Aerospace and Electronic Systems Magazine September 2017 - 9

Layh and Gebre-Egziabher

Figure 5.

Time history of attitude errors for the open-loop GNSS/INS filter (green square), the AHRS filter (red triangle), and the attitude blender (blue circle).

ATTITUDE ESTIMATION PERFORMANCE
Figure 5 shows the attitude estimation performance during the first
flight test in which GNSS denial was simulated. The figure compares the attitude errors from the GNSS/INS filter running open
loop (i.e., without GPS aiding), the AHRS filter, and the attitude
blender. It can be seen that the attitude errors of the blender are
smaller than those of the GNSS/INS filter running in open loop.
While it is not readily apparent from the traces in Figure 5, the
blender attitude errors are also smaller than those from the AHRS
filter. This can be seen when examining the attitude error statistics
in Table 2. The magnitude of these errors is small enough to allow
the FCS to continue stabilizing the UAV during the GNSS denial.
It can also be seen that the transition from GNSS available to
GNSS denied and subsequently back to GNSS available occurs
smoothly and without sudden transients. This is a desirable feature
of an attitude solution used by a feedback controller for attitude
stabilization of a flight vehicle. This shows that the decentraliza-

tion allows the FCS to gracefully degrade when GNSS signals
are lost and smoothly recover when the signals become available
again.
Figure 5 is a single time history of attitude errors. Making a
more definitive statement about performance or confirming the results shown in Figure 5 are not unrealistically optimistic requires
either a large number of Monte Carlo simulations or performance of
a covariance analysis. In this article, the latter approach was used.
The results are plotted in Figure 6, which shows the time history of
the square root of the first three diagonal elements of the attitude
blender's covariance matrix in (10). In general, the one-sigma errors appear to be larger than the actual attitude errors. This indicates
that the results shown in Figure 5 are not unrealistically optimistic.
The transition from GNSS available to GNSS denied occurs automatically and smoothly because the blender weights are continuously updated. When the GNSS signal is lost, the open-loop GNSS/
INS covariance becomes large. This, in turn, causes the blender
weight on the GNSS/INS solution to become small. This can be

Table 2.

Attitude Error Statistics for Time History Shown in Figure 5
Heading
rms

Pitch
rms

Roll
rms

13.38°

5.73°

5.84°

AHRS

7.16°

2.93°

4.49°

Blending filter

6.61°

2.85°

4.45°

Open-loop GNSS/INS

SEPTEMBER 2017

IEEE A&E SYSTEMS MAGAZINE

9



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