We propose a new recursive method for simultaneous estimation of both the pose and the shape of a three-dimensional extended object. The key idea of the presented method is to represent the shape of the object using spherical harmonics, similar to the way Fourier series can be used in the two-dimensional case. This allows us to derive a measurement equation that can be used within the framework of nonlinear filters such as the UKF. We provide both simulative and experimental evaluations of the novel techniques.