An innovative neuro-evolutionary approach for mobile robot egomotion estimation with a 3D ToF camera is proposed. The system is composed of two main modules following a preprocessing step. The first module is a Neural Gas network that computes a Vector Quantization of the preprocessed camera 3D point cloud. The second module is an Evolution Strategy that estimates the robot motion parameters by performing a registration process, searching on the space of linear transformations, restricted to the translation and rotation, between the codebooks obtained for successive camera readings. The fitness function is the matching error between the predicted and the observed codebook corresponding to the next camera readings. In this paper, we report results of an implementation of this system tested on data from a real mobile robot, and provide several comparisons between our and other well-known registration algorithms.