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60 Autonomous Mobile Robots

2.4.4 Initial Range Spectra Prediction
The tools are now complete to simulate/predict RADAR spectra. In Figure 2.10,
2
an object with a known RCS (10 m ) is assumed to be at a distance of 10.25 m.
A Monte Carlo method has been used for simulating the noise in the figure.
2
A Gaussian noise distribution with a variance of 26.57 dB is used when there is
signal presence, and during signal absence Weibull distributions with paramet-
ers explained in the previous section have been used. The values are obtained
from the experimental estimation of the noise distributions in target absence and
presence (Figure 2.7 and Figure 2.4.3). The simulated result of applying the
high pass 60 dB/decade filter is shown in Figure 2.11a. Analyzing the predicted
(Figure 2.11a) and actual range bin (Figure 2.11b) shows a slight mismatch in
the noise frequency with respect to range which is evident in the real spectra.
This mismatch is due to the phase noise throughout the entire range bin. The
phase noise, approximately quantified in Section 2.4.2, is taken into account
only during the parts of the range bin which are predicted to have targets, as
explained above. During sections of the range bin with no targets (i.e., beyond
11 m in Figure 2.11a) it is not modeled, since this part of the spectra is of little
interest in target estimation.
A predicted and actual RADAR range spectra, obtained from an outdoor
environment, is shown in Figure 2.12. Figure 2.13a and b show the results of a
chi-squared test to determine any bias or inconsistency in the power–range
bin predictions. The difference between the measured and the predicted
range bins is plotted together with 99% confidence interval. The value of
99% bound, = ±16.35 dB, has been found experimentally by recording several
noisy power–range bins in target absence (RADAR pointing toward open space)
as explained previously (3 × steady state standard deviation of Figure 2.6b)
[15]. Close analysis of Figure 2.13a shows that the error has a negative bias.
This is due to the approximate assumption of the high pass filter gain. For the
RADAR used here, the gain of the high pass filter used in the predicted power–
range bins was set to 60 dB/decade, as explained earlier. Figure 2.13b shows
a chi-squared test on the difference between a measured bin and its predicted
bin with the mean high pass filter bias of Figure 2.6a subtracted. Although the
error in Figure 2.13b is less biased than Figure 2.13a, a gain of 60 dB/decade
with the small bias (Figure 2.13a) is still acceptable as most of the error values
are well within 99% confidence limit and also taking the high pass filter effect
role into consideration.
A method for predicting the RADAR range spectra has been shown here
which can be used for predicting observations, based on an estimate of a targets
range and RCS value. Clearly a restriction of this method is that as a mobile
robot moves with respect to objects within the environment, range bins can only
be predicted assuming that the RCS does not change as the RADAR to target
angle of incidence changes. In general this is clearly not a valid assumption, but

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 60 — #20