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Definition 2 The probability of target detection and reliable tracking P dT ,
is defined as the probability
of making a correct target detection and of recovering a target trajectory such that each retrieved
state, ( iˆ
ˆ
k, lk)
, k = 1,... K , is within ε
r
cells in range and ε d
cells in Doppler from the actual location, and
the estimated ambiguity number sequence ˆ K
Μ = ( mˆ ˆ
1,..., m K
) is equal to the true one. Hence
PdT ,
= Pr
⎛(
max
K( K, mK)
V
⎞
⎜ Γ x >
T
∪
dT , ⎟
⎝ xK,
m
) E (57)
K
⎠
where the event
E dT ,
is expressed as
abs( iˆ
k
−ik)
≤ ε
r, abs( lˆ
k
−lk)
≤ εd, k = 1,... K , Μˆ K = Μ
K
(58)
It’s evident that the overall system performance depends on the choice of the tolerance factors: ε r
and ε d
. The smaller the tolerance factors, the larger the SNR is required in order to maintain a certain
value of detection probability P d
and P under a preset probability of false alarm rate. In the
dT ,
following, the detection and tracking performance with respect to average SNR and tolerance factors
are investigated.
We first consider the case that the nuisance parameters are known in advance; the corresponding
−6
implementation of the DP recursive is given in (33). In Fig.9, we set P fa
= 10 , and plot P
d
and P versus average SNR under different settings of tolerance factor. The tolerance
dT ,
factor ( ε
r, ε
d)
from up to down is (4,2) , (2,1) and (0,0) . ( ε
r, ε
d) = (0,0) means correct detection and
estimation. We note that as the tolerance factor becomes smaller (i.e., the estimation accuracy
becomes higher), both P d
and P dT ,
decreases considerably. We can also notice that compared to P dT ,
,
P is less sensitive to the tolerance factor. Satisfactory detection and tracking performance can be
d
achieved when the tolerance factor is (4,2) .
Fig. 9. P and
d
P dT ,
versus the average SNR in range-Doppler domain, with known nuisance parameters,
( ε , ε ) = (4, 2), (2, 1), (0, 0) from up to down
r
d
We now investigate the situation when the nuisance parameters are unknown; the DP recursive with
−6
unknown nuisance parameters is given in (50). In Fig. 10, we set P fa
= 10 , and report P d
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