Aerospace and Electronic Systems Magazine September 2017 - 8

Graceful Degradation and Recovery from GNSS Interruptions
some filter design details might change, the basic architecture of
decentralization and blending described here remains applicable.

AHRS FILTER
The second filter is an AHRS, which uses rate gyro measurements
to estimate the UAV's attitude. Attitude drift errors caused by gyro
biases are kept in check using a second attitude solution derived by
the fusion of measurements from an accelerometer triad, a magnetometer triad, and an airspeed sensor. Earth's gravitational acceleration vector g derived from accelerometer measurements and the
magnetometer measurement of Earth's magnetic field vector are
used to generate an attitude solution by vector matching (or solving Whabah's problem). The airspeed measurement, along with a
kinematic model of the aircraft's attitude dynamics, is used to extract g from the accelerometer measurement of specific force. The
solution from the vector matching is used to arrest attitude drift, as
well as estimate gyro biases. A more thorough description of this
filter can be found in [9].
The AHRS filter's state vector is denoted x 2 ∈  6×1 and consists of roll (ϕ), pitch (θ), and yaw (ψ) attitude states of the vehicle, as well as the three gyro biases (bp, bq, and br). Because
the AHRS uses the same IMU as the GNSS/INS filter, the AHRS
state vector x2 and GNSS/INS state vector x1 are correlated.
This correlation is specifically accounted for and handled by the
blending filters.

DR FILTER
The third filter is a DR filter, which uses airspeed measurements,
barometric altitude measurements, and the output of the AHRS filter to generate a position and velocity solution at 50 Hz. The AHRS
solution is used to calculate a direction cosine matrix, which is used
to resolve airspeed measurements from the body axes to the north-
east-down navigation axes. A single integration yields a position
estimate. However, the airspeed sensor measures speed relative to
the air mass in which the UAV is flying. Therefore, an estimate of
wind speed must be added to the resolved airspeed measurements
before they are integrated to yield position. Periodic GPS position
and velocity measurements are used to estimate the wind speed. A
more thorough description of this filter can be found in [9].
The state vector of the DR filter is denoted x3 ∈ 11×1 and consists of the following states: latitude (Λ), longitude (λ), altitude (h),
local north wind speed (Wn), local east wind speed (We), yaw angle
offset (δψ), pitch angle offset (δθ), three airspeed measurement biases (Ub, Vb, and Wb), and altitude offset (δh).

MAPPING MATRICES
The final objective of the decentralized blending described in this
article was to generate the state vectors xa,k and xb,k, which are defined as follows:
T

x a , k = φk θ k ψ k 

(13)

xb , k = Λ k

λk

hk 

(14)

The attitude states xa,k are used by the FCS to stabilize the small
UAV. The position states xb,k are used for guiding the small UAV
along a desired trajectory in space. To generate xa,k, the attitude
states from the GNSS/INS filter are blended with the attitude states
from the AHRS. This requires mapping matrices M1a and M2,
which are used to shape x1,k and x2,k, respectively. These shaping
matrices are defined as
M1a =  Z3×6 I 3×3 Z 3×6 

(15)

M 2 = I 3×3 Z3×3 

(16)

where Ij×k is a j × k identity matrix and Zj×k is a j × k matrix of zeros.
To generate xb,k, the position states from the GNSS/INS filter are
blended with the position states from the DR filter. To accomplish
this, matrices M1b and M3 are used to shape x1,k and x3,k, respectively. These shaping matrices are defined as follows:
M1b = I 3×3 Z3×12 

(17)

M 3 = I 3×3 Z 3×8 

(18)

EXPERIMENTAL VALIDATION
Validation was accomplished by postprocessing data collected
from series of flight tests of a small UAV instrumented with the
Goldy FCS. In what follows, the results from two flight tests
are presented. In the first flight test, the UAV was operated autonomously by the FCS and GNSS denial was simulated using
a procedure that is described later. In the second flight test, the
UAV was operated remotely by a pilot in visual line of sight of
the vehicle. During the second flight, an actual but unplanned
GPS receiver malfunction resulted in GNSS denial for approximately 88 s.
In the first test, GPS was available to the filters from the moment the FCS was turned on until shortly after takeoff. After reaching altitude, GPS services were interrupted for approximately 3
min and then restored shortly before landing. The GNSS denial
was simulated by suspending the 1-Hz GPS measurement updates
to the GNSS/INS and DR filters.
To have ground-truth for assessing the performance of the
blenders, a fourth GNSS/INS filter was always running as a background process of the flight computer. This reference GNSS/INS
filter had uninterrupted GPS service for the entire first flight. The
error plots that are shown and discussed later were generated by
taking a difference between the output of the blenders and the reference filter.

IEEE A&E SYSTEMS MAGAZINE

SEPTEMBER 2017

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine September 2017