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and Rps _k(t m ) is the instantaneous range from P k to o and ψ(t m ) is the residual video phase (RVP).
Thus, the instantaneous range R between the radar and the target P can be obtained based on the law of cosines as shown in the following expressions.
The instantaneous range from scattering center at (x, y) to radar is given by r t = R t + x sin θ t − y cos θ t (1).
where δ R t) denotes the instantaneous range displacement induced by motion errors, and R t) represents the nominal instantaneous two-way range.
Defining R cen = H c 2 + r p − r a 2, we perform Taylor expansion to the instantaneous range neglecting the terms whose order are higher than the fourth order.
The instantaneous range difference can then be calculated between the ideal range history for the target at (x Ta (u), y Ta (u), z Ta (u)), given by (11), and the real range history in (6): Δ R R u = R R u − R Rn u (12).
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The instantaneous slant range equation (or history) is the key to high precision SAR processing.
To implement RMC fitting, R i which indicates the instantaneous slant range between antenna phase center (APC) and the scattering center should be well understood.
The instantaneous slant range becomes Rleft eta right)=rleft eta right)+{r}_vleft eta right)=rleft eta right)+{r}_{v0}left eta right cdot cos theta left eta right) (2).
The analytical FMCW SAIS PTRS generally expresses FMCW SAIS signal by accurately addressing the variation of the instantaneous slant range during the pulse duration time [2].
ζ i, R i, and σ i are defined as the ith scattering center's beam center time, the instantaneous slant range, and the complex backscattering envelope, respectively.
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