Flight Tests results

Static Points

In all static tests points GADA's performance was satisfactory. As example for the lateral attitude stabilization maneuver with f = +25.86º ± 2.76º @1s (Fig. 9), it is possible to verify that SV #14 LOS were mostly bellow HAP (Fig. 10). As results it is also possible to verify that in this flight condition GADA kept its accuracy while REQUEST diverged (Fig. 11 to 13).

Dynamic Points

The analysis of the dynamic maneuvers it was noticed that GADA's errors increased with the angular speed. When the aircraft is performing the capture of the longitudinal attitude maneuver (Fig. 14) with a roll rate ?±55º/s, it is possible to notice the error build up between the FTI reference attitude and the GADA's computed attitude (Fig. 15 to 17).

Dynamic error analysis
The functional analysis of the Phase Locked Loop - PLL (Fig. 18) of a GPS receiver [17], could explain these dynamic errors (Fig. 15 to 17). When the aircraft is maneuvering, the rate of change of the Doppler shift may result in a difference between the real phase (i.e. the input at the PLL) and the corresponding NCO phase measurement (i.e. output measurement).
Considering the topology presented Fig. 11 - ? Attitude error during the Lateral Attitude Stabilization Maneuver. Fig. 12 - f Attitude error during the Lateral Attitude Stabilization Maneuver Fig. 10 - Angle between satellite LOS and HAP during the Lateral Attitude Stabilization Maneuver. 28 | May 2009 in fig. 18, the transfer function of the PLL is expressed by:

Where: ? is the damping factor (adm); and ?N is the natural frequency (rd/s). In dynamic conditions there is a phase delay error between the true phase (i.e. what we want to measure) and the NCO generated phase (i.e. the resulting measurement provided by the receiver). The capture of the longitudinal attitude maneuver increases the phase rate (Fig. 19) and the associated phase error.

To investigate this effect it would be necessary to:
1. Simulate the same flight condition in order to get the true phase measurement;
2. Apply the simulated phase to the receiver PLL model;
3. To compute GADA attitude solution with the PLL resulting phase; and
4. To compare the resulting GADA attitudes (i.e. Simulated and the flight tests ones).
But the true characteristics of a commercial off the shelf GPS receiver PLL is proprietary and the manufacturer does not disclosures such information. So alternatively it was employed a system identification process (Fig. 21) to best estimate the PLL coefficients and topology for each GPS receiver. Then it was possible to compare the dynamic errors measured at the flight tests campaign with the simulated errors. The resulting analysis presents an acceptable DPLL modeling (Fig. 22 to 24).

Conclusions
The development and the evaluation of GADA’s static and dynamic characteristics are presented and the results are considered satisfactory for the application.
The results show that GADA’s accuracy is dependent of the receiver DPLL characteristics.
Future works should use a software GPS receiver, where the setup of the DPLL coefficients and topology, allows:
1) The validation of the dynamic behavior of an off-theshelf GPS receiver; and
2) The design of customized GPS receivers, for specific high dynamics applications. Also GADA should be evaluated in other test beds, that flies over an extended envelope and thus in a higher dynamic range.

Acknowledgments
We wish to thank the partial support given by the Flight Test Group, for supporting the measurement and the flight tests campaigns. Also we like to tank FINEP under agreement 01.07.0663.00 and 01.07.0540.00 that respectively funded the telemetry system used for the flight tests campaign and its spares parts.

Fig. 18 - GPS receiver phase tracking loop block diagram

Reference:
[1] ETKIN, B. Dynamics of Atmospheric Flight. New York:John Willey & Sons, 1972.

[2] COHEN, C. E. Attitude Determination. In: AIAA. Global Positioning System: Theory and Applications. Washington: AIAA, 1996, v.2, cap.19, p. 519-537.
[3] Shuster, M. D.; Oh, S. D. Threeaxis Attitude Determination from Vector Observations. IEEE Journal of Guidance and Control, Washington, v. 4, n.1, p. 70-77, 1981.
[4] BAR-ITZHACK, I., Y. REQUEST: A Recursive Quest Algorithm for Sequential Attitude Determination. IEEE Journal of Guidance and Control and Dynamics, Washington, v.19, n.5, p. 1034-1038, 1996.
[5] STEVENS, B. L., and LEWIS, F. L., Aircraft Control and Simulation,2nd ed. Hoboken, NJ: John Wiley& Sons, Inc. 2003, ch. 1.3.

[6] BAR-ITZHACK, I, Y; Y. MONTGOMERY, Y; and GARRICK J. C., Algorithms for Attitude Determination using the Global Positioning System, IEEE Journal of Guidance and Control and Dynamics, vol. 21, nº 6, pp. 846–852, 1998.
[7] BALANIS, C. A. Antenna Theory Analysis and Design. New Jersey: John Willey & Sons, 2005, 3rd ed., cap. 2.2, p. 33-38.
[8] ELROD. B. D; BALTROP. K; DIERENDOCK. V. A. J. Testing GPS Augmented with Pseudolites for Precision Approach Applications. In: Institute of Navigation National Technical Meeting of the Satellite Division (ION-GPS), 1994, Salt Lake, Proceedings … Salt Lake: ION-GPS, 1994. p. 1269-1278.
[9] ELROD B. D; DIERENDONK. V. A. J. Pseudolites. In: AIAA. Global Positioning System: Theory and Applications. Washington: AIAA, 1996, v.2, cap.2, p. 51-79.
[10] Leite, N. P. O; Walter, F. The Development and Simulation Results of a GPS Attitude Determination System. In: Institute of Navigation National Technical Meeting of the Satellite Division (ION-GPS), 2002, Portland. Proceedings … Portland: ION-GPS, 2002. p. 1100-1107.
[11] SOUSA, L. B. R.; Leite, N. P. O.; CUNHA, W. C.; and Walter, F. Automation System for the Flight Test Laboratory (SALEV). In: International Telemetering Conference (ITC/USA), 2006, SanDiego. Proceedings … San Diego: ITC/USA, 2006. p. 94-103.

[12] EUROPEAN ACCREDITATION. EA-4/02 - Expression of the Uncertainty of Measurement in Calibration., 1999. 79p.
[13] Leite, N. P. O.; Walter, F. Multiple Time Base Synchronization Process Applied to the Flight Tests Campaign of a GPS Attitude Determination Algorithm. In: International Telemetering Conference (ITC/USA), 2007, Las Vegas. Proceedings … Las Vegas: ITC/USA, 2007. p. 1048-1057.
[14] Leite, N. P. O.; Walter, F. The Development of an Alignment Process to be Used on Flight Test Campaign of a GPS Attitude Determination System. In: Institute of Navigation National Technical
Meeting (ION-NTM), 2003, Anaheim. Proceedings … Anaheim: ION-NTM, 2003. p. 152-162.
[15] SPILKER, J. J. Satellite Constellation and Geometric Dilution of Precision. In: AIAA. Global Positioning System: Theory and Applications. Washington: AIAA, 1996, v.1, cap.5, p. 177-208.
[16] Yoon, S; Lundberg, J. B. Euler Angle Dilution of Precision in GPS Attitude Determination. IEEE Transactions on Aerospace and
Electronic Systems, New York, v. 37, n.03, p. 1077-1083, 2001.
[17] DIERENDOCK. V. A. J. GPS Receivers. In: AIAA. Global Positioning System: Theory and Applications. Washington: AIAA,
1996, v.1, cap.8, p. 329-407.