Page 88 - Autonomous Mobile Robots

Millimeter Wave RADAR Power-Range Spectra Interpretation 71

7
where δ is a threshold, H 0 and H 1 designate hypothetical target absence
and presence respectively. p(P SNP |H 0 ) and p(P SNP |H 1 ) are the conditional
probability density functions. The decision rule of Equation (2.18) can be
expressed as

H 1
P SNP (k, l) ≷ δ (2.19)
H 0

An indicator function, I(k, l) is defined where, I(k, l) = 1 for P SNP >δ and
I(k, l) = 0 otherwise.
8
The estimate of the conditional target presence probability, ˆp (k, l) is

ˆ p (k, l) = α p ˆp (k, l − 1) + (1 − α p )I(k, l) (2.20)
This target presence probability can be used as a target likelihood
within mobile robot navigation formulations. α p is a smoothing parameter
(0 ≤ α p ≤ 1). The value of α p is chosen in such a way that the probability
of target presence in the previous range bin has very small correlation with the
next range bin (in this case α p = 0.1).
It is of interest to note that, as a consequence of the above analysis, the
noise power, ˆ λ d (k, l) in kth range bin is given by

˘
ˆ λ d (k, l) =˜α d (k, l) ˆ λ d (k, l − 1) +[(1 −˜α d (k, l))] P(k, l) (2.21)
where

˜ α d (k, l) = α d + (1 − α d )p (k, l) (2.22)
and α d is a smoothing parameter (0 ≤ α d ≤ 1). This can be used to obtain a
ˆ
noisereducedbin, P NR (k, l)usingthemethodofpowerspectralsubtraction[34].
In the basic spectral subtraction algorithm, the average noise power, ˆ λ d (k, l)
is subtracted from the noisy range bin. To overcome the inaccuracies in the
noise power estimate, and also the occasional occurrence of negative power
estimates, the following method can be used [35]

˘
˘
P(k, l) − c × ˆ λ d (k, l) if P(k, l)> c × ˆ λ d (k, l)
ˆ
P NR (k, l) =
d × ˆ λ d (k, l) otherwise
7 This threshold can be chosen based upon the received SNP, at which the signal can be trusted
not to be noise. Note that this does not have to be changed for differing environments, or types of
targets.
8 Conditioned on the indicator function I(k, l) [33].

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 71 — #31