Page 186 - Innovations in Intelligent Machines

178 R.W. Beard
Altitude Sensor

Pressure is a measure of force per unit area or
F
P = ,
A
where P is the pressure, F is the force, and A is the area. The static pressure
at a particular altitude is determined by the force exerted by a column of air
at that altitude:
m column g
P = ,
A
where m column is the mass of the column of air, g is the gravitational constant,
and A is the area upon which the column is exerting pressure. The density of
air is the mass per unit volume. Since the volume is given by the area times
the height we get
P = ρhg,
where ρ is the density of air and h is the altitude [8, 11].
Therefore, the output of the static pressure sensor is given by

y static pres = ρgh + β static pres + η static pres ,

where β static pres is a slowly varying bias and η static pres is a zero mean Gaussian
process. To remove the bias, we collect multiple measurements of the pressure
on the ground and average to remove the Gaussian noise to obtain

¯ y static pres (h ground )= ρgh ground + β static pres .

If we know the altitude of the ground station above sea level and the
density of the surrounding air, then the bias β static pres can be determined. If,
on the other hand, we are interested in the height above the ground station
then we can subtract the calibrated ground measurement to obtain

y
y static pres (∆h) = y static pres (h) − ¯ static pres (h ground )
= ρg(h − h ground )+ η static pres (t),
= ρg∆h + η static pres (t),

where ∆h is the height above the ground station.

Air Speed Sensor
When the UAV is in motion, the atmosphere exerts dynamic pressure on the
UAV in the direction of airflow. The dynamic pressure is given by [8]
1 2
P I = ρV ,
a
2