A single Er³⁺ centre in CaGdAlO₄:Er³⁺ has been identified to have C_4v symmetry from polarized laser selective excitation. This is consistent with isovalent substitution of the Er³⁺ ions for host crystal Gd³⁺ ions. Using both optical and infrared absorption and polarized laser excited fluorescence, 59 crystal-field energy levels and their wavefunction symmetries have been identified and used to perform comprehensive single electron crystal-field analyses for the Er³⁺ ion centre. For excitation of the ⁴F_9/2 multiplet, blue and green upconversion fluorescence is observed. Self-absorption dips recorded in upconversion excitation spectra are indicative of the presence of radiative energy transfer processes.