Page 67 - Autonomous Mobile Robots

50 Autonomous Mobile Robots

2.4.1 RADAR Range Equation
According to the simple RADAR equation, the returned powerP r isproportional
to the RCS of the object, σ and inversely proportional to the fourth power of
range, R [21]. The simple RADAR range equation is formally written as

2 2
P t G λ σ
P r = (2.7)
3 4
(4π) R L
where P t is the RADAR’s transmitted power, G is the antenna gain, λ is the
wavelength (i.e., 3.89 mm in this case), and L the RADAR system losses. A high
pass filter (shown in Figure 2.2) is used to compensate for the R 4 drop in received
signal power. In an FMCW RADAR, closer objects produce signals with low
beat frequencies and vice-versa (Equation [2.5]). Therefore by attenuating low
frequencies and amplifying high frequencies, it is possible to correct the range-
based signal attenuation [18]. To compensate the returned power loss due to
increased range, the high pass filter is modeled in two ways:

1. The bias in the received power spectra is estimated.
2. By modeling the high pass filter with a gain of 60 dB/decade, instead
of the usual 40 dB/decade, to comply with the characteristics of the
particular RADAR used here.

The aim of this is to give a constant received signal power with range. The
actual compensation which results in our system was shown in Figure 2.2 where
it can be seen that the ideal flat response is not achieved by the internal high
pass filter.

2.4.2 Interpretation of RADAR Noise
This section analyzes the sources of noise in MMW RADARs and quantifies
the noise power in the received range spectra (seen in Figure 2.3). In most robot
navigation formulations, observations must be predicted, and for the estimation
algorithms to run correctly, the actual observations are assumed to equal the
predictions, except that they are corrupted with Gaussian noise. It is therefore
the aim of this section to determine the type of noise distributions in the actual
received power and range values to determine how the predicted power–range
spectra can be used correctly in a robot navigation formulation.
RADAR noise is the unwanted power that impedes the performance of
the RADAR. For the accurate prediction of range bins, the characterization of
noise is important. The two main components are thermal and phase noise.
Thermal noise affects the power reading while phase noise affects the range
estimate.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 50 — #10