Page 182 - Innovations in Intelligent Machines

174 R.W. Beard
The limited payload capacity of small UAVs not only restricts the type and
quality of the sensors, it also limits the computational resources that can be
placed on-board the UAV. For example, the Procerus Kestrel autopilot has an
8-bit Rabbit microcontroller with 512K of memory. Therefore, Kalman filters
that estimate all of the states as well as the sensor biases are not feasible. The
objective of this chapter is to describe simple attitude estimation techniques
for small UAVs that require limited computational resources.
The chapter is organized as follows. In Section 1 we define and briefly
describe the states that need to be estimated. In Section 2 we describe the
sensors that are generally available on small UAVs and develop mathematical
models of their behavior. Section 3 briefly describes the simulation environ-
ment that is used to demonstrate the algorithms described in this chapter.
Section 4 describes simple state estimation techniques that use digital low pass
filters and sensor model inversion. In Section 5 we provide a brief review of the
continuous-discrete Kalman filter. Finally, Section 6 describes the application
of the continuous-discrete extended Kalman filter to roll, pitch, position, and
heading estimation.

1 UAV State Variables

Aircraft have three degrees of translational motion and three degrees of rota-
tional motion. Therefore, there are twelve state variables as listed below:

p n = the inertial north (latitude) position of the UAV,
p e = the inertial east (longitude) position of the UAV,
h = the altitude of the UAV,
u = the body frame velocity measured out the nose,
v = the body frame velocity measured out the right wing,
w = the body frame velocity measured through the belly,
φ = the roll angle,
θ = the pitch angle,
ψ = the yaw angle,
p = the roll rate,
q = the pitch rate,
r = the yaw rate.

The state variables are shown schematically in Figure 1. As an alternative to
T
expressing the velocity vector as (u, v, w) , it can be expressed in terms of
the airspeed V a , the angle-of-attack α, and the side-slip angle β. The trans-
formation between the two representations is given by [22]