双站多普勒跟踪定位

假设k时刻的目标的状态为\(\left[ {x_k,{\dot x}_k,y_k,\dot y}_k \right]^T\)，发射站的位置为 $ [x_t,y_t] $， 接收站的位置为 \([x_r,y_r]\)，发射载频为\(f_c\)，则多普勒频移量测可以表示为:

\[{z_k} = h({x_k}) + {w_k} \]

其中\({w_k}\)为量测噪声，波长\(\lambda = c/{f_c}\),c为光速,且

\[h({x_k}) = - \left[ {\frac{{{{\dot d}_{k,r}}}}{\lambda } + \frac{{{{\dot d}_{k,t}}}}{\lambda }} \right], \]

\[{d_{k,r}}{\rm{ = }}\sqrt {{{({x_k} - {x_r})}^2} + {{({y_k} - {y_r})}^2}}, \]

\[{d_{k,t}}{\rm{ = }}\sqrt {{{({x_k} - {x_t})}^2} + {{({y_k} - {y_t})}^2}}, \]

\[{\dot d_{k,t}}{\rm{ = }}\left[ {{{\dot x}_k}({x_k} - {x_t}) + {{\dot y}_k}({y_k} - {y_t})} \right]/{d_{k,t}}, \]

\[{\dot d_{k,r}}{\rm{ = }}\left[ {{{\dot x}_k}({x_k} - {x_r}) + {{\dot y}_k}({y_k} - {y_r})} \right]/{d_{k,r}}. \]