A Polaroid acoustic transducer, mounted on the helicopter, continuously
broadcasts a 
kHz. tone downward onto a cone-shaped reflector that
spreads the signal in the horizontal plane.
Three Polaroid microphones at each end of the field receive the signal
and electronics amplify it so that the resulting saturated waveform is a
square-wave. Each sensor counts the number of pulses that it receives.
The ground computer reads the pulse counts through an interface board
over a serial line at 
Hz.
The 
wave is emitted from the helicopter at time 
. The wave crest is received at sensor 1 at
time 
where 
is the distance
from the helicopter to sensor 1 when the wave is emitted, and a is the
speed of sound.
If receiver 1 starts listening at time 
, the number of pulses
counted at time t equals the number of pulses
emitted since time 
minus the number of pulses between the vehicle
and the sensor. Therefore, each sensor measures the distance to the
helicopter at some previous time, depending on the relative locations of the
vehicle and sensor.
The sensor measurements drive a Kalman filter which estimates the
vehicle's 2-D position and velocity. The state of the system is
propagated to the time of the sensor measurement and the measurement
is corrected for the vehicle's velocity.
For small velocities, a correction for the velocity was not considered
necessary. Therefore, (1) reduces to:
Each sensor may be initialized by knowing the initial
distance to the vehicle and solving (2) for the value of for
that sensor.
By counting pulses, at any future time, the current distance
may be determined by solving (2) using this value of .
To protect against sensor dropout, measurements are checked for
reasonability before being incorporated into the state estimate.
If a sensor drops out, the position estimate from the other sensors
is sufficient to re-initialize the failed sensor.