This paper proposes a Multiband Shunt Hybrid Active Filter (SHAF) with sensorless control. A plant is modeled in the discrete- time domain and a controller is designed using the Pole shifting law in the polynomial domain. This control approach is very useful for filtering the load harmonics with reduced sensor counts where a low cost solution like SHAF is required. Multiple Synchronous Reference Frames (MSRF) and low pass filters are used to measure the $5^{th}$ and $7^{th}$ harmonic components separately from the load and filter currents. Individual current controllers are designed for the $5^{th}$ and $7^{th}$ harmonic currents. Control is realized in the stationary, three-phase (abc) reference frame. Performance of the controller is validated through simulation, using realistic plant and controller models, as well as experimentally on a full-scale distribution system.