Aerospace and Electronic Systems Magazine January 2018 - 46

Focus-Before-Detection: Part II

Figure 15.

Figure 16.

when κ = 1, which demonstrates that RFT is a special case of the
WSRFT when scale effect can be omitted. Also, the RFT detection performance decreases with the change of the scale factor as
Figure 16(a). On the contrary, the proposed WSRFT can obtain the
ideal performance regardless of the scale effect as Figure 16(b). In
the future, the scale effect on the high-order motion and its compensation need much more study.

information of target motion. The essence of FBD is the long time
coherent integration and the SNR gain is the main pursuit in different scenarios. Therefore, as long as the SNR is not too low, e.g.,
higher than 10 dB, an FBD may be blindly implemented for coherent integration, i.e., it is not necessary to retrieve the unknown
parameters one-by-one, like the well-known phase gradient autofocusing (PGA) [40, 41] algorithm in SAR imaging. For example, the
MTD outputs of a highly maneuvering target with high acceleration
is smeared and missed as Figure 17(a) while the PGA outputs as
Figure 17(b) can be used to detect the target with blind compensation of high-order phase modulation. Interestingly, the PGA algorithm only adopts some simple operations, e.g., center shifting,
windowing, phase gradient calculation, and interactions, to realize
the coherent integration [40, 41]. The following problems may be
attractive in the future: what kind of motions can be nonparametrically/blindly processed and how to apply a nonparametric method
in a low SNR scenario?

Outputs of different methods for ultrahigh-speed targets. (a) RFT outputs. (b) WSRFT outputs.

NONPARAMETRIC PROCESSING
In the previous studies, it seems that the parametric model is the
foundation of the FBD methods and the parametric methods like
RFT. GRFT, ST-RFT, 3DS-RFT, and WSRFT are introduced, accordingly. Because retrieving those unknown parameters one-byone may be burdensome in real applications, it is attractive to ask
whether the parametric methods are necessary for an FBD method
and whether an FBD can be implemented blindly without the prior
46

Detection performance comparison between different methods versus
scale coefficient. (a) RFT outputs. (b) WSRFT outputs.

IEEE A&E SYSTEMS MAGAZINE

JANUARY 2018



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