For navigation of a wheeled mobile robot, the dead reckoning method is frequently used to estimate its current position. A conventional dead reckoner, however, is prone to give us false information on the robot's position, especially when the wheels are slipping, because the method depends merely on the angular velocities of the wheels. In this paper, we improve its estimation performance by detecting the wheel slip and estimating the linear velocity of each wheel using neural network, so that the improved dead reckoner can estimate the robot's position well even if the wheel slip occurs during navigation. In order to determine the structure and input variables of the neural net, we investigate the phenomena of the wheel slipping through the analysis of its dynamic characteristics; slip motion is modeled and simulated for a mobile robot. The networks with the capability of slip detection and linear velocity estimation are trained for various sample patterns obtained from the slip motion model. Through a series of simulations with the trained networks, we investigate the performance of the improved dead reckoning system.