Aerospace and Electronic Systems Magazine September 2017 - 56

Focus Before Detection: Part I
ingly. It can be proven that GRFT, GFT, and GRT are the maximum
likelihood estimators (MLEs) [42] of the motion parameters in an
AGWN background via joint envelope and phase measurement,
phase-only measurement, and envelope-only measurement in the
high SNR case, respectively. Besides, GFT and GRT are the two
special cases of GRFT in which phase-only or envelope-only information is used. Furthermore, by approximating the RM function of
a maneuvering target into an Mth-order polynomial, Cramer-Rao
lower bounds (CRLBs) have been obtained for different motion parameters, such as range, velocity, acceleration, and jerk. To compare
the effectiveness of GRFT and GRT, the accuracy gains on the root
mean square error (RMSE) have been derived in decibels [42] as
 CRLB ( a )
1
m
GRMSE ( am ) = 10log10 
 CRLB2 ( am )

 f 
≈ 10log10  c  + 5.4,
B





0 < m < M,

(6)

where am, m = 1,...,M, is the mth order polynomial coefficient and
CRLB1(ãm) and CRLB2(ãm) are the derived CRLB for parameters
am, 0 < m < M, via GRT and GRFT, respectively. It is clear from (6)
that the accuracy gain in RMSE of GRFT over GRT, i.e., the joint
envelope and phase over the envelope only, may be approximately
linearly increased with the ratio fc/B.

THE PROPOSED FBD RSP FRAMEWORK

Figure 7.

Outputs of the second-order GRFT in different planes. (a) Range-velocity. (b) Acceleration-range. (c) Acceleration-velocity.

will not easily exceed a range cell during a second-level long TOT.
Therefore, a unified framework has been provided in [42] for target
motion estimation by introducing the generalized Fourier transform
(GFT) and generalized Radon transform (GRT) as follows:
GFT (α1 , ,α N ) = 

∞

−∞

GRT (α1 ,,α N ) = 

∞

−∞

 2πεη (α1 ,,α N , t ) 
f ( t , r0 ) exp 
dt , (4)

λ



(

)

f t ,η (α1 ,,α N , t )0 dt.

(5)

That is, the range-compressed data f(t,r0) are converted into the parameter space via GRFT, GFT, or GRT as (3), (4), or (5), respectively, and the peaks are extracted, as well as their coordination values,
as the estimations of the corresponding motion parameters, accord56

From Figures 6 and 7, target energy will be coherently focused by
the proposed projection as GRFT or RFT, and the peaks of targets
will become increasingly sharper in the parameter space with the
increase of TOT. Besides, unlike conventional target imaging and
focusing after target detection (Figure 1), the target existence decision in a noisy background will be declared in the parameter space
with a focused response. Therefore, based on the proposed RFT,
GRFT, and GFT to overcome the effects of ARC, ADC, and ABW,
we can define a unified and optimal long-time coherent integration
RSP framework as the FBD shown in Figure 9. Before the successive steps like target detection, estimation, imaging, and recognition, the focused and sharp peaks have been formed in the parameter space via the proposed FBD processing for multiple targets by
using RFT, GRFT, or GFT. With the improved SNR by the peaks
in the parameter space, the performance can be improved for target
detection, estimation, imaging, and recognition. The terminology of
focus herein means effective coherent integration to generate peaklike responses, while the conventional MTD can be regarded as a
special case of FBD in a short TOT. A block has been used in Figure 9 to introduce an auxiliary prior environment and geographical
and target information for improving radar target detection by using
GPS, GIS, or ADS-B. Specifically, this prior information can be
used for managing system resources and adjusting parameters for
clutter suppression, CFAR-based detection, or feature extraction.
Compared with the existing RSP methods, there are two basic features for the proposed FBD methods. One is that all these
methods are based on the parametric model with a finite number of
parameters, which are sufficient for describing the amplitude fluc-

IEEE A&E SYSTEMS MAGAZINE

SEPTEMBER 2017



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine September 2017

No label
Aerospace and Electronic Systems Magazine September 2017 - No label
Aerospace and Electronic Systems Magazine September 2017 - Cover2
Aerospace and Electronic Systems Magazine September 2017 - 1
Aerospace and Electronic Systems Magazine September 2017 - 2
Aerospace and Electronic Systems Magazine September 2017 - 3
Aerospace and Electronic Systems Magazine September 2017 - 4
Aerospace and Electronic Systems Magazine September 2017 - 5
Aerospace and Electronic Systems Magazine September 2017 - 6
Aerospace and Electronic Systems Magazine September 2017 - 7
Aerospace and Electronic Systems Magazine September 2017 - 8
Aerospace and Electronic Systems Magazine September 2017 - 9
Aerospace and Electronic Systems Magazine September 2017 - 10
Aerospace and Electronic Systems Magazine September 2017 - 11
Aerospace and Electronic Systems Magazine September 2017 - 12
Aerospace and Electronic Systems Magazine September 2017 - 13
Aerospace and Electronic Systems Magazine September 2017 - 14
Aerospace and Electronic Systems Magazine September 2017 - 15
Aerospace and Electronic Systems Magazine September 2017 - 16
Aerospace and Electronic Systems Magazine September 2017 - 17
Aerospace and Electronic Systems Magazine September 2017 - 18
Aerospace and Electronic Systems Magazine September 2017 - 19
Aerospace and Electronic Systems Magazine September 2017 - 20
Aerospace and Electronic Systems Magazine September 2017 - 21
Aerospace and Electronic Systems Magazine September 2017 - 22
Aerospace and Electronic Systems Magazine September 2017 - 23
Aerospace and Electronic Systems Magazine September 2017 - 24
Aerospace and Electronic Systems Magazine September 2017 - 25
Aerospace and Electronic Systems Magazine September 2017 - 26
Aerospace and Electronic Systems Magazine September 2017 - 27
Aerospace and Electronic Systems Magazine September 2017 - 28
Aerospace and Electronic Systems Magazine September 2017 - 29
Aerospace and Electronic Systems Magazine September 2017 - 30
Aerospace and Electronic Systems Magazine September 2017 - 31
Aerospace and Electronic Systems Magazine September 2017 - 32
Aerospace and Electronic Systems Magazine September 2017 - 33
Aerospace and Electronic Systems Magazine September 2017 - 34
Aerospace and Electronic Systems Magazine September 2017 - 35
Aerospace and Electronic Systems Magazine September 2017 - 36
Aerospace and Electronic Systems Magazine September 2017 - 37
Aerospace and Electronic Systems Magazine September 2017 - 38
Aerospace and Electronic Systems Magazine September 2017 - 39
Aerospace and Electronic Systems Magazine September 2017 - 40
Aerospace and Electronic Systems Magazine September 2017 - 41
Aerospace and Electronic Systems Magazine September 2017 - 42
Aerospace and Electronic Systems Magazine September 2017 - 43
Aerospace and Electronic Systems Magazine September 2017 - 44
Aerospace and Electronic Systems Magazine September 2017 - 45
Aerospace and Electronic Systems Magazine September 2017 - 46
Aerospace and Electronic Systems Magazine September 2017 - 47
Aerospace and Electronic Systems Magazine September 2017 - 48
Aerospace and Electronic Systems Magazine September 2017 - 49
Aerospace and Electronic Systems Magazine September 2017 - 50
Aerospace and Electronic Systems Magazine September 2017 - 51
Aerospace and Electronic Systems Magazine September 2017 - 52
Aerospace and Electronic Systems Magazine September 2017 - 53
Aerospace and Electronic Systems Magazine September 2017 - 54
Aerospace and Electronic Systems Magazine September 2017 - 55
Aerospace and Electronic Systems Magazine September 2017 - 56
Aerospace and Electronic Systems Magazine September 2017 - 57
Aerospace and Electronic Systems Magazine September 2017 - 58
Aerospace and Electronic Systems Magazine September 2017 - 59
Aerospace and Electronic Systems Magazine September 2017 - 60
Aerospace and Electronic Systems Magazine September 2017 - 61
Aerospace and Electronic Systems Magazine September 2017 - 62
Aerospace and Electronic Systems Magazine September 2017 - 63
Aerospace and Electronic Systems Magazine September 2017 - 64
Aerospace and Electronic Systems Magazine September 2017 - Cover3
Aerospace and Electronic Systems Magazine September 2017 - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com