It tells us to go for approximation — more approximate solutions, which find many right answers, but not all right answers.
The future cost-to-go approximation defined as ({tilde{V}}_t(x_t)) in (19) was implemented through Kernel Regression applied with a Gaussian Kernel [50].
(2) The second simulation experiment is based on the traditional SAR signal PTRS model, which is developed under stop-and-go approximation.
In [5], the author developed a signal model under synthetic aperture acoustic (SAA) imaging system, where the invalidation of stop-and-go approximation is taken into account.
However, the stop-and-go approximation used in conventional pulsed SAIR (e.g., synthetic aperture radar SAR) is no longer valid due to the long signal duration time or low wave propagation speed.
The stop-and-go approximation is commonly used in conventional-pulsed SAR focusing algorithms, where the instantaneous slant range from the antenna to the target is assumed to remain constant during the pulse duration time.
In [5], the author has considered the invalidation of stop-and-go approximation, but took an approximation that the time from the transmitter to the reflector equals to half of the round-trip delay time.
When a monostatic SAR receives echoes, the stop-go approximation is applied and therefore the received echo is expressed by S rec = ∫ y ∈ antenna E B sc ω, y W ω, y d y (13).
Unlike conventional pulse SAR system, the signal PTRS model is based on the stop-and-go approximation, which assumes that the instantaneous slant range remains constant during the pulse duration time [6].
However, for FMCW imaging mode, in fact, the variation of instantaneous slant range during each pulse could not be neglected due to the long signal duration, thus the stop-and-go approximation used in conventional SAR PTRS is no longer valid.
Using the stop-and-go approximation, the signal model in conventional pulse SAR system is achieved [6], which is formulated as G SAR ( f τ, f, τ 0, r 0 ) = σ τ 0, r 0 exp { − j [ 4 π r 0 c f 0 + f 2 − c f τ 2 v 2 − 2 π f 2 K r + 2 π f τ τ 0 − 4 π r c c f τ + f 0 + f ] } (6).
