Aerospace and Electronic Systems Magazine January 2018 - 35

the literature but also to discuss the possible applications or topics which may exploit new FBD methods to further improve target detection, parameter estimation, high-resolution imaging, etc.
Furthermore, some FBD-related topics are still in development.
Therefore, more attention and effort are needed for future research.

SOME RECENT DEVELOPMENTS AND CHALLENGES OF FBD
METHODS
Since the introduction of the concept of FBD [8] and RFT/GRFT
[9] in 2011, the proposed FBD-based methods have attracted considerable attention. Some interesting FBD-related works have been
developed or are still developing for dealing with many challenges
in real applications as well as theoretical foundations. In this section, nine recent research developments are introduced.

FAST IMPLEMENTATIONS OF FBD
From the definitions in [1], the natural implementations of GRFT,
general Radon transform (GRT), and generalized Fourier transform (GFT) can be converted into the optimization in a multivariant space (α1 ,α 2 ,,α N ) as

χ1 = arg max GRFTs ( t ) (α1 , α 2 ,α N )

(1)

χ 2 = arg max GRTs ( t ) (α1 ,α 2 ,α N )

(2)

χ 3 = arg max GFTs ( t ) (α1 ,α 2 ,α N )

(3)

α1 ,α 2 ,α N

α1 ,α 2 ,α N

α1 ,α 2 ,α N

where s(t) is the range-compressed radar echoes, α1 , α 2 ,,α N are
the N parameters of the target's parametric motion model, χ1, χ 2,
and χ 3 are the estimations of (α ,α ,,α ) obtained by GRFT,
1

2

N

GRT, and GFT, respectively. When peaks of GRFT, GRT, and GFT
are searched via (1)-(3), targets are possibly detected and their motion parameters can be obtained accordingly. Obviously, the maximizations via different transforms (1)-(3) are just the different
multidimensional optimizations with different objective functions.
Therefore, GRFT, GRT, and GFT can be directly accomplished
via ergodic search, i.e., brute force search, to try all the possible
parameter combinations, which can guarantee the global optimization in the parameter space. Unfortunately, the complexity of
the ergodic search is exponentially increased with the number
of unknown parameters, and the high computational complexity
may be unaffordable for multidimensional searches. Enlightened
by the development of artificial intelligence as shown in Figure 1
[14], the implementation of FBD can also be realized via heuristic
search like genetic algorithm, ants system, and particle swarm optimization (PSO) [14]. Compared with ergodic search, a heuristic
search cannot guarantee the global optimization but its probability
of the global optimization can be remarkably increased as long as
an objective function can be well designed, such as BSSL-learning-based PSO (BPSO) [15]. In addition, the techniques of subaperture, subspace, and noncoherent integration [16] can also speed
up the point-by-point search-based FBD method as Figure 2.
Furthermore, it has been found that in the pulse-range frequency domain the calculation of GRFT can be realized lineby-line as Figure 2 for many parameters simultaneously. That is,
many points in the parameter space can be calculated jointly by
the low-complexity fast Fourier transform (FFT) and matrix operators. Therefore, the computational complexity of these methods can be reduced accordingly. Specifically, chirp-Z transform

Figure 1.

The heuristic search methods in
artificial intelligence.

JANUARY 2018

IEEE A&E SYSTEMS MAGAZINE

35



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine January 2018

No label
Aerospace and Electronic Systems Magazine January 2018 - No label
Aerospace and Electronic Systems Magazine January 2018 - Cover2
Aerospace and Electronic Systems Magazine January 2018 - 1
Aerospace and Electronic Systems Magazine January 2018 - 2
Aerospace and Electronic Systems Magazine January 2018 - 3
Aerospace and Electronic Systems Magazine January 2018 - 4
Aerospace and Electronic Systems Magazine January 2018 - 5
Aerospace and Electronic Systems Magazine January 2018 - 6
Aerospace and Electronic Systems Magazine January 2018 - 7
Aerospace and Electronic Systems Magazine January 2018 - 8
Aerospace and Electronic Systems Magazine January 2018 - 9
Aerospace and Electronic Systems Magazine January 2018 - 10
Aerospace and Electronic Systems Magazine January 2018 - 11
Aerospace and Electronic Systems Magazine January 2018 - 12
Aerospace and Electronic Systems Magazine January 2018 - 13
Aerospace and Electronic Systems Magazine January 2018 - 14
Aerospace and Electronic Systems Magazine January 2018 - 15
Aerospace and Electronic Systems Magazine January 2018 - 16
Aerospace and Electronic Systems Magazine January 2018 - 17
Aerospace and Electronic Systems Magazine January 2018 - 18
Aerospace and Electronic Systems Magazine January 2018 - 19
Aerospace and Electronic Systems Magazine January 2018 - 20
Aerospace and Electronic Systems Magazine January 2018 - 21
Aerospace and Electronic Systems Magazine January 2018 - 22
Aerospace and Electronic Systems Magazine January 2018 - 23
Aerospace and Electronic Systems Magazine January 2018 - 24
Aerospace and Electronic Systems Magazine January 2018 - 25
Aerospace and Electronic Systems Magazine January 2018 - 26
Aerospace and Electronic Systems Magazine January 2018 - 27
Aerospace and Electronic Systems Magazine January 2018 - 28
Aerospace and Electronic Systems Magazine January 2018 - 29
Aerospace and Electronic Systems Magazine January 2018 - 30
Aerospace and Electronic Systems Magazine January 2018 - 31
Aerospace and Electronic Systems Magazine January 2018 - 32
Aerospace and Electronic Systems Magazine January 2018 - 33
Aerospace and Electronic Systems Magazine January 2018 - 34
Aerospace and Electronic Systems Magazine January 2018 - 35
Aerospace and Electronic Systems Magazine January 2018 - 36
Aerospace and Electronic Systems Magazine January 2018 - 37
Aerospace and Electronic Systems Magazine January 2018 - 38
Aerospace and Electronic Systems Magazine January 2018 - 39
Aerospace and Electronic Systems Magazine January 2018 - 40
Aerospace and Electronic Systems Magazine January 2018 - 41
Aerospace and Electronic Systems Magazine January 2018 - 42
Aerospace and Electronic Systems Magazine January 2018 - 43
Aerospace and Electronic Systems Magazine January 2018 - 44
Aerospace and Electronic Systems Magazine January 2018 - 45
Aerospace and Electronic Systems Magazine January 2018 - 46
Aerospace and Electronic Systems Magazine January 2018 - 47
Aerospace and Electronic Systems Magazine January 2018 - 48
Aerospace and Electronic Systems Magazine January 2018 - 49
Aerospace and Electronic Systems Magazine January 2018 - 50
Aerospace and Electronic Systems Magazine January 2018 - 51
Aerospace and Electronic Systems Magazine January 2018 - 52
Aerospace and Electronic Systems Magazine January 2018 - 53
Aerospace and Electronic Systems Magazine January 2018 - 54
Aerospace and Electronic Systems Magazine January 2018 - 55
Aerospace and Electronic Systems Magazine January 2018 - 56
Aerospace and Electronic Systems Magazine January 2018 - 57
Aerospace and Electronic Systems Magazine January 2018 - 58
Aerospace and Electronic Systems Magazine January 2018 - 59
Aerospace and Electronic Systems Magazine January 2018 - 60
Aerospace and Electronic Systems Magazine January 2018 - 61
Aerospace and Electronic Systems Magazine January 2018 - 62
Aerospace and Electronic Systems Magazine January 2018 - 63
Aerospace and Electronic Systems Magazine January 2018 - 64
Aerospace and Electronic Systems Magazine January 2018 - Cover3
Aerospace and Electronic Systems Magazine January 2018 - 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