Electromagnetic (EM) vector sensor arrays can track both the polarisation and direction of arrival (DOA) of the impinging signals. For linear crossed-dipole arrays, as shown by our analysis, due to inherent limitation of the structure, it can only track one DOA parameter and two polarisation parameters. For full four-dimensional (4-D, 2 DOA and 2 polarization parameters) estimation, we could extend the linear crossed-dipole array to the planar case. In this paper, instead of extending the array geometry, we replace the crossed-dipoles by tripoles and construct a linear tripole array. It is proved that such a structure can estimate the 2-D DOA and 2-D polarisation information effectively in general and a dimension-reduction based MUSIC algorithm is developed so that the 4-D estimation problem can be simplified into two separate 2-D estimation problems, significantly reducing the computational complexity of the solution. The Cramr-Rao Bound (CRB) is also derived as a reference for algorithm performance. A brief comparison between the planar crossed-dipole array and the linear tripole array is performed at last, showing that although the planar structure has a better performance, it is achieved at the cost of increased physical size.