Multiple detection of a slowly fluctuating target (Corresp.)

A "slowly" fluctuating target is assumed to keep its radar cross section constant for the duration of several
(M)
dwells on target. To resolve multiple range and/or Doppler ambiguities, the received signal, which is presumably coherently processed (i.e., predetection integrated or matched filtered) over each dwell, must often be tested against a threshold, {\em independently} of those on other dwells. Such a procedure is referred to as {\em multiple detection}. A technique for the evaluation of a tight lower bound on the multiple-detection probability
P_{M}
, under Swerling case I statistics for the cross section, is presented in term of an infinite series and worked out in detail for
P_{2}
and
P_{3}
. Estimates on the computation error due to the truncation of the series are derived. Numerical results indicate that
P_{3}
comes much closer to
P_{1}
than to
p_{1}^{3}
or even to
P_{1}P_{2}
; at an expected signal-to-noise ratio of
13
dB and at
P_{1} = 0.51
, it obtains that
P_{3} \geq 0.40
, whereas
P_{1}P_{2} = 0.23
and
p_{1}^{3} = 0.17
.