A probilistic markov model-based framework for indoor localization

In recent years, the demand for indoor localization has increased significantly, primarily due to its important applications in healthcare, security, and other location aware services. However accurate indoor positioning remains challenging because of measurement noise, multipath propagation, and complex and crowded evironments. Moreover, many conventional methods estimate the position at each time instant independently, which may result in unstable predictions and unrealistic jumps between consecutive locations. To address these limitations, this paper proposes a Markov-based indoor localization method that models transition probabilities among discrete location states. In the proposed framework, each indoor position is represented as a state, and a transition probability matrix (TPM) is constructed to describe the likelihood of movement between neighboring states. By incorporating temporal dependency and spatial motion constraints, the proposed method produces more consistent and robust future position estimates in noisy indoor environments. The main contribution of this work lies in exploiting the state transition structure to capture the relationships among indoor locations and improve localization stability by enforcing physically plausible movements. In addition, the proposed method offers fast processing, low computational complexity, and low localization error while maintaining satisfactory accuracy. The proposed approach was evaluated using three datasets collected from distinct indoor environments, including the Network and Embedded Systems Research Laboratory (NetSys Lab) located on the second floor of the Faculty of Engineering, a corridor on the same floor, and an area on the first floor of the Faculty. Experimental results demonstrated that the proposed Markov model (MM) achieved mean root mean square error (RMSE) values of 0.26 m, 0.30 m, and 0.33 m with corresponding standard deviations (SD) of 0.38 m, 0.17 m, and 0.57 m for the NetSys Lab, corridor, and first-floor environments, respectively. In terms of localization accuracy, the proposed model achieved Mean Absolute Error (MAE) values of 0.3794 m, 0.1793 m, and 0.5781 m across the three environments, respectively. Furthermore, the corresponding median localization errors were 0.1974 m for the NetSys Lab, 0.1563 m for the corridor, and 0.1687 m for the first-floor environment. These findings confirm that the proposed approach provides accurate, stable, and computationally efficient indoor localization performance across diverse indoor scenarios.