High Resolution Tactical Synthetic Aperture Radar (TSAR) - MATLAB Simulations for Radar Systems Design - page 596

z

T ob

v

h

β i

y

µ i

kth

range bin

C i

x

projection of
radar LOS

Figure 12.9. A scatterer C i within the k th range bin.

2 r i ( t µ i , )

τ i ( t µ i , ) = ---------------------

(12.36)

c

where is the speed of light and is the scatterer slant range. From the
geometry in Fig. 12.9, one can write the expression for the slant range to the
scatterer within the

c r i ( t µ i , )

ith kth range bin as

 2

h 2 vt

h

vt
----



------------- --------

r i ( t µ i , ) = 1 – cos β i cos µ i sin β i + cos β i

(12.37)

 

cos β i

And by using Eq. (12.36) the round-trip delay can be written as

 2

2
---

h 2 vt

h

vt
----



------------- --------

τ i ( t µ i , ) = 1 – cos β i cos µ i sin β i + cos β i (12.38)

 

cos β i

The round-trip delay can be approximated using a two-dimensional second
order Taylor series expansion about the reference state ( t µ , ) = ( 00 , ) . Per-

forming this Taylor series expansion yields