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Kalman filter (KF) algorithm is a form of recursive optimal estimations, which utilizes information in time domain with less computational efforts to reduce the system errors. Recently, Kalman filtering technique has become a standard approach for reducing errors in a least squares sense and is widely applied in navigation and positioning fields. Unfortunately, the traditional KF needs accurate statistical information about mobile terminal; otherwise, it will result in lower precision and even divergence. To make up for the deficiency of KF algorithm, this paper presents a novel robust single global position system (GPS) navigation algorithm based on dead reckoning and strong tracking filter (STF), which still has strong tracking ability even when precise knowledge of the system models is not available. The proposed algorithm utilizes adaptive fading factor to adjust the gain matrix in real time to satisfy the orthogonality principle (OP), which indicates all useful information has been extracted from residual. Furthermore, we define residual covariance (RC) as an important index to evaluate the performance of the filtering algorithm and deduce the closed relationship of RCs in KF under the case of: 1) inaccurate system model; 2) erroneous initial value; and 3) abrupt change of states, respectively. We find that the RCs of the KF algorithm under all three above-mentioned cases have a bias compared with desired ones; as a result, they do not conform to the OP and have poor tracking ability, while the RC of STF conforms to the OP due to the fading factor which indicates the tracking performance is greatly improved in the proposed algorithm. The theoretical analysis and simulation results demonstrate that the performance of the proposed single GPS navigation algorithm based on STF outperforms that of the traditional KF algorithm.