The geometry model of bistatic SAR is shown in Fig. 1. Assume that the transmitter is fixed, and the receiver moves along the $x$-axis direction and works at side looking mode with velocity $VR$. $RT0$, and $RR0$ are the slant range from the transmitter and receiver to ground moving target at $ta=0$, while $RT1$ and $RR1$ stand for the instantaneous slant ranges of the transmitter and receiver from the target. $\theta T$ and $\theta R$ are the squint angles from the two platforms to the target, $ta$ is the slow time. $vTa$, $vRa$, $vTr$, and $vRr$ denote the relative lateral and radial velocities between the moving target and platforms, respectively. The velocity of the moving target $v$ can be decomposed into $vTa$ and $vTr\u02dc$. Thus, the instantaneous slant range $R(ta)$ is given by Display Formula
$R(ta)=(RT0\u2212vTrta)2+(vTata)2+2(RT0\u2212vTrta)(vTata)sin\u2009\theta T+(RR0\u2212vRrta)2+(VRta\u2212vRata)2.$(1)
According to the geometry of bistatic SAR model with one stationary configuration, we have Display Formula$v/sin(\pi /2\u2212\theta T1)=vTa/sin(\pi /2+\theta T1\u2212\theta 1)=vTr\u02dc/sin\u2009\theta 1.$
Thus, $vTa$, $vRa$, $vTr$, and $vRr$ is given by Display Formula${vTr=vTr\u02dc\u2009cos\u2009\u03f5T=v\u2009sin\u2009\theta 1\u2009cos\u2009\u03f5T/sin(\pi /2\u2212\theta T1)vTa=v\u2009sin(\pi /2+\theta T1\u2212\theta 1)/sin(\pi /2\u2212\theta T1).$(2)
Similarly, we have Display Formula${vRr=v\u2009cos\u2009\theta 1\u2009cos\u2009\u03f5RvRa=v\u2009sin\u2009\theta 1,$(3)
where $\theta 1$ and $\theta 2$ represent the angles between $vTa$, $vRa$, and $v$, respectively. $\u03f5T$ and $\u03f5R$ are the grazing angles of transmitter and receiver. Obviously, $\theta 1$, $\theta 2$, and $\theta T1$ satisfies Display Formula${\theta 1+\theta 2+(\pi /2\u2212\theta T1)=\pi \theta T1=sin\u22121(sin\u2009\theta T/cos\u2009\u03f5T).$(4)
From Eqs. (2)–(4), one obtains six equations with eight variables, i.e., $vTa$, $vRa$, $vTr$, $vRr$, $\theta 1$, $\theta 2$, $\theta T1$, and $v$. In order to calculate these variables, range walk and range curvature term are estimated in the following procedures, both of which are the functions of the unknown parameters. In this way, the moving target-related variables can be achieved.