This paper focuses on the design of a linear Kalman filter and an extended Kalman filter for the estimation of an octorotor unmanned aerial vehicle's (UAV) state in the context of Synthetic Aperture Radar image reconstruction. A comparison to a linear interpolation method is also proposed. The Kalman filters are developed based on a complete nonlinear model of the UAV and its linearized form. A particularity of the considered platform is that the control signals are not measured and have to be estimated as well as the UAV's state. The proposed techniques are then tested on a UAV simulator and a radar imaging simulator.