One perspective (heh) involves the following relation among position vectors:
$$\vec{r}_{A\rightarrow C} = \vec{r}_{A\rightarrow B} + \vec{r}_{B\rightarrow C}.$$
These position vectors can be for anything; object $A$ could be a house, object $B$ an ant, and object $C$ a leaf on the river. In particular,
$$\vec{r}_{\mathrm{Sun} \rightarrow X} = \vec{r}_{\mathrm{Sun} \rightarrow \mathrm{Earth}} + \vec{r}_{\mathrm{Earth} \rightarrow X}.$$
The position of planet $X$ relative to the sun can be found if we know Earth's position relative to the Sun and planet $X$'s position relative to Earth. In this way, measurements of a planet's position relative to Earth can be used.

There is the added complication of knowing distance to planets and coming up with a convenient coordinate system in order to actually come up with values for these position vectors. Others may have better information on that.