Mobile robot navigation and obstacle avoidance in dynamic and unknown environments is one of the most challenging problems in the field of robotics. Considering that a robot must be able to interact with the surrounding environment and respond to it in real time, and given the limited sensing range, inaccurate data, and noisy sensor readings, this problem becomes even more acute. In this paper, we attempt to develop a neural network approach equipped with statistical dimension reduction techniques to perform exact and fast robot navigation, as well as obstacle avoidance in such a manner. In order to increase the speed and precision of the network learning and reduce the noise, kernel principal component analysis is applied to the training patterns of the network. The proposed method uses two feedforward neural networks based on function approximation with a backpropagation learning algorithm. Two different data sets are used for training the networks. In order to visualize the robot environment, 180$^{\circ}$ laser range sensor (SICK) readings are employed. The method is tested on real-world data and experimental results are included to verify the effectiveness of the proposed method.