The complementary filter here proposed, described in the next, is a further method which contributes to integrate position and speed measures, coming from GPS, with accelerations, attitude and orientation measures, coming from an AHRS (Attitude and Heading Reference Systems). In this case, it is not necessary the use of a sophisticated INS with its algorithms for estimating, independently from the GPS, position and speed of the vehicle. This filter aims to determine in the best way the aircraft position and speed, in the NEU reference system, by using both the raw measures from the inertial sensors and the measures supplied by the GPS.

The general concept of the complementary filter is the integration of acceleration measures supplied by the AHRS, in order to obtain position and speed measures affected by lower noise and with a larger band in comparison with GPS measures. However, even if the AHRS measures are little noisy, they are affected from remarkable bias errors, so speed and position calculated only by integration of the accelerations can quickly diverge from the real values. In order to limit the effects due to the bias, therefore, it can be thought to integrate the accelerations and to process them through a high-pass filter, obtaining the medium-high frequency component of the considered signals. The low frequency components can be obtained by a filtering stage of the GPS measures through a low-pass filter. The final estimate of position and speed is equal to the sum of the two components above mentioned.

The resulting architecture of the complementary filter we developed is, therefore, the one shown in the schematic representation of Figure 1.

It is important to emphasize that, in both velocity and position measures estimation, the high-pass filter applied to AHRS measures and the low-pass filter applied to GPS measures must be “complementary”, in the sense that the sum of the transfer functions of the two filters must be equal to one. This is the reason why the navigation measures integration method here proposed is defined “complementary filter”.

The specific cut-off frequencies used in the filters shown in Figure 1 have to be chosen to reach the following two contrasting aims: minimizing the noise power due to the GPS and avoiding the error arising from the integration of the AHRS accelerometers bias.

The method above described applies in normal no-failure conditions, where INS and GPS sensors correctly work. However, also in the case of GPS failure it is necessary obtain estimation, even if not optimal, of vehicle navigation data. The strategy adopted in this situation is described in the next.

In the case of GPS failure, the basic idea is to replace the GPS measures with the ones provided by a sensor characterized by the same characteristics, even if with lower precisions: in this case ADS, with an appropriate offset adjustment, represents a good solution. Pressure altitude (PALT) is used regarding the vertical position measure, while for the vertical speed is used the PALT RATE measure. Regarding position and velocity in the horizontal plane, instead, ADS does not directly supply such measures, but they can be opportunely obtained. In particular, for the velocity in the horizontal plane estimation the procedure described in the next is used. As long as GPS correctly works, it is continuously performed wind estimation, based on the relation:

W = Vin - TAS

where W, Vin and TAS represent respectively wind, inertial velocity and true air speed vectors, in the inertial reference frame. When a GPS failure is detected, this wind estimation is frozen and constant wind is considered, so from the TAS measure derived from ADS it is possible to approximately estimate the inertial speed as:

Such components are used in place of GPS velocity measures as inputs in the complementary filter, which supplies in output velocity and position estimation.

This idea correctly works when the aircraft is following a trajectory in a midair flight mission. In the case of GPS failure during landing, to obtain a better estimation of the measures of interest, it is also possible to use laser altimeter measures. During landing phase, therefore, PALT and PALT RATE ADS measures are replaced by altitude and vertical speed estimations derived from laser altimeter measures. In this case too, of course, the cut-off filtering frequencies applied on the laser are specifically optimized. For what concerns the use of the navigation measures integration method here proposed in the future Global Navigation Satellite Systems (GNSS) framework, furthermore, it is very relevant to emphasize that the described sensor fusion algorithm can be used in this framework too, by simply replacing the GPS receiver with one able to receive EGNOS (European Geostationary Navigation Overlay Service) and GALILEO signals.

Moreover, in the future GNSS framework it will be possible to improve the proposed algorithm, by including new safety features. In particular, the basic idea consists in using the EGNOS performance information (in terms of accuracy, integrity, continuity and availability) to improve the sensor fusion algorithm efficiency and to add an integrated diagnostic function for detecting system failures. Based on this integrated diagnostic function, it will be possible to switch, in case of failure, in an appropriate degraded navigation mode. This will constitute a very relevant enhancement of the proposed navigation system, considering that integrity issues, important in general for many applications, are particularly critical in the aviation field, where vehicles can travel at high speed and can quickly deviate from the flight path.