In this contribution, we presented approaches for the determination of tokamak plasma column shift based on multipole moments and magnetic techniques. First, we presented analytical details for using this technique. Then, the principle of different models based on this technique for the design and fabrication of six coils will be presented: four modified Rogowski coils (two cosine coils and two sine coils) and two saddle coils (saddle sine coil and saddle cosine coil). Also, to compare the results, the flux loops technique is used. Because of continuous measurements of magnetic field distribution around the tokamak plasma using multipole coils, this technique gives us more reliable information about the plasma current displacement. Moreover, we deduced the plasma current and plasma boundary centers shift using the two semi-empirical techniques in the IR-T1 tokamak. First, the plasma current center is calculated from the vertical field coil characteristics. The calculation is made focusing on the vertical field coil current and voltage changes due to a horizontal displacement of the plasma column. Also, the plasma boundary center shift was measured from the external magnetic coils. The results from these two techniques are compared and discussed.