in offline simulations. For instance, this is shown in the figures reported in the next, referred to different in flight tests and selected to emphasize the performances of the complementary filter with regard to altitude (see Figure 4, referred to a real world autonomous landing manoeuvre) and to vertical speed estimations (see Figure 5, which refers to a real world mid-air flight phase).

Figure 3 - Comparison among measures obtained by complimentary filter and GPS and real value of vertical speed during off-line simulated autonomous landing

Figure 4 - Comparison among altitude measures obtained by complimentary filter and GPS during real world autonomous landing manoeuvre

The complementary filter has a further feature: it is able to delete the frequency content due to a sudden GPS precision loss. This is shown in the figures reported in the next, which refer to GPS precision loss cases experienced during real flights. In particular, these figures show altitude (see Figure 6) and XNEU position (see Figure 7) measures when the GPS precision decreases (as confirmed by increasing value of GPS measure standard deviation).

Conclusions

In this paper a new algorithm has been described for the integration of measures provided by satellite navigation system with the ones provided by other sensors, such as ADS, AHRS and laser altimeter, in order to allow a more accurate determination of vehicle position and speed, in both no-failure and GPS failure conditions. The effectiveness of the proposed algorithm has been demonstrated by means of both off-line and real world in-flight tests, referred to an aeronautical application. It must be emphasized yet that the proposed algorithm is not limited to aeronautical use only but it can be implemented in all satellite-based navigation applications.

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Figure 5 - Comparison among vertical speed measures obtained by complimentary filter and GPS during real world autonomous landing manoeuvre

Figure 6 - Comparison among altitude measures obtained by complimentary filter and GPS during real flight in case of GPS precision loss
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Figure 7 - Comparison among XNEU position measures obtained by complimentary filter and GPS during real flight in case of GPS precision loss

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