We have developed a dead reckoning sensor system and a tracking algorithm for mobile robots to estimate the path when a mobile robot explores an unknown, enclosed region where GPS access or landmarks are unavailable. A dead reckoning sensor system consists of a low-cost MEMS IMU and a navigation sensor (used in laser mice), which provide complementary functions. The IMU has benefits such as compact size, a self-contained system, and an extremely low failure rate but has a bias drift problem, which can accumulate substantial error over time. A navigation sensor measures the motion of a mobile robot directly without the slip error in the case of a wheel-type odometer, but it often fails to read a surface. A tracking algorithm consists of an extended Kalman filter (EKF) to fuse data from the IMU and the navigation sensor and a least-squares method to estimate acceleration bias in the EKF. We obtained experimental data by driving a radio-controlled car equipped with the sensor system in a 3D pipeline and compared the path estimated by the tracking algorithm with the path of the pipeline. The tracking algorithm combined data from the IMU and the navigation sensor and correctly estimated the path of the radio-controlled car. Our study can be applied to estimate position or path of mobile robots without external aids such as GPS, landmarks, and beacons.