- A sensor $i$ with coordinates $(x_i,y_i)$ and its sensing angle $\varphi$ is given.
- A target with its coordinates $(x_k,y_k)$ and its face orientation (measured in radians) f_k is given.
- $d_{ij}$ is the vector joining the sensor $i$ with a point located on the bisector of the angle $\varphi$, as show in figure.
My question: I wan to write a mathematical formula in order to calculate the angles shown in red in the picture above. Precisely, $\theta_{ik}$ represents the angle at which the target can be seen from $i$ and $\psi$ represents viewing angle of the target. How could I proceed?