Workshop proceeding - final.pdf - Faculty of Information and ...

(a)
(b)
Fig. 7. mesh plot of the reflected power in ambiguous range-Doppler maps: (a) SNR=13dB, (b)
SNR=10dB
Fig. 8 shows the final merit function for a fixed mode m
K
= 5 . When no target exists, it’s obvious that
the merit function tends to noisy (Fig.8(a)). When a target with an average SNR=10dB is present (the
nuisance parameters are assumed known), it’s clear that the noisy merit function has a distinct peak at
a particular location in the ambiguous range-Doppler map (Fig.8(b)). The corresponding target final
state can be extracted by thresholding the resultant merit function.
6.1 Selection of Threshold
In order to calculate the threshold, we first have to define the probability of false alarm P fa
. In our
situation, Pfa
is defined as the probability of detecting a false track in the absence of target (i.e., under
the hypothesis H
0
). This is equal to the probability of the maximum noise merit function exceeding
the threshold VT
P
fa
= Pr ( max Γ
K
(
K
, mK ) >
T
xK,
mK
x V ) (54)
where x K
∈{noise states} .
Given the desired P fa
, the threshold is determined as the (1−
Pfa
)-quantile of the test statistic, i.e.,
max
x ,
( , ) given in
K m
Γ
K K
x
K
mK
(54). Unfortunately, the statistical distribution of the test statistic is rather
complicated [11], sometimes even infeasible. This mainly because 1) the max operator in the DP
recursion brings in nontrivial nonlinearities and non-Gaussianity; 2) the samples of the test statistic are
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