Page 330 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

TIME-OF-FLIGHT ESTIMATION OF AN ACOUSTIC TONE BURST 319

complexity as the variance in the error estimate would be lowest. How-
ever, the two optimal networks here have roughly the same number of
parameters. So, there is no clear best choice between the two.
The cross-validation errors of networks trained with neurc show
more variation (Figure 9.3). The minimal cross-validation error is again
10.5% for a network with a single hidden layer of 30 units. Given that
the graph for bpxnc is much smoother than that of neurc, we would
prefer to use a bpxnc-trained network.

9.1.6 Conclusions

The best overall result on the housing data set was obtained using a
bpxnc-trained neural network (10.5% cross-validation error), slightly
better than the best SVC (11.9%) or a simple linear classifier (13.0%).
However, remember that neural network training is a more noisy pro-
cess than training an SVC or linear classifier: the latter two will find the
same solution when run twice on the same data set, whereas a neural
network may give different results due to the random initialization.
Therefore, using an SVC in the end may be preferable.
Of course, the analysis above is not exhaustive. We could still have tried
more exotic classifiers, performed feature selection using different criteria
and search methods, searched through a wider range of parameters for the
SVCs and neural networks, investigated the influence of possible outlier
objects and so on. However, this will take a lot of computation, and for
this application there seems to be no reason to believe we might obtain
a significantly better classifier than those found above.

9.2 TIME-OF-FLIGHT ESTIMATION OF AN
ACOUSTIC TONE BURST

The determination of the time of flight (ToF) of a tone burst is a key
issue in acoustic position and distance measurement systems. The length
of the acoustic path between a transmitter and receiver is proportional to
the ToF, that is, the time evolved between the departure of the waveform
from the transmitter and the arrival at the receiver (Figure 9.4).
The position of an object is obtained, for instance, by measuring the
distances from the object to a number of acoustic beacons. See also
Figure 1.2.