Page 188 - Innovations in Intelligent Machines

180 R.W. Beard
Multipath is a function of the position of the UAV. Therefore we will
√
assume that the error is a sinusoidal signal with a magnitude of 0.6 2, a
frequency equal to ω multipath and a random phase drawn from a uniform distri-
bution over [−π, π].
We will model the measurement noise as a zero mean Gaussian process
with a variance equal to 0.3 meters. The model for the GPS signal is therefore
given by
y GPS,n (t)= p n + ν n,atmosphere + ν clock + η n,measurement (t)
√
+2.5 2sin(ω geometry t + ν n,geometry )
√
+0.6 2sin(ω multipath t + ν n,multipath )
y GPS,e (t)= p e + ν e,atmosphere + ν e,clock + η e,measurement (t)
√
+2.5 2sin(ω geometry t + ν e,geometry )
√
+0.6 2sin(ω multipath t + ν e,multipath )
y GPS,h (t)= h + ν h,atmosphere + ν h,clock + η h,measurement (t),
√
+15 2sin(ω geometry t + ν h,geometry )
√
+0.6 2sin(ω multipath t + ν h,multipath ),
where p n , p e ,and h are the actual earth coordinates and altitude above sea
level respectively. The GPS receiver also computes estimated ground speed
and heading from the measurements listed above. Accordingly, we have
#
! " 2 ! " 2
y GPS,n(t + T s) − y GPS,n(t) y GPS,e(t + T s) − y GPS,e(t)
y GPS,V g = +
T s T s
! "
−1 y GPS,e(t + T s) − y GPS,e(t)
y GPS,course =tan .
y GPS,n(t + T s) − y GPS,n(t)
The update rate of a GPS receiver is typically on the order of T GPS =1
second. However, the update rate can vary between 0.1−2 seconds, depending
on the GPS receiver.

3 Simulation Environment

We will illustrate the quality of the state estimation techniques proposed
in this chapter via simulation. This section briefly describes the simula-
tion environment which is a six degree-of-freedom nonlinear flight simulator
called Aviones, developed at Brigham Young University using C/C++, and
which runs on the Microsoft Windows operating system. The sensor mod-
els described in the previous section were implemented in Aviones using the
parameters shown in Table 2. We have assumed that sensor biases are esti-
mated before flight and are therefore not included in the simulator, with the
exception of GPS, where it is not possible to estimate the biases.